Fraction Word Problems

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Answer Key & Explanations

Fraction Word Problems · Grade 5 · Worksheet 1

1. 5/8 + 2/3 = ? Answer: 31/24 Solution: Find a common denominator for 5/8 and 2/3. The least common multiple of 8 and 3 is 24.
   Full step-by-step solution

   Step 1: Find a common denominator for 5/8 and 2/3. The least common multiple of 8 and 3 is 24. Step 2: Convert 5/8 to have denominator 24: 5/8 = (5 × 3)/(8 × 3) = 15/24 Step 3: Convert 2/3 to have denominator 24: 2/3 = (2 × 8)/(3 × 8) = 16/24 Step 4: Add the fractions: 15/24 + 16/24 = 31/24 Step 5: Check if the fraction can be simplified: 31/24 is already in simplest form since 31 and 24 have no common factors. The answer is 31/24.

2. A baker used 2/3 cup of sugar for a cake and 3/8 cup for cookies. How much sugar did she use 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: Check if the fraction can be simplified: 25/24 is already in simplest form since 25 and 24 have no common factors. The total amount of sugar used is 25/24 cups.

3. A rectangular prism is drawn with dimensions: length = 6.4 cm, width = 5.2 cm, and height = 8.7 cm. What is the volume of this prism? Answer: 289.536 Solution: Write the volume formula for a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 6.4 × 5.2 × 8.7 First multiply 6.4 × 5.2 = 33.28 Then multiply 33.28 × 8.7 = 289.536 Include the units: 289.536 cubic centimeters The volume of the rectangular prism is…
   Full step-by-step solution

   Step 1: Write the volume formula for a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 6.4 × 5.2 × 8.7 Step 3: First multiply 6.4 × 5.2 = 33.28 Step 4: Then multiply 33.28 × 8.7 = 289.536 Step 5: Include the units: 289.536 cubic centimeters The volume of the rectangular prism is 289.536 cm³.

4. Emma is painting two walls in her room. The first wall requires 5/8 of a gallon of paint, and the second wall requires 3/4 of a gallon. What is the total amount of paint, in gallons, that Emma needs to paint both walls? Answer: 11/8 Solution: Identify the fractions to add: 5/8 and 3/4 Find a common denominator. The denominators are 8 and 4. The least common multiple is 8.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 5/8 and 3/4 Step 2: Find a common denominator. The denominators are 8 and 4. The least common multiple is 8. Step 3: Convert 3/4 to have a denominator of 8. Multiply both numerator and denominator by 2: (3 × 2)/(4 × 2) = 6/8 Step 4: Now add the fractions: 5/8 + 6/8 = 11/8 Step 5: The total amount of paint needed is 11/8 gallons. The answer is 11/8.

5. A triangular garden is drawn on a coordinate plane with vertices at (0,0), (5,0), and (0,12). What is the area of this triangle in square units? Answer: 30 Solution: - The points (0,0) and (5,0) are on the x-axis, so the distance between them is 5 units (base) - The points (0,0) and (0,12) are on the y-axis, so the distance between them is 12 units (height) Area = (1/2) × base × height Area = (1/2) × 5 × 12 (1/2) × 5 = 2.5 2.5 × 12 = 30 The area of the…
   Full step-by-step solution

   Step 1: Identify the base and height from the coordinates - The points (0,0) and (5,0) are on the x-axis, so the distance between them is 5 units (base) - The points (0,0) and (0,12) are on the y-axis, so the distance between them is 12 units (height) Step 2: Use the triangle area formula Area = (1/2) × base × height Step 3: Substitute the values Area = (1/2) × 5 × 12 Step 4: Calculate step by step (1/2) × 5 = 2.5 2.5 × 12 = 30 Step 5: State the final answer The area of the triangle is 30 square units.

6. A recipe calls for 3/5 cup of flour for the cake and 2/7 cup for the frosting. How much flour is needed in total? Answer: 31/35 Solution: Identify the fractions to add: 3/5 and 2/7. 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: 3/5 and 2/7. Step 2: Find a common denominator. 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 flour needed is 31/35 cup.

7. Lily used 3 cup of sugar and 1 cup of flour to make cookies. How many cups of ingredients did Lily use in all? Answer: 4 Solution: Add the amounts: 3 + 1. 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: 3 + 1. 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: 4. The answer is 4 cups.

8. 3/5 + 2/7 = ? Answer: 31/35 Solution: Find a common denominator for 3/5 and 2/7. The least common multiple of 5 and 7 is 35.
   Full step-by-step solution

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

9. A farmer planted 3/8 of his field with corn and 2/5 with wheat. What fraction of his field is planted with these crops? 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 fraction of the field planted is 31/40.