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Add/Subtract Like Denominators

Grade 4 · Fractions · Worksheet 2

  1. Noah walked 3/10 of a mile to the park and then 4/10 of a mile to the library. What fraction of a mile did Noah walk in total? Answer: ______________
  2. Lily baked a large pizza for her family dinner. She cut it into 8 equal slices. During dinner, her brother ate 3 slices and her sister ate 2 slices. What fraction of the whole pizza did they eat together? Answer: ______________
  3. A rectangular quilt is divided into 15 equal square patches. The quilter uses blue fabric for 7 patches and yellow fabric for 6 patches. What fraction of the quilt is made with either blue or yellow fabric? Answer: ______________
  4. A construction crew paved 5/12 of a mile of road on Monday and 7/12 of a mile on Tuesday. How many miles of road did they pave in total over these two days? Answer: ______________
  5. 11/15 - 6/15 = ? Answer: ______________
  6. 7/9 - 4/9 = ? Answer: ______________
  7. 13/17 - 8/17 = ? Answer: ______________
  8. 13/19 - 8/19 = ? Answer: ______________
  9. A rectangular garden is divided into 8 equal sections. The gardener plants flowers in 3 sections and vegetables in 2 sections. What fraction of the garden is planted with either flowers or vegetables? Answer: ______________
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Answer Key & Explanations

Add/Subtract Like Denominators · Grade 4 · Worksheet 2

  1. Noah walked 3/10 of a mile to the park and then 4/10 of a mile to the library. What fraction of a mile did Noah walk in total? Answer: 7/10 Solution: Noah walked 3/10 of a mile to the park. He then walked 4/10 of a mile to the library. To find the total distance, add the fractions: 3/10 + 4/10.
    Full step-by-step solution

    Step 1: Noah walked 3/10 of a mile to the park. Step 2: He then walked 4/10 of a mile to the library. Step 3: To find the total distance, add the fractions: 3/10 + 4/10. Step 4: Since the denominators are the same, add the numerators: 3 + 4 = 7. Step 5: Keep the denominator the same: 7/10. Noah walked a total of 7/10 of a mile.

  2. Lily baked a large pizza for her family dinner. She cut it into 8 equal slices. During dinner, her brother ate 3 slices and her sister ate 2 slices. What fraction of the whole pizza did they eat together? Answer: 5/8 Solution: The pizza is cut into 8 equal slices, so each slice is 1/8 of the whole pizza. Determine how many slices the brother and sister ate together. Brother ate 3 slices.
    Full step-by-step solution

    Step 1: Understand the problem. The pizza is cut into 8 equal slices, so each slice is 1/8 of the whole pizza. Step 2: Determine how many slices the brother and sister ate together. Brother ate 3 slices. Sister ate 2 slices. Total slices eaten = 3 + 2 = 5 slices. Step 3: Find the fraction of the whole pizza that these 5 slices represent. Since 1 slice = 1/8 of the pizza, 5 slices = 5 × (1/8) = 5/8 of the pizza. Step 4: Conclusion. Together, they ate 5/8 of the whole pizza. Final answer: 5/8

  3. A rectangular quilt is divided into 15 equal square patches. The quilter uses blue fabric for 7 patches and yellow fabric for 6 patches. What fraction of the quilt is made with either blue or yellow fabric? Answer: 13/15 Solution: The quilt is divided into 15 equal patches, so each patch represents 1/15 of the quilt. Blue fabric covers 7 patches, which is 7/15 of the quilt. Yellow fabric covers 6 patches, which is 6/15 of the quilt.
    Full step-by-step solution

    Step 1: The quilt is divided into 15 equal patches, so each patch represents 1/15 of the quilt. Step 2: Blue fabric covers 7 patches, which is 7/15 of the quilt. Step 3: Yellow fabric covers 6 patches, which is 6/15 of the quilt. Step 4: Add the fractions for blue and yellow fabric: 7/15 + 6/15 = 13/15. Step 5: The fraction of the quilt made with either blue or yellow fabric is 13/15.

  4. A construction crew paved 5/12 of a mile of road on Monday and 7/12 of a mile on Tuesday. How many miles of road did they pave in total over these two days? Answer: 1 Solution: The crew paved 5/12 of a mile on Monday and 7/12 of a mile on Tuesday.
    Full step-by-step solution

    Step 1: The crew paved 5/12 of a mile on Monday and 7/12 of a mile on Tuesday. Step 2: Add the fractions: 5/12 + 7/12 = (5 + 7)/12 Step 3: Calculate the numerator: 5 + 7 = 12 Step 4: Write the result: 12/12 Step 5: Simplify the fraction: 12/12 = 1 The answer is 1.

  5. 11/15 - 6/15 = ? Answer: 5/15 Solution: Both fractions have the same denominator (15), so we can subtract the numerators directly.
    Full step-by-step solution

    Step 1: Both fractions have the same denominator (15), so we can subtract the numerators directly. Step 2: Subtract the numerators: 11 - 6 = 5 Step 3: Write the result over the common denominator: 5/15 Step 4: The fraction 5/15 is already in simplest form for Grade 4 standards. The answer is 5/15.

  6. 7/9 - 4/9 = ? Answer: 1/3 Solution: Both fractions have the same denominator (9), so we can subtract the numerators directly.
    Full step-by-step solution

    Step 1: Both fractions have the same denominator (9), so we can subtract the numerators directly. Step 2: Subtract the numerators: 7 - 4 = 3 Step 3: Write the result over the common denominator: 3/9 Step 4: Simplify the fraction by dividing numerator and denominator by their greatest common factor (3): 3 ÷ 3 = 1 and 9 ÷ 3 = 3 Step 5: The simplified fraction is 1/3 The answer is 1/3.

  7. 13/17 - 8/17 = ? Answer: 5/17 Solution: Both fractions have the same denominator (17), so we can subtract the numerators directly.
    Full step-by-step solution

    Step 1: Both fractions have the same denominator (17), so we can subtract the numerators directly. Step 2: Subtract the numerators: 13 - 8 = 5 Step 3: Write the result over the common denominator: 5/17 Step 4: The fraction 5/17 is already in simplest form. The answer is 5/17.

  8. 13/19 - 8/19 = ? Answer: 5/19 Solution: Both fractions have the same denominator (19), so we can subtract the numerators directly. Subtract the numerators: 13 - 8 = 5 Keep the same denominator: 5/19 The fraction 5/19 is already in simplest form.
    Full step-by-step solution

    Step 1: Both fractions have the same denominator (19), so we can subtract the numerators directly. Step 2: Subtract the numerators: 13 - 8 = 5 Step 3: Keep the same denominator: 5/19 Step 4: The fraction 5/19 is already in simplest form. The answer is 5/19.

  9. A rectangular garden is divided into 8 equal sections. The gardener plants flowers in 3 sections and vegetables in 2 sections. What fraction of the garden is planted with either flowers or vegetables? Answer: 5/8 Solution: The garden is divided into 8 equal sections, so each section is 1/8 of the garden. Identify the sections used. Flowers are planted in 3 sections, so the fraction for flowers is 3/8.
    Full step-by-step solution

    Step 1: Understand the problem. The garden is divided into 8 equal sections, so each section is 1/8 of the garden. Step 2: Identify the sections used. Flowers are planted in 3 sections, so the fraction for flowers is 3/8. Vegetables are planted in 2 sections, so the fraction for vegetables is 2/8. Step 3: Combine the fractions. We want the fraction of the garden planted with either flowers or vegetables. Since these sections are different (no overlap mentioned), we add the fractions: 3/8 + 2/8 = (3 + 2)/8 = 5/8. Step 4: Interpret the result. 5/8 of the garden is planted with either flowers or vegetables. Final answer: 5/8