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• Top Questions

Convert the following readings of pressureto kPa absolute, assuming that the barometer reads 760mm Hg:...

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Latest stories, 20 grade-school math questions so hard you'll wonder how you graduated, seriously, who can do these.

Unless you grew up to be an engineer, a banker, or an accountant, odds are that elementary and middle school math were the bane of your existence. You would study relentlessly for weeks for those silly standardized tests—and yet, come exam day, you'd still somehow have no idea what any of the equations or hard math problems were asking for. Trust us, we get it.

While logic might lead you to believe that your math skills have naturally gotten better as you've aged, the unfortunate reality is that, unless you've been solving algebra and geometry problems on a daily basis, the opposite is more likely the case.

Don't believe us? Then put your number crunching wisdom to the test with these tricky math questions taken straight from grade school tests and homework assignments and see for yourself.

1. Question: What is the number of the parking space covered by the car?

This tricky math problem went viral a few years back after it appeared on an entrance exam in Hong Kong... for six-year-olds. Supposedly the students had just 20 seconds to solve the problem!

Answer: 87.

Believe it or not, this "math" question actually requires no math whatsoever. If you flip the image upside down, you'll see that what you're dealing with is a simple number sequence.

2. Question: Replace the question mark in the above problem with the appropriate number.

This problem shouldn't be too difficult to solve if you play a lot of sudoku.

All of the numbers in every row and column add up to 15! (Also, 6 is the only number not represented out of numbers 1 through 9.)

3. Question: Find the equivalent number.

This problem comes straight from a standardized test given in New York in 2014.

You're forgiven if you don't remember exactly how exponents work. In order to solve this problem, you simply need to subtract the exponents (4-2) and solve for 3 2 , which expands into 3 x 3 and equals 9.

4. Question: How many small dogs are signed up to compete in the dog show?

This question comes directly from a second grader's math homework. Yikes.

Answer: 42.5 dogs.

In order to figure out how many small dogs are competing, you have to subtract 36 from 49 and then divide that answer, 13, by 2, to get 6.5 dogs, or the number of big dogs competing. But you're not done yet! You then have to add 6.5 to 36 to get the number of small dogs competing, which is 42.5. Of course, it's not actually possible for half a dog to compete in a dog show, but for the sake of this math problem let's assume that it is.

5. Question: Find the area of the red triangle.

This question was used in China to identify gifted 5th graders. Supposedly, some of the smart students were able to solve this in less than one minute.

In order to solve this problem, you need to understand how the area of a parallelogram works. If you already know how the area of a parallelogram and the area of a triangle are related, then adding 79 and 10 and subsequently subtracting 72 and 8 to get 9 should make sense—but if you're still confused, then check out this YouTube video for a more in-depth explanation.

6. Question: How tall is the table?

YouTuber MindYourDecisions adapted this mind-boggling math question from a similar one found on an elementary school student's homework in China.

Answer: 150 cm.

Since one measurement includes the cat's height and subtracts the turtle's and the other does the opposite, you can essentially just act like the two animals aren't there. Therefore, all you have to do is add the two measurements—170 cm and 130 cm—together and divided them by 2 to get the table's height, 150 cm.

7. Question: If the cost of a bat and a baseball combined is $1.10 and the bat costs $1.00 more than the ball, how much is the ball?

This problem, mathematically speaking, is very similar to one of the other ones on this list.

Answer: $0.05.

Think back to that problem about the dogs at the dog show and use the same logic to solve this problem. All you have to do is subtract $1.00 from $1.10 and then divide that answer, $0.10 by 2, to get your final answer, $0.05.

8. Question: When is Cheryl's birthday?

If you're having trouble reading that, see here:

"Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

May 15 May 16 May 19

June 17 June 18

July 14 July 16

August 14 August 15 August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't not know too.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

Albert: Then I also know when Cheryl's birthday is.

So when is Cheryl's birthday?"

It's unclear why Cheryl couldn't just tell both Albert and Bernard the month and day she was born, but that's irrelevant to solving this problem.

Answer: July 16.

Confused about how one could possibly find any answer to this question? Don't worry, so was most of the world when this question, taken from a Singapore and Asian Schools Math Olympiad competition, went viral a few years ago. Thankfully, though, the New York Times explains step-by-step how to get to July 16, and you can read their detailed deduction here.

9. Question: Find the missing letter.

This one comes from a first grader's homework.

Answer: The missing letter is J.

When you add together the values given for S, B, and G, the sum comes out to 40, and making the missing letter J (which has a value of 14) makes the other diagonal's sum the same.

10. Question: Solve the equation.

This problem might look easy, but a surprising number of adults are unable to solve it correctly.

Start by solving the division part of the equation. In order to do that, in case you forgot, you have to flip the fraction and switch from division to multiplication, thus getting 3 x 3 = 9. Now you have 9 - 9 + 1, and from there you can simply work from left to right and get your final answer: 1.

11. Question: Where should a line be drawn to make the below equation accurate?

5 + 5 + 5 + 5 = 555.

Answer: A line should be drawn on a "+" sign.

When you draw a slanted line in the upper left quadrant of a "+," it becomes the number 4 and the equation thusly becomes 5 + 545 + 5 = 555.

12. Question: Solve the unfinished equation.

Try to figure out what all of the equations have in common.

Answer: 4 = 256.

The formula used in each equation is 4 x = Y. So, 4 1 = 4, 4 2 = 16, 4 3 = 64, and 4 4 = 256.

13. Question: How many triangles are in the image above?

When Best Life first wrote about this deceiving question, we had to ask a mathematician to explain the answer!

Answer: 18.

Some people get stumped by the triangles hiding inside of the triangles and others forget to include the giant triangle housing all of the others. Either way, very few individuals—even math teachers—have been able to find the correct answer to this problem. And for more questions that will put your former education to the test, check out these 30 Questions You'd Need to Ace to Pass 6th Grade Geography.

14. Question: Add 8.563 and 4.8292.

Adding two decimals together is easier than it looks.

Answer: 13.3922.

Don't let the fact that 8.563 has fewer numberrs than 4.8292 trip you up. All you have to do is add a 0 to the end of 8.563 and then add like you normally would.

15. Question: There is a patch of lily pads on a lake. Every day, the patch doubles in size...

... If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

Answer: 47 days.

Most people automatically assume that half of the lake would be covered in half the time, but this assumption is wrong. Since the patch of pads doubles in size every day, the lake would be half covered just one day before it was covered entirely.

16. Question: How many feet are in a mile?

This elementary school-level problem is a little less problem solving and a little more memorization.

Answer: 5,280.

This was one of the questions featured on the popular show Are You Smarter Than a 5th Grader?

17. Question: What value of "x" makes the equation below true?

-15 + (-5x) = 0

Answer: -3.

You'd be forgiven for thinking that the answer was 3. However, since the number alongside x is negative, we need x to be negative as well in order to get to 0. Therefore, x has to be -3.

18. Question: What is 1.92 divided by 3?

You might need to ask your kids for help on this one.

Answer: 0.64.

In order to solve this seemingly simple problem, you need to remove the decimal from 1.92 and act like it isn't there. Once you've divided 192 by 3 to get 64, you can put the decimal place back where it belongs and get your final answer of 0.64.

19. Question: Solve the math equation above.

Don't forget about PEMDAS!

Using PEMDAS (an acronym laying out the order in which you solve it: "parenthesis, exponents, multiplication, division, addition, subtraction"), you would first solve the addition inside of the parentheses (1 + 2 = 3), and from there finish the equation as it's written from left to right.

20. Question: How many zombies are there?

Finding the answer to this final question will require using fractions.

Answer: 34.

Since we know that there are two zombies for every three humans and that 2 + 3 = 5, we can divide 85 by 5 to figure out that in total, there are 17 groups of humans and zombies. From there, we can then multiply 17 by 2 and 3 and learn that there are 34 zombies and 51 humans respectively. Not too bad, right?

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120 Math Word Problems To Challenge Students Grades 1 to 8

Written by Marcus Guido

• Teaching Tools

• Subtraction
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• Mixed operations
• Ordering and number sense
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• Physical measurement
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You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

A jolt of creativity would help. But it doesn’t come.

Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes . ( See our entire list of back to school resources for teachers here .)

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

120 Math word problems, categorized by skill

Addition word problems.

Best for: 1st grade, 2nd grade

1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?

2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?

3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?

5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?

6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?

8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?

Subtraction word problems

Best for: 1st grade, second grade

9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?

10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?

11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

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12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?

13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?

14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?

15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?

16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?

Multiplication word problems

Best for: 2nd grade, 3rd grade

17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?

18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?

19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?

21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?

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Division word problems

Best for: 3rd grade, 4th grade, 5th grade

22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?

23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?

24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?

25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?

26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?

Mixed operations word problems

27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?

28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?

29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?

30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?

Ordering and number sense word problems

31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?

32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?

33. Composing Numbers: What number is 6 tens and 10 ones?

34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?

35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?

Fractions word problems

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?

37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?

38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?

39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?

40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?

41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?

42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?

43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?

44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.

45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?

46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.

Decimals word problems

Best for: 4th grade, 5th grade

47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?

48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?

49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?

50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?

51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?

52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?

Comparing and sequencing word problems

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?

56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?

57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?

58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?

59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?

Time word problems

66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?

69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?

70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?

71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?

Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?

61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?

62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?

63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?

64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?

65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?

67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.

68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?

Physical measurement word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?

73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?

74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?

75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?

76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?

77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?

78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?

79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?

80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?

81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?

Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?

84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?

87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

Probability and data relationships word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade

89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?

90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?

91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.

92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?

93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?

94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?

95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .

Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

96. Introducing Perimeter:  The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?

97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?

98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?

101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?

104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?

105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?

106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?

107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?

108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?

109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?

110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?

111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?

112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?

113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?

Variables word problems

Best for: 6th grade, 7th grade, 8th grade

115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?

116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.

117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.

118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.

119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?

How to easily make your own math word problems & word problems worksheets

Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:

• Link to Student Interests:  By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
• Make Questions Topical:  Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
• Include Student Names:  Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
• Be Explicit:  Repeating keywords distills the question, helping students focus on the core problem.
• Test Reading Comprehension:  Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
• Focus on Similar Interests:  Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
• Feature Red Herrings:  Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.

Final thoughts about math word problems

You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.

Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.

The result?

A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.

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Hard Algebra Questions – Challenging Problems and Step-by-Step Solutions

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Understanding the Fundamentals of Algebra

Solving algebraic operations, linear equations and their graphs, solving quadratic equations, systems of equations, applications of algebra.

Algebra is a fundamental branch of mathematics that deals with symbols and the rules for manipulating these symbols . In its most basic form, it is about finding the unknowns or the variables within equations.

As a student progresses, the questions in algebra can evolve from simple linear equations to more complex problems involving multiple steps, functions, or advanced concepts. Advanced algebra questions often probe one’s understanding of concepts like polynomial functions, rational expressions, exponents, and logarithms.

Navigating the web for reliable and challenging algebra problems and solutions I’ve found to be quite a task, but essential for anyone looking to master the subject. Websites and apps aimed at providing mathematics resources offer a range of problems, from basic to complex, helping learners tackle various topics effectively.

Engaging with these platforms allows for practice and reinforcement of algebraic concepts, which is crucial for solidifying one’s understanding and proficiency in mathematics.

I have to admit, that algebra can sometimes seem like a puzzle with a missing piece. But it’s that moment of clarity when the pieces fall into place that makes solving algebra questions incredibly rewarding. Stick around as we explore some hard algebra questions along with their solutions – the satisfaction of cracking them is just around the corner.

Algebra can seem challenging, but by grasping some key concepts, I can work through even the tough problems.

The backbone of algebra is the equation, which is a statement that two expressions are equal, often containing an unknown quantity, usually represented by a letter like ( x ) or ( y ).

For instance, in the equation ( x + 3 = 7 ), my goal is to find the value of ( x ) that makes this statement true. To do this, I simplify the equation to find ( x ). Simplification might involve combining like terms or using inverse operations. So, in this case, I subtract 3 from both sides to isolate ( x ), yielding ( x = 4 ).

Inequalities are like equations, but instead of equality, they express a relation where one value is larger or smaller than another. This can be represented by symbols such as “>,” “<,” “≤,” or “≥.” For example, if I have ( x – 5 > 10 ), I’m looking for all values of ( x ) that make this inequality true.

Solving this, I add 5 to both sides to get ( x > 15 ).

Here’s a simple way to visualize the process of solving an inequality :

Remember, if I multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign flips. So, if I had ( -2x < 8 ), by dividing both sides by -2, it becomes ( x > -4 ).

Understanding the foundation allows me to simplify and solve equations and inequalities, providing the confidence to tackle more complex algebraic questions.

When I approach algebraic operations, I prioritize understanding the core concepts—exponents, factoring, complex numbers, and simplification.

These elements are the building blocks to solving more intricate algebra problems.

For exponents , remember that the base raised to the power of an exponent reflects how many times the base is multiplied by itself. For instance, $3^4$ means $3 \times 3 \times 3 \times 3$. When dealing with exponents, it’s essential to be familiar with the laws of exponents for simplification purposes.

Next is factoring . I look for the greatest common factor (GCF) or use techniques like the difference of squares, and the quadratic formula for trinomials. For example, factoring $x^2 – 9$ would yield $(x + 3)(x – 3)$ because it is the difference of squares.

When it comes to complex numbers , which are in the form $a + bi$, where $i$ is the imaginary unit $(i^2 = -1)$, I remember that these numbers can be added, subtracted, and multiplied just like real numbers, with special attention to the property of $i$.

Finally, simplification is a matter of combining like terms and using the distributive property where necessary. For instance, to simplify the expression $2(x + 3) + x$, I first distribute the $2$ to get $2x + 6 + x$ and combine like terms to get $3x + 6$.

By mastering these components, I set a strong foundation for tackling hard algebra questions effectively.

Solving Advanced Algebraic Equations

Advanced algebra often serves as the foundation for calculus, statistics, and even programming. Let’s take a look at some of the core types of equations and how to approach them, including linear, quadratic, and systems of equations.

I’ll start by discussing linear equations , characterized by their straight-line graphs. A basic form of a linear equation is the slope-intercept form, expressed as ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Converting to standard form , ( Ax + By = C ), may be necessary for some applications. To graph these equations, I find two points by plugging in values for ( x ) and then plotting those points. Connecting these will give me a straight line.

Moving on to quadratic equations , these are typically presented in the general form ( a$x^2$ + bx + c = 0 ). These equations form parabolas when graphed.

I can solve quadratic equations using methods such as factoring, completing the square, or using the quadratic formula, ( x = $\frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$ ). Each method has its own use cases; for example, factoring is efficient when the equation easily decomposes into binomials.

Lastly, I’ll tackle systems of equations , where I have to find the solution set of two or more equations. When solving linear systems , I can use methods such as substitution, elimination, or graphing.

Substitution involves solving one equation for a variable and then substituting that expression into the other equation, while elimination adds or subtracts equations to eliminate a variable. Graphing requires drawing lines of each equation to find their point of intersection.

These are standard approaches that I often use to find the solutions to various types of algebraic equations.

Algebra has countless applications in the real world, and one of the most practical applications is in calculating areas and perimeters of geometric shapes. Let me guide you through some examples:

Area of a Rectangle : To find the area of a rectangle, I use the formula:

$$ A = l \times w $$

where ( A ) represents the area, ( l ) is the length, and ( w ) is the width.

Perimeter of a Rectangle : Similarly, finding the perimeter is just as straightforward with the equation:

$$ P = 2(l + w) $$

where ( P ) stands for the perimeter.

Area of a Circle : When I look at circles, the area is found using:

$$ A = \pi r^2 $$

Here, ( A ) is the area and ( r ) is the radius of the circle.

Circumference of a Circle: And for the circumference, which is the perimeter of a circle, the formula is:

$$ C = 2\pi r $$

where ( C ) is the circumference.

Understanding these formulas allows me to solve real-life problems, such as calculating the amount of paint needed to cover a wall or the fencing required for a circular garden.

With the help of algebra, I can create equations from word problems and solve them; the results help me make informed decisions and solve practical problems efficiently.

In our exploration of challenging algebra questions , I’ve presented a range of problems that test our understanding and application of algebraic concepts. From the intricacies of trigonometric equations to the puzzles of algebraic word problems, the journey through these issues illuminates the beauty of mathematics.

I sincerely hope that the solutions and strategies discussed have helped shed light on the complexity and elegance of algebra. Remember, practicing these tough problems not only sharpens your skills but also prepares you for more advanced mathematical challenges.

Whether you’re preparing for exams or simply indulging in the joy of problem-solving, the resilience and adaptability gained here are invaluable.

Algebra does not always yield its secrets easily, but patience and persistence in working through these tough problems can be immensely rewarding. Keep this momentum going, continue nurturing your mathematical curiosity, and let your confidence grow with each equation you solve.

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