Fraction Benchmarks

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Answer Key & Explanations

Fraction Benchmarks · Grade 3 · Worksheet 1

1. Liam baked a large rectangular cake for his class party. He cut the cake into 8 equal slices. During the party, students ate 3 slices of the cake. What fraction of the whole cake was eaten? Answer: 3/8 Solution: The whole cake is represented as 1. Understand how the cake is cut. Liam cut the cake into 8 equal slices.
   Full step-by-step solution

   Step 1: Understand the whole cake. The whole cake is represented as 1. Step 2: Understand how the cake is cut. Liam cut the cake into 8 equal slices. This means each slice is 1/8 of the whole cake. Step 3: Determine how many slices were eaten. The students ate 3 slices. Step 4: Calculate the fraction of the cake eaten. Since each slice is 1/8 of the cake, 3 slices would be: 3 × (1/8) = 3/8 Step 5: Interpret the result. The fraction 3/8 means that 3 out of the 8 equal parts of the cake were eaten. Final Answer: 3/8

2. A rectangular vegetable garden is divided into 12 equal sections. If 5 sections are planted with corn and 4 sections are planted with beans, what fraction of the garden is planted with vegetables? Answer: 3/4 Solution: Find the total number of sections planted with vegetables. Corn sections: 5 Bean sections: 4 Total vegetable sections: 5 + 4 = 9 Write this as a fraction of the whole garden. The garden has 12 equal sections total.
   Full step-by-step solution

   Step 1: Find the total number of sections planted with vegetables. Corn sections: 5 Bean sections: 4 Total vegetable sections: 5 + 4 = 9 Step 2: Write this as a fraction of the whole garden. The garden has 12 equal sections total. Fraction with vegetables = 9/12 Step 3: Simplify the fraction. Both 9 and 12 can be divided by 3. 9 ÷ 3 = 3 12 ÷ 3 = 4 So 9/12 = 3/4 The answer is 3/4.

3. Liam is baking cookies for his class party. He needs 3/4 cup of sugar for the cookie dough and 1/2 cup of sugar for the frosting. Does Liam need more than 1 cup of sugar in total for his cookies? Answer: A. no Solution: When working with fractions, it helps to think about how parts relate to a whole. Comparing fractions to benchmarks like 1/2 and 1 can help determine if their sum is greater or less than 1.
   Full step-by-step solution

   When working with fractions, it helps to think about how parts relate to a whole. For example, if you have less than half of something and another amount that is also less than half, together they might not make a whole. Comparing fractions to benchmarks like 1/2 and 1 can help determine if their sum is greater or less than 1.

4. Noah is making a fruit punch for a party. He has a measuring cup that shows fractions. He needs to add 1/6 of a cup of lemon juice. Is 1/6 of a cup closer to 0, 1/2, or 1 cup? Answer: 0 Solution: We compare 1/6 to 0, 1/2, and 1. Think about 1/2 of a cup. If a cup is divided into 6 equal parts, half the cup would be 3 out of 6 parts, or 3/6.
   Full step-by-step solution

   Step 1: Understand the benchmarks. We compare 1/6 to 0, 1/2, and 1. Step 2: Think about 1/2 of a cup. If a cup is divided into 6 equal parts, half the cup would be 3 out of 6 parts, or 3/6. So 1/2 is equal to 3/6. Step 3: Compare 1/6 to 3/6. Since 1 is much smaller than 3, 1/6 is much less than 1/2. Step 4: Compare 1/6 to 0. Since 1/6 is only 1 part out of 6, it is very close to 0 and far from 1/2 and 1. Step 5: Conclusion. 1/6 is closest to 0. The answer is 0.

5. 3/4 + 2/8 = ? Answer: 1 Solution: Look at the fractions 3/4 and 2/8. They have different denominators. Find a common denominator.
   Full step-by-step solution

   Step 1: Look at the fractions 3/4 and 2/8. They have different denominators. Step 2: Find a common denominator. Since 4 is a factor of 8, we can use 8 as the common denominator. Step 3: Convert 3/4 to eighths: 3/4 = 6/8 (because 3 × 2 = 6 and 4 × 2 = 8). Step 4: Now add the fractions: 6/8 + 2/8 = 8/8. Step 5: Simplify 8/8: 8 ÷ 8 = 1. The answer is 1.

6. Lily baked a large rectangular cake for her class party. She cut it into 8 equal slices. During the party, her friends ate 3 slices. What fraction of the whole cake was eaten? Answer: 3/8 Solution: The cake is cut into 8 equal slices, so each slice is 1/8 of the whole cake. Determine how many slices were eaten. Her friends ate 3 slices.
   Full step-by-step solution

   Step 1: Understand the cake is divided into equal slices. The cake is cut into 8 equal slices, so each slice is 1/8 of the whole cake. Step 2: Determine how many slices were eaten. Her friends ate 3 slices. Step 3: Find the fraction of the whole cake that was eaten. If 1 slice = 1/8 of the cake, then 3 slices = 3 × (1/8) = 3/8 of the cake. Step 4: Conclusion. The fraction of the whole cake that was eaten is 3/8.

7. Mere is painting a fence. She has painted 5/12 of the fence. Is the fraction of the fence she has painted closer to 0, 1/2, or 1? Answer: closer to 1/2 Solution: Find the benchmark 1/2 written with a denominator of 12. Since 1/2 = 6/12, the benchmark is 6/12. Compare 5/12 to 6/12.
   Full step-by-step solution

   Step 1: Find the benchmark 1/2 written with a denominator of 12. Since 1/2 = 6/12, the benchmark is 6/12. Step 2: Compare 5/12 to 6/12. 5/12 is only 1/12 less than 6/12. Step 3: Compare 5/12 to 0. 5/12 is much larger than 0 (it is 5/12 away from 0). Step 4: Compare 5/12 to 1. 1 = 12/12, so 5/12 is 7/12 away from 1. Step 5: The distance from 5/12 to 1/2 is 1/12, which is smaller than the distance to 0 (5/12) or to 1 (7/12). So 5/12 is closest to 1/2. The answer is closer to 1/2.

8. Aroha is painting a large wooden fence. She has painted 3/7 of the fence. Is the portion she has painted closer to 0, 1/2, or 1 of the whole fence? Answer: closer to 1/2 Solution: 0 means none of the fence is painted, 1/2 means exactly half, and 1 means the whole fence is painted. Compare 3/7 to 1/2. Since 1/2 = 3.5/7 (because 1/2 = 7/14 = 3.5/7), we see that 3/7 is just a little less than 3.5/7.
   Full step-by-step solution

   Step 1: Understand the benchmarks. 0 means none of the fence is painted, 1/2 means exactly half, and 1 means the whole fence is painted. Step 2: Compare 3/7 to 1/2. Since 1/2 = 3.5/7 (because 1/2 = 7/14 = 3.5/7), we see that 3/7 is just a little less than 3.5/7. Step 3: Compare 3/7 to 0. 3/7 is much closer to 1/2 than to 0 because 3/7 is about 0.43 and 1/2 is 0.5, while 0 is far away at 0. Step 4: Compare 3/7 to 1. 3/7 is less than half, so it is much closer to 1/2 than to 1. Step 5: Conclusion: 3/7 is closest to 1/2. Answer: The portion Aroha has painted is closer to 1/2.

9. A rectangular vegetable garden is divided into 12 equal sections. The gardener plants corn in 5 sections, beans in 4 sections, and squash in the remaining sections. If you drew a diagram showing all 12 sections with different colors for each vegetable, what fraction of the garden is planted with squash? Answer: 1/4 Solution: Find the total number of sections used for corn and beans: 5 + 4 = 9 sections Find the number of sections left for squash: 12 - 9 = 3 sections Write the fraction of garden with squash: 3/12 Simplify the fraction: 3/12 = 1/4 The answer is 1/4.
   Full step-by-step solution

   Step 1: Find the total number of sections used for corn and beans: 5 + 4 = 9 sections Step 2: Find the number of sections left for squash: 12 - 9 = 3 sections Step 3: Write the fraction of garden with squash: 3/12 Step 4: Simplify the fraction: 3/12 = 1/4 The answer is 1/4.