Add/Subtract Like Denominators

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Answer Key & Explanations

Add/Subtract Like Denominators · Grade 4 · Worksheet 3

1. Noah was measuring fabric for a school project. He needed 3/4 of a yard of blue fabric and 2/4 of a yard of red fabric. What fraction of a yard of fabric did Noah need in total? Answer: 5/4 Solution: Noah needs 3/4 yard of blue fabric and 2/4 yard of red fabric.
   Full step-by-step solution

   Step 1: Noah needs 3/4 yard of blue fabric and 2/4 yard of red fabric. Step 2: To find the total fabric, add the fractions: 3/4 + 2/4 Step 3: Since the denominators are the same, add the numerators: 3 + 2 = 5 Step 4: Keep the same denominator: 5/4 Step 5: The total fabric needed is 5/4 yards. The answer is 5/4.

2. 3/5 + 4/5 = ? Answer: 7/5 Solution: Both fractions have the same denominator of 5. Add the numerators: 3 + 4 = 7. Keep the denominator the same: 7/5.
   Full step-by-step solution

   Step 1: Both fractions have the same denominator of 5. Step 2: Add the numerators: 3 + 4 = 7. Step 3: Keep the denominator the same: 7/5. The answer is 7/5.

3. Noah was measuring fabric for a school project. He needed 5/12 of a yard of blue fabric and 3/12 of a yard of red fabric. What fraction of a yard of fabric did Noah need in total? Answer: 8/12 Solution: Noah needs 5/12 yard of blue fabric and 3/12 yard of red fabric. Since the denominators are the same (both are twelfths), we can add the numerators: 5 + 3 = 8. Keep the denominator the same: 12.
   Full step-by-step solution

   Step 1: Noah needs 5/12 yard of blue fabric and 3/12 yard of red fabric. Step 2: Since the denominators are the same (both are twelfths), we can add the numerators: 5 + 3 = 8. Step 3: Keep the denominator the same: 12. Step 4: The total fabric needed is 8/12 of a yard. The answer is 8/12.

4. 5/8 + 2/8 = ? Answer: 7/8 Solution: Identify the problem. We are adding two fractions: 5/8 and 2/8. Check the denominators.
   Full step-by-step solution

   Step 1: Identify the problem. We are adding two fractions: 5/8 and 2/8. Step 2: Check the denominators. Both fractions have the same denominator, which is 8. When fractions have the same denominator, it means we are adding parts of the same size. Step 3: Add the numerators. Since the denominators are the same, we keep the denominator and add the numerators together. Numerator: 5 + 2 = 7 Denominator: 8 Step 4: Write the result. Combining the new numerator with the denominator gives us the fraction 7/8. Step 5: Check if the fraction can be simplified. The fraction 7/8 is already in its simplest form because 7 and 8 have no common factors other than 1. Final Answer: 7/8

5. Hana is baking cookies. The recipe calls for 5/8 of a cup of sugar. Hana already added 3/8 of a cup. How much more sugar in eighths of a cup does Hana need to add? Answer: 2 Solution: The recipe needs 5/8 cup of sugar in total. Hana has already added 3/8 cup. Subtract to find how much more is needed: 5/8 - 3/8 = 2/8 cup.
   Full step-by-step solution

   Step 1: The recipe needs 5/8 cup of sugar in total. Step 2: Hana has already added 3/8 cup. Step 3: Subtract to find how much more is needed: 5/8 - 3/8 = 2/8 cup. The answer is 2/8.

6. A rectangular mural is painted on a wall and divided into 10 equal vertical stripes. The artist uses blue paint for 4 stripes and yellow paint for 3 stripes. What fraction of the mural is painted with either blue or yellow? Answer: 7/10 Solution: The mural is divided into 10 equal stripes, so each stripe represents 1/10 of the mural. Blue paint covers 4 stripes, which is 4/10 of the mural. Yellow paint covers 3 stripes, which is 3/10 of the mural.
   Full step-by-step solution

   Step 1: The mural is divided into 10 equal stripes, so each stripe represents 1/10 of the mural. Step 2: Blue paint covers 4 stripes, which is 4/10 of the mural. Step 3: Yellow paint covers 3 stripes, which is 3/10 of the mural. Step 4: Add the fractions for blue and yellow: 4/10 + 3/10 = 7/10. Step 5: The fraction of the mural painted with either blue or yellow is 7/10.

7. A rectangular quilt is divided into 15 equal square patches. The quilt maker sews floral patterns on 6 patches and geometric patterns on 7 patches. What fraction of the quilt has patterned patches? Answer: 13/15 Solution: The quilt is divided into 15 equal patches, so each patch represents 1/15 of the quilt. Floral patterns are on 6 patches, which is 6/15 of the quilt. Geometric patterns are on 7 patches, which is 7/15 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: Floral patterns are on 6 patches, which is 6/15 of the quilt. Step 3: Geometric patterns are on 7 patches, which is 7/15 of the quilt. Step 4: Add the fractions to find the total patterned portion: 6/15 + 7/15 = 13/15. Step 5: The fraction 13/15 represents the portion of the quilt that has patterned patches. The answer is 13/15.

8. A rectangular garden is divided into 8 equal sections. The gardener plants flowers in 3 sections and vegetables in 4 sections. What fraction of the garden is planted with either flowers or vegetables? Answer: 7/8 Solution: 1. The garden is divided into 8 equal sections. So each section is 1/8 of the garden.
   Full step-by-step solution

   Let's go step by step. 1. The garden is divided into 8 equal sections. So each section is 1/8 of the garden. 2. Flowers are planted in 3 sections. Fraction for flowers = 3 × (1/8) = 3/8. 3. Vegetables are planted in 4 sections. Fraction for vegetables = 4 × (1/8) = 4/8. 4. The problem asks for the fraction planted with either flowers or vegetables. Since no section is mentioned to have both, we can add the fractions: 3/8 + 4/8 = 7/8. 5. Check: 7 sections out of 8 are planted, so 7/8 is correct. Final answer: 7/8

9. 11/15 + 7/15 = ? Answer: 18/15 Solution: Both fractions have the same denominator (15), so we can add the numerators directly.
   Full step-by-step solution

   Step 1: Both fractions have the same denominator (15), so we can add the numerators directly. Step 2: Add the numerators: 11 + 7 = 18 Step 3: Write the result over the common denominator: 18/15 Step 4: The fraction 18/15 is already in simplest form for Grade 4 standards. The answer is 18/15.