Fraction Word Problems

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Answer Key & Explanations

Fraction Word Problems · Grade 5 · Worksheet 3

1. A rectangular prism is drawn with a length of 7.5 cm, a width of 4.2 cm, and a height of 3.8 cm. What is the volume of this prism? Answer: 119.7 Solution: Recall the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 7.5 × 4.2 × 3.8 First multiply 7.5 × 4.2 = 31.5 Then multiply 31.5 × 3.8 = 119.7 The volume is 119.7 cubic centimeters The answer is 119.7.
   Full step-by-step solution

   Step 1: Recall the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 7.5 × 4.2 × 3.8 Step 3: First multiply 7.5 × 4.2 = 31.5 Step 4: Then multiply 31.5 × 3.8 = 119.7 Step 5: The volume is 119.7 cubic centimeters The answer is 119.7.

2. A baker used 3/8 cup of sugar for cookies and 2/5 cup for frosting. How much sugar was used in total? Answer: 31/40 Solution: Identify the fractions to add: 3/8 and 2/5 Find a common denominator. The least common multiple of 8 and 5 is 40.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/8 and 2/5 Step 2: Find a common denominator. The least common multiple of 8 and 5 is 40. Step 3: Convert 3/8 to have denominator 40: (3 × 5)/(8 × 5) = 15/40 Step 4: Convert 2/5 to have denominator 40: (2 × 8)/(5 × 8) = 16/40 Step 5: Add the fractions: 15/40 + 16/40 = 31/40 Step 6: Check if the fraction can be simplified: 31/40 is already in simplest form since 31 and 40 have no common factors. The total sugar used was 31/40 cup.

3. Sam used 2 cup of sugar and 4 cup of flour to make cookies. How many cups of ingredients did Sam use in all? Answer: 6 Solution: Add the amounts: 2 + 4. Find a common denominator for the two fractions. Convert each fraction to an equivalent fraction with the common denominator.
   Full step-by-step solution

   Step 1: Add the amounts: 2 + 4. Step 2: Find a common denominator for the two fractions. Step 3: Convert each fraction to an equivalent fraction with the common denominator. Step 4: Add the numerators: 6. The answer is 6 cups.

4. Emma is painting a mural on her bedroom wall. She used 2/3 of a gallon of blue paint for the sky and 3/8 of a gallon of green paint for the grass. What fraction of a gallon of paint did Emma use in total for her mural? Answer: 25/24 Solution: Identify the fractions to add: 2/3 and 3/8 Find a common denominator for 3 and 8. The least common multiple is 24.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 2/3 and 3/8 Step 2: Find a common denominator for 3 and 8. The least common multiple is 24. Step 3: Convert 2/3 to have denominator 24: (2 × 8)/(3 × 8) = 16/24 Step 4: Convert 3/8 to have denominator 24: (3 × 3)/(8 × 3) = 9/24 Step 5: Add the fractions: 16/24 + 9/24 = 25/24 Step 6: The fraction 25/24 represents the total paint used. The answer is 25/24.

5. Liam was baking cookies and needed 3/4 cup of sugar for the chocolate chip batch and 2/3 cup of sugar for the oatmeal raisin batch. What is the total amount of sugar Liam needs for both batches of cookies? Answer: 1 5/12 cups Solution: Identify the amounts of sugar needed for each batch. Liam needs 3/4 cup for chocolate chip cookies and 2/3 cup for oatmeal raisin cookies. Write the addition problem.
   Full step-by-step solution

   Step 1: Identify the amounts of sugar needed for each batch. Liam needs 3/4 cup for chocolate chip cookies and 2/3 cup for oatmeal raisin cookies. Step 2: Write the addition problem. Total sugar = 3/4 + 2/3 Step 3: Find a common denominator for the fractions. The denominators are 4 and 3. The least common denominator is 12. Step 4: Convert each fraction to have denominator 12. For 3/4: Multiply numerator and denominator by 3 → (3 × 3)/(4 × 3) = 9/12 For 2/3: Multiply numerator and denominator by 4 → (2 × 4)/(3 × 4) = 8/12 Step 5: Add the fractions. 9/12 + 8/12 = (9 + 8)/12 = 17/12 Step 6: Convert the improper fraction to a mixed number. 17 ÷ 12 = 1 with remainder 5, so 17/12 = 1 5/12 Step 7: State the final answer. Liam needs a total of 1 5/12 cups of sugar for both batches.

6. A baker used 5/8 cup of butter for cookies and 2/5 cup for frosting. How much butter did she use in total? Answer: 41/40 Solution: Identify the fractions to add: 5/8 and 2/5 Find a common denominator. The least common multiple of 8 and 5 is 40.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 5/8 and 2/5 Step 2: Find a common denominator. The least common multiple of 8 and 5 is 40. Step 3: Convert 5/8 to have denominator 40: (5 × 5)/(8 × 5) = 25/40 Step 4: Convert 2/5 to have denominator 40: (2 × 8)/(5 × 8) = 16/40 Step 5: Add the fractions: 25/40 + 16/40 = 41/40 Step 6: Check if the fraction can be simplified: 41/40 is already in simplest form since 41 and 40 have no common factors. The total amount of butter used is 41/40 cup.

7. Charlotte walked 5 mile to the library, then walked 3 mile to the park. How far did Charlotte walk in total? Answer: 8 Solution: Write the two distances as fractions: 5 + 3. Find a common denominator. Convert 5 and 3 to equivalent fractions with the same denominator.
   Full step-by-step solution

   Step 1: Write the two distances as fractions: 5 + 3. Step 2: Find a common denominator. Convert 5 and 3 to equivalent fractions with the same denominator. Step 3: Add the numerators: 8. The answer is 8 miles.

8. A baker used 2/5 cup of sugar for cookies and 3/7 cup for frosting. How much sugar was used in total? Answer: 29/35 Solution: Identify the fractions to add: 2/5 and 3/7 Find a common denominator. The least common multiple of 5 and 7 is 35.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 2/5 and 3/7 Step 2: Find a common denominator. The least common multiple of 5 and 7 is 35. Step 3: Convert 2/5 to have denominator 35: (2 × 7)/(5 × 7) = 14/35 Step 4: Convert 3/7 to have denominator 35: (3 × 5)/(7 × 5) = 15/35 Step 5: Add the fractions: 14/35 + 15/35 = 29/35 Step 6: Check if the fraction can be simplified: 29/35 is already in simplest form since 29 and 35 have no common factors. The total sugar used was 29/35 cup.