my homework lesson 5 add unlike fractions

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Adding Fractions with Unlike Denominators

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Online Math Game: Adding Fractions with Unlike Denominators

Add fractions with unlike denominators in this interactive math game for kids. Students will have the opportunity to practice addition with fractions that do not have the same denominator. Students will be required to find common denominators in order to add the fractions. They will be asked to simplify the fractions if possible. Here are the types of questions students can expect to encounter in this online math lesson:

* Solve a word problem containing fractions with unlike denominators.

* Solve addition problems with fractions in a vertical format.

* Solve fractional addition problems in a horizontal format. Use fraction strips to visualize the math problem.

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This lesson is labeled as Level D and is targeted toward fourth graders.

Common Core Standard

5.NF.2, MA.5.FR.2.1, MA.5.AR.1.2 , 5.3H Number And Operations - Fractions Use Equivalent Fractions As A Strategy To Add And Subtract Fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions

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Grade 5 - Number and Operations - Fractions

Standard 5.NF.A.1 - Practice adding fractions with unlike denominators.

Included Skills:

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

If you notice any problems, please let us know .

Addition of Unlike Fractions

We will learn how to solve addition of unlike fractions.

In order to add unlike fractions, first we convert them as like fractions with same denominator in each fraction with the help of method explained earlier and then we add the fractions.

Let us consider some of the examples of adding unlike fractions:

1.  Add \(\frac{1}{2}\), \(\frac{2}{3}\) and \(\frac{4}{7}\).

Let us find the LCM of the denominators 2, 3 and 7. 

The LCM of 2, 3 and 7 is 42.

\(\frac{1}{2}\) = \(\frac{1 × 21}{2 × 21}\) = \(\frac{21}{42}\)

\(\frac{2}{3}\) = \(\frac{2 × 14}{3 × 14}\) = \(\frac{28}{42}\)

\(\frac{4}{7}\) = \(\frac{4 × 6}{7 × 6}\) = \(\frac{24}{42}\)

Therefore, we get the like fractions \(\frac{1}{2}\), \(\frac{2}{3}\) and \(\frac{4}{7}\).

Now, \(\frac{21}{42}\) + \(\frac{28}{42}\) + \(\frac{24}{42}\)

       = \(\frac{21 + 28 + 24}{42}\)

       = \(\frac{73}{42}\)

2. Add \(\frac{7}{8}\) and \(\frac{9}{10}\)

The L.C.M. of the denominators 8 and 10 is 40.

 \(\frac{7}{8}\) = \(\frac{7 × 5}{8 × 5}\) =  \(\frac{35}{40}\), (because 40 ÷ 8 = 5)

 \(\frac{7}{8}\) = \(\frac{9 × 4}{10 × 4}\) = \(\frac{36}{40}\), (because 40 ÷ 10 = 4)

Thus, \(\frac{7}{8}\) + \(\frac{9}{10}\)

      = \(\frac{35}{40}\) + \(\frac{36}{40}\)

      = \(\frac{35 + 36}{40}\)

      = \(\frac{71}{40}\)

      = 1\(\frac{31}{40}\)

3.  Add \(\frac{1}{6}\) and \(\frac{5}{12}\)

Let L.C.M. of the denominators 6 and 12 is 12.

\(\frac{1}{6}\) = \(\frac{1 × 2}{6 × 2}\) = \(\frac{2}{12}\), (because 12 ÷ 6 = 2)

\(\frac{5}{12}\) = \(\frac{5 × 1}{12 × 1}\) = \(\frac{5}{12}\), (because 12 ÷ 12 = 1)

Thus, \(\frac{1}{6}\) + \(\frac{5}{12}\)

      = \(\frac{2}{12}\) + \(\frac{5}{12}\)

      = \(\frac{2 + 5}{12}\)

      = \(\frac{7}{12}\)

4.  Add \(\frac{2}{3}\), \(\frac{1}{15}\) and \(\frac{5}{6}\)

The L.C.M. of the denominators 3, 15 and 6 is 30.

\(\frac{2}{3}\) = \(\frac{2 × 10}{3 × 10}\) = \(\frac{20}{30}\), (because 30 ÷ 3 = 10)

\(\frac{1}{15}\) = \(\frac{1 × 2}{15 × 2}\) = \(\frac{2}{30}\), (because 30 ÷ 15 = 2)

\(\frac{5}{6}\)  = \(\frac{5 × 5}{6 × 5}\) = \(\frac{25}{30}\), (because 30 ÷ 6 = 5)

Thus, \(\frac{2}{3}\) + \(\frac{1}{15}\) + \(\frac{5}{6}\)

      = \(\frac{20}{30}\) + \(\frac{2}{30}\) + \(\frac{25}{30}\)

      = \(\frac{20 + 2 + 25}{30}\)

      = \(\frac{47}{30}\)

      = 1\(\frac{17}{30}\)

More examples on Addition of Unlike Fractions (Fractions having Different Denominators)

5.  Add \(\frac{1}{6}\) + \(\frac{3}{4}\)

Step II: Write the equivalent fractions of \(\frac{1}{6}\) and \(\frac{3}{4}\) with denominator 12.

\(\frac{1 × 2}{6 × 2}\) =  \(\frac{2}{12}\)

\(\frac{3 × 3}{4 × 3}\) =  \(\frac{9}{12}\)

Step III: Add the equivalent fractions

\(\frac{1}{6}\) + \(\frac{3}{4}\)

=  \(\frac{2}{12}\) + \(\frac{9}{12}\)

= \(\frac{2 + 9}{12}\)

= \(\frac{11}{12}\)

Add \(\frac{1}{6}\) + \(\frac{3}{4}\)

Second Method:

Addition of Mixed Numbers

7. Add 2\(\frac{2}{6}\) + 5\(\frac{1}{3}\) + 1\(\frac{4}{5}\)

First Method:

Separate the whole numbers and proper fractions.

2\(\frac{2}{6}\) + 5\(\frac{1}{3}\) + 1\(\frac{4}{5}\) = (2 + 5 + 1) + \(\frac{2}{6}\) + \(\frac{1}{3}\) + \(\frac{4}{5}\)

= 8 + \(\frac{2}{6}\) + \(\frac{1}{3}\) + \(\frac{4}{5}\)

L.C.M. of 6, 3 and 5 is 30.

= 8 + \(\frac{(30 ÷ 6) × 2 + (30 ÷ 3) × 1 + (30 ÷ 5) × 4}{30}\)

= 8 + \(\frac{(5 × 2) + (10 × 1) + (6 × 4)}{30}\)

= 8 + \(\frac{10 + 10 + 24}{30}\)

= 8 + \(\frac{44}{30}\)

= 8 + \(\frac{22}{15}\)

= 8 + 1\(\frac{7}{15}\)

Add 2\(\frac{2}{6}\) + 5\(\frac{1}{3}\) + 1\(\frac{4}{5}\)

Convert the mixed number into improper fractions and find the sum

2\(\frac{2}{6}\) = \(\frac{(2 × 6) + 2}{6}\) = \(\frac{14}{6}\)

5\(\frac{1}{3}\) = \(\frac{(5 × 3) + 1}{3}\) = \(\frac{16}{3}\)

1\(\frac{4}{5}\) = \(\frac{(1 × 5) + 4}{5}\) = \(\frac{9}{5}\)

Therefore, 2\(\frac{2}{6}\) + 5\(\frac{1}{3}\) + 1\(\frac{4}{5}\) = \(\frac{14}{6}\) + \(\frac{16}{3}\) + \(\frac{9}{5}\)

                          = \(\frac{14 × 5}{6 × 5}\) + \(\frac{16 × 10}{3 × 10}\) + \(\frac{9 × 6}{5 × 6}\)

                          = \(\frac{70}{30}\) + \(\frac{160}{30}\) + \(\frac{54}{30}\)

                          = \(\frac{70 + 160 + 54}{30}\)

                          = \(\frac{284}{30}\)

                          = \(\frac{142}{15}\)

                          = 9\(\frac{7}{15}\)

8. Add \(\frac{2}{6}\), 4 and \(\frac{7}{12}\)

To add unlike fractions, we first convert them into like fractions. In order to make a common denominator we find the LCM of all different denominators of the given fractions and then make them equivalent fractions with a common denominator.

Word Problems on Addition of Unlike Fractions:

1. On Monday Michael read \(\frac{5}{16}\) of the book. On Wednesday he reads \(\frac{4}{8}\) of the book. What fraction of the book has Michael read?

On Monday Michael read \(\frac{5}{16}\)  of the book.

On Wednesday he reads \(\frac{4}{8}\)  of the book.

Now add the two fractions

\(\frac{5}{16}\) +  \(\frac{4}{8}\)

Let us find the LCM of the denominators 16 and 8. 

The LCM of 16 and 8 is 16.

\(\frac{5}{16}\) = \(\frac{5 × 1}{16 × 1}\) = \(\frac{5}{16}\)

\(\frac{4}{8}\) = \(\frac{4 × 2}{8 × 2}\) = \(\frac{8}{16}\)

Therefore, we get the like fractions \(\frac{5}{16}\) and \(\frac{8}{16}\).

Now, \(\frac{5}{16}\) + \(\frac{8}{16}\)

       = \(\frac{5 + 8}{16}\)

       = \(\frac{13}{16}\)

Therefore, Michael read in two days \(\frac{13}{16}\) of the book.

2. Sarah ate \(\frac{1}{3}\) part of the pizza and her sister ate \(\frac{1}{2}\) of the pizza. What fraction of the pizza was eaten by both sisters?

Sarah ate \(\frac{1}{3}\) part of the pizza.

Her sister ate \(\frac{1}{2}\) of the pizza.

\(\frac{1}{3}\) +  \(\frac{1}{2}\)

Let us find the LCM of the denominators 3 and 2. 

The LCM of 3 and 2 is 6.

\(\frac{1}{3}\) = \(\frac{1 × 2}{3 × 2}\) = \(\frac{2}{6}\)

\(\frac{1}{2}\) = \(\frac{1 × 3}{2 × 3}\) = \(\frac{3}{6}\)

Therefore, we get the like fractions \(\frac{2}{6}\) and \(\frac{3}{6}\).

Now, \(\frac{2}{6}\) + \(\frac{3}{6}\)

       = \(\frac{2 + 3}{6}\)

       = \(\frac{5}{6}\)

Therefore, \(\frac{5}{6}\) of the pizza was eaten by both sisters.

3.  Catherine is preparing for her final exam. She study \(\frac{9}{22}\) hours on Wednesday and \(\frac{5}{11}\) hours on Sunday. How many hours she studied in two days?

Catherine study \(\frac{9}{22}\) hours on Wednesday.

Again, she study \(\frac{5}{11}\) hours on Sunday.

\(\frac{9}{22}\) +  \(\frac{5}{11}\)

Let us find the LCM of the denominators 22 and 11. 

The LCM of 22 and 11 is 22.

\(\frac{9}{22}\) = \(\frac{9 × 1}{22 × 1}\) = \(\frac{9}{22}\)

\(\frac{5}{11}\) = \(\frac{5 × 2}{11 × 2}\) = \(\frac{10}{22}\)

Therefore, we get the like fractions \(\frac{9}{22}\) and \(\frac{10}{22}\).

Now, \(\frac{9}{22}\) + \(\frac{10}{22}\)

       = \(\frac{9 + 10}{22}\)

       = \(\frac{19}{22}\)

Therefore, Catherine studied a total \(\frac{9}{22}\) hours in two days.

Questions and Answers Addition of Unlike Fractions:

1. Add the following Unlike Fractions:

(i) \(\frac{3}{4}\) + \(\frac{5}{6}\)

(ii) \(\frac{1}{7}\) + \(\frac{2}{3}\) + \(\frac{6}{7}\)

(iii) \(\frac{7}{8}\) + \(\frac{5}{6}\) + \(\frac{4}{10}\)

(iv) \(\frac{3}{7}\) + \(\frac{2}{5}\) + \(\frac{6}{11}\)

(v) 3\(\frac{5}{8}\) + 4\(\frac{1}{6}\) + 4\(\frac{7}{12}\)

1. (i) 1\(\frac{7}{12}\)

(ii) 1\(\frac{2}{3}\) 

(iii) 2\(\frac{13}{120}\)

(iv) 1\(\frac{144}{385}\) 

(v) 12\(\frac{3}{8}\)

Related Concept

• Fraction of a Whole Numbers
• Representation of a Fraction
• Equivalent Fractions
• Properties of Equivalent Fractions
• Like and Unlike Fractions
• Comparison of Like Fractions
• Comparison of Fractions having the same Numerator
• Types of Fractions
• Changing Fractions
• Conversion of Fractions into Fractions having Same Denominator
• Conversion of a Fraction into its Smallest and Simplest Form
• Addition of Fractions having the Same Denominator
• Subtraction of Fractions having the Same Denominator
• Addition and Subtraction of Fractions on the Fraction Number Line

4th Grade Math Activities

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Add Fractions - Unlike Units

Related Topics: Lesson Plans and Worksheets for Grade 5 Lesson Plans and Worksheets for all Grades More Lessons for Grade 5 Common Core For Grade 5

Videos, examples, and solutions to help Grade 5 students learn how to add fractions with unlike units using the strategy of creating equivalent fractions. Common Core Standards: 5.NF.1, 5.NF.2

New York State Common Core Math Grade 5, Module 3, Lesson 3

Worksheets for Grade 5

Lesson 3 Application Problem Alex squeezed 2 liters of juice for breakfast. If he pours the juice equally into 5 glasses, how many liters of juice will be in each glass? (Bonus: How many milliliters are in each glass?) Lesson 3 Concept Development Problem 1: 1/2 + 1/4 Problem 2: 1/3 + 1/2 Problem 3: 2/3 + 1/4 Problem 4: 2/5 + 2/3 Problem 5: 2/7 + 2/3

Lesson 3 Problem Set

• For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer. c) 1/4 + 1/6 d) 1/3 + 1/7 e) 3/4 + 1/5 f) 2/3 + 2/7

Lesson 3 Homework This video demonstrates how to add simple fractions with unlike denominators using rectangular models.

• For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer. a) 1/4 + 1/3 b) 1/4 + 1/5

Lesson 3 Homework

• For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer. a) 1/4 + 1/3 b) 1/4 + 1/5 f) 3/5 + 3/7 Solve the following problems. Draw a picture and/or write the number sentence that proves the answer.
• Cynthia completed 2/3 of the items on her to-do list in the morning, and finished 1/8 of the items during her lunch break. How much of her to-do list is finished by the end of her lunch break? (Bonus: How much of her to-do list does she still have to do after lunch?)

• For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer. e) 1/4 + 2/5 Solve the following problems. Draw a picture and/or write the number sentence that proves the answer.
• Rajesh jogged 3/4 mile, and then walked 1/6 mile to cool down. How far did he travel?

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Add Fractions With Unlike Units

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Students add fractions with unlike units using the strategy of creating equivalent fractions. Students practice making these models extensively until they internalize the process of making like units.

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• Grade 5 Mathematics Module 3, Topic B, Lesson 3

Prerequisites

• 4.NF.B.3.A ,
• 4.NF.B.3.B ,
• 4.NF.B.3.C ,
• CCSS Standard:

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My Math - 5th Grade - Chapter 9 - Add and Subtract Fractions

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• 5th Grade Math
• Title: My Math
• Author: McGraw Hill
• Edition: Volume 2

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McGraw Hill My Math Grade 5 Chapter 9 Lesson 7 Answer Key Subtract Unlike Fractions

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 9 Lesson 7 Subtract Unlike Fractions  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 9 Lesson 7 Subtract Unlike Fractions

Math in My World

Check for Reasonableness Use benchmark fractions to check. Since, \(\frac{1}{6}\) < \(\frac{1}{2}\), your answer is reasonable.

Talk Math Describe the steps you can use to find \(\frac{3}{4}\) – \(\frac{1}{12}\). Answer: The above-given unlike fractions: 3/4 – 1/12 step 1: Find the common denominator 12 is the least common multiple of denominators 4 and 12. Use it to convert to equivalent fractions with this common denominator. = 3 x 3/4 x 3 – 1 x 1/12 x 1 = 9/12 – 1/12 Step 2: Now the denominators are equal so subtract. = (9 – 1)/12 = 8/12 Here we can simplify 8/12 by reducing the fractions to the lowest terms. 4 is the greatest common divisor of 8 and 12. Reduce by dividing both the numerator and denominator by 4. = 8 ÷ 4/12 ÷ 4 = 2/3

Guided Practice

Independent Practice

Subtract. Write each in simplest form.

Question 2. \(\frac{5}{6}\) – \(\frac{1}{2}\) = ____ Answer: The above-given unlike fraction: 5/6 – 1/2 Step 1: Find a common denominator 6 is the least common multiple of denominators 6 and 2. Use it to convert to equivalent fractions with this common denominator. = 5 x 1/6 x 1 – 1 x 3/2 x 3 = 5/6 – 3/6 Step 2: Here the denominators are equal so subtract directly. = (5 – 3)/6 = 2/6 Here we can simplify further by reducing the fractions to the lowest terms. 2 is the greatest common divisor of 2 and 6. Reduce by dividing both the numerator and denominator by 2. = 2 ÷ 2/6 ÷ 2 = 1/3 Therefore, \(\frac{5}{6}\) – \(\frac{1}{2}\) = 1/3.

Question 3. \(\frac{2}{5}\) – \(\frac{1}{4}\) = ____ Answer: The above-given unlike fraction: 2/5 – 1/4 Step 1: Find a common denominator 20 is the least common multiple of denominators 5 and 4. Use it to convert to equivalent fractions with this common denominator. = 2 x 4/5 x 4 – 1 x 5/4 x 5 = 8/20 – 5/20 Step 2: Now the denominators are equal so subtract directly. = (8 – 5)/20 = 3/20 Therefore, \(\frac{2}{5}\) – \(\frac{1}{4}\) = 3/20

Question 4. \(\frac{4}{5}\) – \(\frac{1}{6}\) = ____ Answer: The above-given unlike fraction: 4/5 – 1/6 Step 1: Find a common denominator 30 is the least common multiple of denominators 5 and 6. Use it to convert to equivalent fractions with this common denominator. = 4 x 6/5 x 6 – 1 x 5/6 x 5 = 24/30 – 5/30 Step 2: Now the denominators are equal so subtract directly. = (24 – 5)/30 = 19/30 Therefore, \(\frac{4}{5}\) – \(\frac{1}{6}\) = 19/30

Question 5. \(\frac{7}{8}\) – \(\frac{1}{2}\) = ____ Answer: The above-given unlike fraction: 7/8 – 1/2 Step 1: Find a common denominator 8 is the least common multiple of denominators 8 and 2. Use it to convert to equivalent fractions with this common denominator. = 7 x 1/8 x 1 – 1 x 4/2 x 4 = 7/8 – 4/8 Step 2: Here the denominators are equal so subtract directly. = (7 – 4)/8 = 3/8 Therefore, \(\frac{7}{8}\) – \(\frac{1}{2}\) = 3/8

Question 6. \(\frac{7}{12}\) – \(\frac{1}{3}\) = ____ Answer: The above-given unlike fraction: 7/12 – 1/3 Step 1: Find a common denominator 12 is the least common multiple of denominators 12 and 3. Use it to convert to equivalent fractions with this common denominator. = 7 x 1/12 x 1 – 1 x 4/3 x 4 = 7/12 – 4/12 Step 2: Here the denominators are equal so subtract directly. = (7 – 4)/12 = 3/12 Here we can simplify further by reducing the fractions to the lowest terms. 3 is the greatest common divisor of 3 and 12. Reduce by dividing both the numerator and denominator by 2. = 3 ÷ 3/12 ÷ 3 = 1/4 Therefore, \(\frac{7}{12}\) – \(\frac{1}{3}\) = 1/4

Question 7. \(\frac{5}{6}\) – \(\frac{1}{3}\) = ____ Answer: The above-given unlike fraction: 5/6 – 1/3 Step 1: Find a common denominator 6 is the least common multiple of denominators 6 and 3. Use it to convert to equivalent fractions with this common denominator. = 5 x 1/6 x 1 – 1 x 2/3 x 2 = 5/6 – 2/6 Step 2: Here the denominators are equal so subtract directly. = (5 – 2)/6 = 3/6 Here we can simplify further by reducing the fractions to the lowest terms. 3 is the greatest common divisor of 3 and 6. Reduce by dividing both the numerator and denominator by 2. = 3 ÷ 3/6 ÷ 3 = 1/2 Therefore, \(\frac{5}{6}\) – \(\frac{1}{3}\) = 1/2

Question 8. \(\frac{2}{3}\) – \(\frac{3}{10}\) = ____ Answer: The above-given unlike fraction: 2/3 – 3/10 Step 1: Find a common denominator 30 is the least common multiple of denominators 3 and 10. Use it to convert to equivalent fractions with this common denominator. = 2 x 10/3 x 10 – 3 x 3/10 x 3 = 20/30 – 9/30 Step 2: Here the denominators are equal so subtract directly. = (20 – 9)/30 = 11/30 Therefore, \(\frac{2}{3}\) – \(\frac{3}{10}\) = 11/30

Question 9. \(\frac{5}{8}\) – \(\frac{1}{2}\) = ____ Answer: The above-given unlike fraction: 5/8 – 1/2 Step 1: Find a common denominator 8 is the least common multiple of denominators 8 and 2. Use it to convert to equivalent fractions with this common denominator. = 5 x 1/8 x 1 – 1 x 4/2 x 4 = 5/8 – 4/8 Step 2: Here the denominators are equal so subtract directly. = (5 – 4)/8 = 1/8 Therefore, \(\frac{5}{8}\) – \(\frac{1}{2}\) = 1/8

Question 10. \(\frac{4}{5}\) – \(\frac{2}{15}\) = ____ Answer: The above-given unlike fraction: 4/5 – 2/15 Step 1: Find a common denominator 15 is the least common multiple of denominators 5 and 15. Use it to convert to equivalent fractions with this common denominator. = 4 x 3/5 x 3 – 2 x 1/15 x 1 = 12/15 – 2/15 Step 2: Here the denominators are equal so subtract directly. = (12 – 2)/15 = 10/15 Here we can simplify further by reducing the fractions to the lowest terms. 5 is the greatest common divisor of 10 and 15. Reduce by dividing both the numerator and denominator by 2. = 10 ÷ 5/15 ÷ 5 = 2/3 Therefore, \(\frac{4}{5}\) – \(\frac{2}{15}\) = 2/3

Algebra Find the unknown.

Question 11. \(\frac{5}{6}\) – \(\frac{3}{4}\) = m m = ____ Answer: The above-given: 5/6 – 3/4 = m we need to find out the value of m. Step 1: Find a common denominator 12 is the least common multiple of denominators 6 and 4. Use it to convert to equivalent fractions with this common denominator. m = 5 x 2/6 x 2 – 3 x 3/4 x 3 m = 10/12 – 9/12 Step 2: Here the denominators are equal so subtract directly. m = (10 – 9)/12 m = 1/12

Question 12. \(\frac{2}{3}\) – \(\frac{3}{5}\) = \(\frac{n}{15}\) n = ____ Answer: The above-given unlike fraction: 2/3 – 3/5 = n/15 we need to find out the value of n. Step 1: Find a common denominator 15 is the least common multiple of denominators 3 and 5. Use it to convert to equivalent fractions with this common denominator. = 2 x 5/3 x 5 – 3 x 3/5 x 3 = 10/15 – 9/15 Step 2: Here the denominators are equal so subtract directly. = (10 – 9)/15 = 1/15 Therefore, the value of n is 1. The denominator is given we found the numerator that is the value of n. 1/15 = 1 is the numerator; 15 is the denominator.

Question 13. \(\frac{5}{12}\) – \(\frac{1}{6}\) = p p = ____ Answer: The above-given unlike fraction: 5/12 – 1/6 = p we need to find out the value of p. Step 1: Find a common denominator 12 is the least common multiple of denominators 12 and 6. Use it to convert to equivalent fractions with this common denominator. p = 5 x 1/12 x 1 – 1 x 2/6 x 2 p = 5/12 – 2/12 Step 2: Here the denominators are equal so subtract directly. p = (5 – 2)/12 p = 3/12 Here we can simplify further by reducing the fractions to the lowest terms. 3 is the greatest common divisor of 3 and 12. Reduce by dividing both the numerator and denominator by 2. = 3 ÷ 3/12 ÷ 3 = 1/4 Therefore, the value of p is 1/4.

Problem Solving

Question 14. Angie rides her bicycle \(\frac{2}{3}\) mile to school. On Friday, she took a shortcut so that the ride to school was \(\frac{1}{9}\)– mile shorter. How long was Angie’s bicycle ride on Friday? Answer: The above-given: The number of miles Angie rides her bicycle to school = 2/3 The number of miles she rides on Friday = 1/9 The number of miles Angie bicycle rode on Friday = x x = 2/3 – 1/9 Step 1: Find a common denominator 9 is the least common multiple of denominators 3 and 9. Use it to convert to equivalent fractions with this common denominator. x = 2 x 3/3 x 3 – 1 x 1/9 x 1 x = 6/9 – 1/9 Step 2: Here the denominators are equal so subtract directly. x = (6 – 1)/9 x = 5/9 Therefore, she rides 5/9 miles on Friday.

Question 15. Mathematical PRACTICE 6 Be Precise ollie used \(\frac{1}{2}\) cup of vegetable oil to make brownies. She used another \(\frac{1}{3}\) cup of oil to make muffins. How much more oil did she use to make brownies? Answer: The above-given: The number of cups of oil used by Ollie to make brownies = 1/2 The number of cups of oil used by Ollie to make muffins = 1/3 The number of more oil she used to make brownies = b b = 1/2 – 1/3 Step 1: Find a common denominator 6 is the least common multiple of denominators 2 and 3. Use it to convert to equivalent fractions with this common denominator. b = 1 x 3/2 x 3 – 1 x 2/3 x 2 b = 3/6 – 2/6 Step 2: Here the denominators are equal so subtract directly. b = (3 – 2)/6 b = 1/6 Therefore, 1/6 more oil is used to make brownies.

Question 16. Danielle poured \(\frac{3}{4}\) gallon of water from a \(\frac{7}{8}\)-gallon bucket How much water is left in the bucket? Answer: The above-given: The number of gallons of water Danielle poured = 3/4 The number of gallons of water in a bucket = 7/8 The number of gallons of water left in the bucket = b b = 7/8 – 3/4 Step 1: Find a common denominator 8 is the least common multiple of denominators 8 and 4. Use it to convert to equivalent fractions with this common denominator. b = 7 x 1/8 x 1 – 3 x 2/4 x 2 b = 7/8 – 6/8 Step 2: Here the denominators are equal so subtract directly. b = (7 – 6)/8 b = 1/8 Therefore, 1/8 gallons of water left in the bucket.

HOT Problems

Question 17. Mathematical PRACTICE 2 Use Number Sense Is finding \(\frac{9}{10}\) – \(\frac{1}{2}\) the same as finding \(\frac{9}{10}\) – \(\frac{1}{4}\) – \(\frac{1}{4}\) ? Explain. Answer: The above-given: 9/10 – 1/2 = 9/10 – 1/4 – 1/4 9/10 – 1/2 = 9/10 – 2/4 we need to find out whether both equations will get the same answer or not 9/10 – 1/2 Step 1: Find a common denominator 10 is the least common multiple of denominators 10 and 2. Use it to convert to equivalent fractions with this common denominator. = 9 x 1/10 x 1 – 1 x 5/2 x 5 = 9/10 – 5/10 = (9 – 5)/10 = 4/10 = 2/5 Now check out the answer for 9/10 – 2/4 Step 1: Find a common denominator 20 is the least common multiple of denominators 10 and 4. Use it to convert to equivalent fractions with this common denominator. = 9 x 2/10 x 2 – 2 x 5/4 x 5 = 18/20 – 10/20 = 8/20 = 2/5 Therefore, both are have the same answer.

Question 18. ? Building on the Essential Question How are equivalent fractions used when subtracting, unlike fractions? Answer: Equivalent fractions are used when adding and subtracting fractions. In order to add or subtract a fraction, the fractions involved must be like fractions. If they are unlike fractions, then the unlike fractions must be converted into equivalent fractions that share the same denominator in order to be added or subtracted.

McGraw Hill My Math Grade 5 Chapter 9 Lesson 7 My Homework Answer Key

Question 1. \(\frac{1}{2}\) – \(\frac{1}{4}\) = ____ Answer: The above-given unlike fraction: 1/2 – 1/4 Step 1: Find a common denominator 4 is the least common multiple of denominators 2 and 4. Use it to convert to equivalent fractions with this common denominator. = 1 x 2/2 x 2 – 1 x 1/4 x 1 = 2/4 – 1/4 Step 2: Here the denominators are equal so subtract directly. = (2 – 1)/4 = 1/4 Therefore, \(\frac{1}{2}\) – \(\frac{1}{4}\) = 1/4.

Question 2. \(\frac{7}{8}\) – \(\frac{1}{4}\) = ____ Answer: The above-given unlike fraction: 7/8 – 1/4 Step 1: Find a common denominator 8 is the least common multiple of denominators 8 and 4. Use it to convert to equivalent fractions with this common denominator. = 7 x 1/8 x 1 – 1 x 2/4 x 2 = 7/8 – 2/8 Step 2: Here the denominators are equal so subtract directly. = (7 – 2)/8 = 5/8 Therefore, \(\frac{7}{8}\) – \(\frac{1}{4}\) = 5/8

Question 3. \(\frac{7}{12}\) – \(\frac{1}{6}\) = ____ Answer: The above-given unlike fraction: 7/12 – 1/6 Step 1: Find a common denominator 12 is the least common multiple of denominators 12 and 6. Use it to convert to equivalent fractions with this common denominator. = 7 x 1/12 x 1 – 1 x 2/6 x 2 = 7/12 – 2/12 Step 2: Here the denominators are equal so subtract directly. = (7 – 2)/12 = 5/12 Therefore, \(\frac{7}{12}\) – \(\frac{1}{6}\) = 5/12

Question 5. Trisha helped clean up her neighbourhood by picking up plastic. She collected \(\frac{3}{4}\) pound of plastic the first day and \(\frac{1}{6}\) pound of plastic the second day. How much more trash did she collect the first day than the second day? Answer: The above-given: The number of pounds of plastic collected on the first day by Trisha = 3/4 The number of pounds of plastic collected on the second day by Trisha =1/6 The number of pounds of trash collected on the first day than the second = f f = 3/4 – 1/6 Step 1: Find a common denominator 12 is the least common multiple of denominators 4 and 6. Use it to convert to equivalent fractions with this common denominator. = 3 x 3/4 x 3 – 1 x 2/6 x 2 = 9/12 – 2/12 = (9 – 2)/12 = 7/12 Therefore, 7/12 pounds more trash was collected on the first day.

Question 6. Wyatt is hiking a trail that is \(\frac{11}{12}\) mile long. After hiking \(\frac{1}{4}\) mile, he stops for water. How much farther must he hike to finish the trail? Answer: The above-given: The number of miles Wyatt is hiking = 11/12 The number of miles after he stopped for water = 1/4 The number of miles there to finish the trail = x x = 11/12 – 1/4 Step 1: Find a common denominator 12 is the least common multiple of denominators 12 and 4. Use it to convert to equivalent fractions with this common denominator. x = 11 x 1/12 x 1 – 1 x 3/4 x 3 x = 11/12 – 3/12 x = 8/12 x = 2/3 Therefore, 2/3 miles are there to finish the trail.

Test Practice

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