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? 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 The answer is 651.
   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 The answer is 651.

2. 2/3 + 5/8 = ? Answer: 31/24 Solution: Identify the fractions to add: 2/3 and 5/8 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 5/8 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 5/8 to have denominator 24: (5 × 3)/(8 × 3) = 15/24 Step 5: Add the fractions: 16/24 + 15/24 = 31/24 Step 6: 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.

3. 5/8 + 3/10 = ? Answer: 37/40 Solution: Find a common denominator for 5/8 and 3/10. The least common multiple of 8 and 10 is 40.
   Full step-by-step solution

   Step 1: Find a common denominator for 5/8 and 3/10. The least common multiple of 8 and 10 is 40. Step 2: Convert 5/8 to have denominator 40: 5/8 = (5 × 5)/(8 × 5) = 25/40 Step 3: Convert 3/10 to have denominator 40: 3/10 = (3 × 4)/(10 × 4) = 12/40 Step 4: Add the fractions: 25/40 + 12/40 = 37/40 Step 5: Check if the fraction can be simplified: 37/40 is already in simplest form since 37 is a prime number. The answer is 37/40.

4. A farmer planted 3/8 of his field with corn and 2/5 with wheat. What fraction of the field was planted with these two crops? Answer: 31/40 Solution: Identify the fractions to add: 3/8 and 2/5. Find a common denominator. The denominators are 8 and 5.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 3/8 and 2/5. 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 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.

5. A painter used 3/5 of a gallon of blue paint and 2/7 of a gallon of yellow paint for a project. What fraction of a gallon of paint was used in total? Answer: 31/35 Solution: Identify the fractions to add: 3/5 and 2/7. Find a common denominator. The denominators are 5 and 7.
   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 paint used is 31/35 of a gallon.

6. Liam is baking cookies and needs 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: Write the problem as an addition expression. Total sugar = 3/4 + 2/3 Find a common denominator so we can add the fractions. The denominators are 4 and 3.
   Full step-by-step solution

   Let's find the total amount of sugar Liam needs by adding 3/4 cup and 2/3 cup. Step 1: Write the problem as an addition expression. Total sugar = 3/4 + 2/3 Step 2: Find a common denominator so we can add the fractions. The denominators are 4 and 3. The smallest number that both 4 and 3 divide into evenly is 12. So the common denominator is 12. Step 3: Convert each fraction to have a denominator of 12. - For 3/4: To change the denominator 4 into 12, we multiply by 3. So we multiply both the numerator and denominator by 3. 3/4 = (3 * 3) / (4 * 3) = 9/12 - For 2/3: To change the denominator 3 into 12, we multiply by 4. So we multiply both the numerator and denominator by 4. 2/3 = (2 * 4) / (3 * 4) = 8/12 Step 4: Add the converted fractions. Now we add: 9/12 + 8/12 = (9 + 8)/12 = 17/12 Step 5: Simplify the improper fraction into a mixed number. 17/12 is an improper fraction (the numerator is larger than the denominator). - 12 goes into 17 one full time (1 * 12 = 12). - The remainder is 17 - 12 = 5. - So, 17/12 = 1 and 5/12. Step 6: State the final answer. The total amount of sugar Liam needs is 1 5/12 cups.

7. A painter used 3/5 gallon of blue paint and 2/7 gallon of yellow paint for a project. How much paint did she use in total? 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 amount of paint used is 31/35 gallon.

8. Emma is painting a mural for her school. On Monday, she painted 2/5 of the total wall area. On Tuesday, she painted another 3/10 of the wall. What fraction of the entire wall has Emma painted so far? Answer: 7/10 Solution: Identify the fractions to add: 2/5 and 3/10. Find a common denominator. The denominators are 5 and 10.
   Full step-by-step solution

   Step 1: Identify the fractions to add: 2/5 and 3/10. Step 2: Find a common denominator. The denominators are 5 and 10. The least common denominator is 10. Step 3: Convert 2/5 to a fraction with denominator 10: (2/5) = (2 × 2)/(5 × 2) = 4/10. Step 4: Add the fractions: 4/10 + 3/10 = 7/10. Step 5: The fraction 7/10 is already in simplest form. The answer is 7/10.