Fraction Word Problems

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Answer Key & Explanations

Fraction Word Problems · Grade 5 · Worksheet 2

1. A rectangular prism is drawn with a length of 12.5 cm, a width of 8.4 cm, and a height of 6.2 cm. What is the volume of this prism in cubic centimeters? Answer: 651 Solution: Recall the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 12.5 × 8.4 × 6.2 First multiply 12.5 × 8.4 = 105 Then multiply 105 × 6.2 = 651 The volume is 651 cubic centimeters.
   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 = 12.5 × 8.4 × 6.2 Step 3: First multiply 12.5 × 8.4 = 105 Step 4: Then multiply 105 × 6.2 = 651 Step 5: The volume is 651 cubic centimeters.

2. Maria had 7/8 of a liter of juice. She drank 3/5 of a liter. How much juice does she have left? Answer: 11/40 Solution: Identify the operation. Maria started with 7/8 liter and drank 3/5 liter, so we subtract: 7/8 - 3/5. Find a common denominator.
   Full step-by-step solution

   Step 1: Identify the operation. Maria started with 7/8 liter and drank 3/5 liter, so we subtract: 7/8 - 3/5. Step 2: Find a common denominator. The denominators are 8 and 5. The least common multiple of 8 and 5 is 40. Step 3: Convert 7/8 to have a denominator of 40. Multiply the numerator and denominator by 5: (7 × 5)/(8 × 5) = 35/40. Step 4: Convert 3/5 to have a denominator of 40. Multiply the numerator and denominator by 8: (3 × 8)/(5 × 8) = 24/40. Step 5: Subtract the fractions: 35/40 - 24/40 = 11/40. Step 6: Check if the fraction can be simplified. The numbers 11 and 40 have no common factors other than 1, so 11/40 is already in its simplest form. Maria has 11/40 of a liter of juice left.

3. 2/3 + 3/5 = ? Answer: 19/15 Solution: Find a common denominator for 2/3 and 3/5. The least common multiple of 3 and 5 is 15.
   Full step-by-step solution

   Step 1: Find a common denominator for 2/3 and 3/5. The least common multiple of 3 and 5 is 15. Step 2: Convert 2/3 to have denominator 15: 2/3 = (2 × 5)/(3 × 5) = 10/15 Step 3: Convert 3/5 to have denominator 15: 3/5 = (3 × 3)/(5 × 3) = 9/15 Step 4: Add the fractions: 10/15 + 9/15 = 19/15 Step 5: Check if the fraction can be simplified: 19/15 is already in simplest form. The answer is 19/15.

4. Moana painted 3 of a fence in the morning and 2 of the same fence in the afternoon. How much more of the fence did Moana paint in the morning than in the afternoon? Answer: 1 Solution: Find the difference: 3 - 2. 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: Find the difference: 3 - 2. 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: Subtract the numerators: 1. The answer is 1 of the fence.

5. A baker used 3/8 cup of sugar for cookies and 1/6 cup for frosting. How much sugar was used in total? Answer: 13/24 Solution: Identify the fractions to add: 3/8 and 1/6 Find a common denominator. The denominators are 8 and 6. The least common multiple of 8 and 6 is 24.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/8 and 1/6 Step 2: Find a common denominator. The denominators are 8 and 6. The least common multiple of 8 and 6 is 24. Step 3: Convert 3/8 to have denominator 24: (3 × 3)/(8 × 3) = 9/24 Step 4: Convert 1/6 to have denominator 24: (1 × 4)/(6 × 4) = 4/24 Step 5: Add the fractions: 9/24 + 4/24 = 13/24 Step 6: Check if the fraction can be simplified: 13/24 is already in simplest form since 13 and 24 have no common factors. The total amount of sugar used is 13/24 cup.

6. A recipe calls for 2/3 cup of flour and 3/8 cup of sugar. How many cups of these dry ingredients are needed in total? Answer: 25/24 Solution: Identify the fractions to add: 2/3 and 3/8 Find a common denominator. The least common multiple of 3 and 8 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. The least common multiple of 3 and 8 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 is an improper fraction, which means it's more than 1 cup. This is acceptable as the answer. The total amount of dry ingredients needed is 25/24 cups.

7. A farmer planted 3/5 of his field with corn and 2/7 of his field with wheat. What fraction of the field was planted with these two crops? Answer: 31/35 Solution: Identify the fractions to add: 3/5 and 2/7 Find a common denominator. The denominators are 5 and 7. The least common multiple of 5 and 7 is 35.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/5 and 2/7 Step 2: Find a common denominator. The denominators are 5 and 7. The least common multiple of 5 and 7 is 35. Step 3: Convert 3/5 to have denominator 35: (3 × 7)/(5 × 7) = 21/35 Step 4: Convert 2/7 to have denominator 35: (2 × 5)/(7 × 5) = 10/35 Step 5: Add the fractions: 21/35 + 10/35 = 31/35 Step 6: Check if the fraction can be simplified: 31/35 is already in simplest form since 31 and 35 have no common factors. The total fraction of the field planted is 31/35.

8. 3/4 + 1/6 = ? Answer: 11/12 Solution: Find a common denominator for 3/4 and 1/6. The least common multiple of 4 and 6 is 12.
   Full step-by-step solution

   Step 1: Find a common denominator for 3/4 and 1/6. The least common multiple of 4 and 6 is 12. Step 2: Convert 3/4 to have denominator 12: 3/4 = (3 × 3)/(4 × 3) = 9/12 Step 3: Convert 1/6 to have denominator 12: 1/6 = (1 × 2)/(6 × 2) = 2/12 Step 4: Add the fractions: 9/12 + 2/12 = 11/12 Step 5: Check if the fraction can be simplified: 11/12 is already in simplest form. The answer is 11/12.