Fraction Word Problems

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Answer Key & Explanations

Fraction Word Problems · Grade 5 · Worksheet 3

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. 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.

3. 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.

4. Emma is painting a mural for her school's art fair. On Monday, she painted 3/8 of the mural. On Tuesday, she painted 1/6 of the mural. What fraction of the entire mural has Emma painted so far? Answer: 13/24 Solution: Identify the fractions to add: 3/8 and 1/6. Find a common denominator for 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 for 8 and 6. The least common multiple of 8 and 6 is 24. Step 3: Convert 3/8 to an equivalent fraction with denominator 24: (3 × 3)/(8 × 3) = 9/24. Step 4: Convert 1/6 to an equivalent fraction with denominator 24: (1 × 4)/(6 × 4) = 4/24. Step 5: Add the fractions: 9/24 + 4/24 = 13/24. The answer is 13/24.

5. A farmer harvested 3/4 of a ton of wheat from his first field and 5/8 of a ton from his second field. How much more wheat did he harvest from the first field than from the second field? Answer: 1/8 Solution: To find how much more wheat was harvested from the first field than the second, we subtract the amount from the second field from the amount from the first field. Write the subtraction expression. Amount from first field: 3/4 ton Amount from second field: 5/8 ton Difference = 3/4 - 5/8 To…
   Full step-by-step solution

   To find how much more wheat was harvested from the first field than the second, we subtract the amount from the second field from the amount from the first field. Step 1: Write the subtraction expression. Amount from first field: 3/4 ton Amount from second field: 5/8 ton Difference = 3/4 - 5/8 Step 2: To subtract these fractions, they need a common denominator. The denominators are 4 and 8. The least common denominator is 8. Step 3: Convert 3/4 to a fraction with denominator 8. Multiply the numerator and denominator by 2: (3 * 2)/(4 * 2) = 6/8 So, 3/4 = 6/8. Step 4: Now subtract the fractions. 6/8 - 5/8 = (6 - 5)/8 = 1/8 Step 5: Interpret the result. The difference is 1/8 of a ton. Therefore, the farmer harvested 1/8 ton more wheat from the first field than from the second field.

6. A recipe calls for 2/3 cup of flour for the cake and 3/8 cup for the frosting. How much flour is 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: Check if the fraction can be simplified: 25/24 is already in simplest form. The total flour needed is 25/24 cups.

7. Emma is painting a mural on her bedroom wall. On Monday, she painted 2/3 of the wall. On Tuesday, she painted 1/4 of the wall. What fraction of the entire wall has Emma painted in total? Answer: 11/12 Solution: Identify the fractions to add: 2/3 and 1/4 Find a common denominator for 3 and 4, which is 12 Convert 2/3 to twelfths: (2/3) × (4/4) = 8/12 Convert 1/4 to twelfths: (1/4) × (3/3) = 3/12 Add the fractions: 8/12 + 3/12 = 11/12 The total fraction painted is 11/12 of the wall
   Full step-by-step solution

   Step 1: Identify the fractions to add: 2/3 and 1/4 Step 2: Find a common denominator for 3 and 4, which is 12 Step 3: Convert 2/3 to twelfths: (2/3) × (4/4) = 8/12 Step 4: Convert 1/4 to twelfths: (1/4) × (3/3) = 3/12 Step 5: Add the fractions: 8/12 + 3/12 = 11/12 Step 6: The total fraction painted is 11/12 of the wall

8. 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.

9. Noah is building a model bridge for his science project. He needs to cut two wooden planks to specific lengths. The first plank should be 5/8 of a meter long, and the second plank should be 3/4 of a meter long. What is the total length of wood Noah needs for these two planks? 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 denominator 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 denominator is 8. Step 3: Convert 3/4 to have denominator 8: (3 × 2)/(4 × 2) = 6/8 Step 4: Now add the fractions: 5/8 + 6/8 = 11/8 Step 5: The total length is 11/8 meters. The answer is 11/8.