Equivalent Fractions

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Answer Key & Explanations

Equivalent Fractions · Grade 4 · Worksheet 2

1. Sophia is making a batch of homemade granola bars. The recipe calls for 2/3 cup of honey. She only has a 1/6 cup measuring spoon. How many scoops of the 1/6 cup measuring spoon will Sophia need to measure out the correct amount of honey? Answer: 4 Solution: We need to find how many 1/6 cups are in 2/3 cup. This is the same as solving 2/3 divided by 1/6, but we can also use equivalent fractions. Find an equivalent fraction for 2/3 with a denominator of 6.
   Full step-by-step solution

   Step 1: We need to find how many 1/6 cups are in 2/3 cup. This is the same as solving 2/3 divided by 1/6, but we can also use equivalent fractions. Step 2: Find an equivalent fraction for 2/3 with a denominator of 6. Multiply the numerator and denominator by 2: (2 × 2) / (3 × 2) = 4/6. Step 3: Now we have 4/6 cup, and each scoop is 1/6 cup. Since 4/6 means 4 parts of 1/6, Sophia needs 4 scoops. Step 4: Check: 4 scoops × 1/6 cup per scoop = 4/6 cup, which simplifies to 2/3 cup. Correct. The answer is 4.

2. 3/5 = __/20 Answer: 12 Solution: The original fraction is 3/5 and the new denominator is 20. Find what number you multiply the original denominator (5) by to get the new denominator (20). 5 × 4 = 20.
   Full step-by-step solution

   Step 1: The original fraction is 3/5 and the new denominator is 20. Step 2: Find what number you multiply the original denominator (5) by to get the new denominator (20). 5 × 4 = 20. Step 3: Multiply the original numerator (3) by the same number (4). 3 × 4 = 12. Step 4: The equivalent fraction is 12/20. The missing numerator is 12.

3. 7/8 = __/96 Answer: 84 Solution: The original fraction is 7/8 and the new denominator is 96. Find what number you multiply the original denominator (8) by to get the new denominator (96). 8 × 12 = 96.
   Full step-by-step solution

   Step 1: The original fraction is 7/8 and the new denominator is 96. Step 2: Find what number you multiply the original denominator (8) by to get the new denominator (96). 8 × 12 = 96. Step 3: Multiply the original numerator (7) by the same number (12). 7 × 12 = 84. Step 4: The equivalent fraction is 84/96. The missing numerator is 84.

4. Aroha is making a traditional Māori cloak. She has a piece of fabric that is 12/16 of a meter long. She needs to cut the fabric into pieces that are each 1/4 of a meter long. How many pieces can Aroha cut from the fabric? Answer: 3 Solution: We need to find how many 1/4 meter pieces fit into 12/16 meter of fabric. This is the same as finding an equivalent fraction for 12/16 with a denominator of 4.
   Full step-by-step solution

   Step 1: We need to find how many 1/4 meter pieces fit into 12/16 meter of fabric. This is the same as finding an equivalent fraction for 12/16 with a denominator of 4. Step 2: To change the denominator from 16 to 4, we divide by 4: 16 divided by 4 = 4. Step 3: Divide the numerator by the same number: 12 divided by 4 = 3. Step 4: So 12/16 = 3/4. Step 5: Since 3/4 means 3 parts of 1/4 each, Aroha can cut 3 pieces of fabric. The answer is 3.

5. Isabella is making friendship bracelets. She has a long string that is 8/9 of a yard long. She cuts the string into pieces that are each 1/9 of a yard long. How many pieces does Isabella get? Answer: 8 Solution: The whole string is 8/9 yard. Each piece is 1/9 yard. To find how many pieces, divide the total length by the length of one piece: 8/9 ÷ 1/9.
   Full step-by-step solution

   Step 1: The whole string is 8/9 yard. Each piece is 1/9 yard. Step 2: To find how many pieces, divide the total length by the length of one piece: 8/9 ÷ 1/9. Step 3: When dividing fractions with the same denominator, divide the numerators: 8 ÷ 1 = 8. Step 4: So 8/9 ÷ 1/9 = 8. Isabella gets 8 pieces of string.

6. Sophia is sewing a quilt. She has a piece of fabric that is 8/10 of a yard long. She needs to cut the fabric into pieces that are each 1/5 of a yard long. How many pieces can Sophia cut from the fabric? Answer: 4 Solution: We need to find how many 1/5 yard pieces fit into 8/10 yard of fabric. This is the same as finding an equivalent fraction for 8/10 with a denominator of 5.
   Full step-by-step solution

   Step 1: We need to find how many 1/5 yard pieces fit into 8/10 yard of fabric. This is the same as finding an equivalent fraction for 8/10 with a denominator of 5. Step 2: To change the denominator from 10 to 5, we divide by 2: 10 divided by 2 = 5. Step 3: Divide the numerator by the same number: 8 divided by 2 = 4. Step 4: So 8/10 = 4/5. Step 5: Since 4/5 means 4 parts of 1/5 each, Sophia can cut 4 pieces of fabric. The answer is 4.

7. 4/7 = __/28 Answer: 16 Solution: The original fraction is 4/7 and the new denominator is 28. Find what number you multiply the original denominator (7) by to get the new denominator (28). 7 × 4 = 28.
   Full step-by-step solution

   Step 1: The original fraction is 4/7 and the new denominator is 28. Step 2: Find what number you multiply the original denominator (7) by to get the new denominator (28). 7 × 4 = 28. Step 3: Multiply the original numerator (4) by the same number (4). 4 × 4 = 16. Step 4: The equivalent fraction is 16/28. The missing numerator is 16.

8. Mason is building a model train track. He has a piece of track that is 7/8 of a meter long. He needs to cut it into pieces that are each 1/8 of a meter long. How many pieces will Mason get? Answer: 7 Solution: The total length of the track is 7/8 meter. Each piece is 1/8 meter. To find how many pieces, divide the total length by the length of one piece: 7/8 divided by 1/8.
   Full step-by-step solution

   Step 1: The total length of the track is 7/8 meter. Each piece is 1/8 meter. Step 2: To find how many pieces, divide the total length by the length of one piece: 7/8 divided by 1/8. Step 3: When dividing fractions with the same denominator, divide the numerators: 7 divided by 1 = 7. Step 4: So 7/8 divided by 1/8 = 7. Mason will get 7 pieces of track.

9. 3/5 = __/25 Answer: 15 Solution: Look at the denominator change from 5 to 25 Determine what number multiplied by 5 equals 25: 5 × 5 = 25 Multiply the numerator by the same number: 3 × 5 = 15 The equivalent fraction is 15/25 The missing number is 15.
   Full step-by-step solution

   Step 1: Look at the denominator change from 5 to 25 Step 2: Determine what number multiplied by 5 equals 25: 5 × 5 = 25 Step 3: Multiply the numerator by the same number: 3 × 5 = 15 Step 4: The equivalent fraction is 15/25 The missing number is 15.