Fraction Benchmarks

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Fraction Benchmarks · Grade 3 · Worksheet 1

1. Liam is baking cookies and needs 3/4 cup of sugar. His measuring cup is divided into eighths. How many eighths of a cup does Liam need to measure 3/4 cup of sugar? Answer: 6 Solution: We know Liam needs 3/4 cup of sugar, and the measuring cup is divided into eighths. We want to find how many eighths of a cup make 3/4 cup. Write the problem as a question.
   Full step-by-step solution

   We know Liam needs 3/4 cup of sugar, and the measuring cup is divided into eighths. We want to find how many eighths of a cup make 3/4 cup. Step 1: Write the problem as a question. We need to find: 3/4 cup = ? eighths of a cup. Step 2: Since "eighths" means 1/8 cup per part, we can set up a relationship: Let x be the number of eighths. Then: x * (1/8) = 3/4 Step 3: Solve for x. Multiply both sides by 8: x = (3/4) * 8 Step 4: Multiply the fraction by 8. (3/4) * 8 = (3 * 8) / 4 = 24 / 4 Step 5: Simplify 24/4. 24 divided by 4 equals 6. So, x = 6. Step 6: Interpretation. This means Liam needs 6 one-eighth cup portions to make 3/4 cup. Final answer: 6

2. Charlotte is helping her mom bake a large rectangular pan of granola bars. They cut the pan into 12 equal bars. Charlotte's dad eats 7 bars after work. Is the fraction of granola bars that were eaten closer to 0, 1/2, or 1? Answer: closer to 1/2 Solution: The pan was cut into 12 equal bars, so the whole is 12/12. Charlotte's dad ate 7 bars, so the fraction eaten is 7/12. Compare 7/12 to the benchmarks 0, 1/2, and 1.
   Full step-by-step solution

   Step 1: Understand the fraction. The pan was cut into 12 equal bars, so the whole is 12/12. Charlotte's dad ate 7 bars, so the fraction eaten is 7/12. Step 2: Compare 7/12 to the benchmarks 0, 1/2, and 1. - 0 would mean 0 bars eaten, but 7 bars were eaten, so it is not close to 0. - 1 would mean all 12 bars eaten, but only 7 were eaten, so it is not close to 1. - 1/2 of 12 is 6 bars (since 12 divided by 2 equals 6). 7 is only 1 more than 6, so 7/12 is just a little more than half. Step 3: Decide which benchmark is closest. Since 7/12 is only 1/12 away from 1/2, and much farther from 0 (7/12 away) and from 1 (5/12 away), the fraction 7/12 is closest to 1/2. Answer: The fraction of granola bars that were eaten is closer to 1/2.

3. Liam's pizza was cut into 8 equal slices. He ate 3 slices for dinner and 2 more slices later as a snack. What fraction of the whole pizza did Liam eat in total? Answer: 5/8 Solution: The pizza is cut into 8 equal slices, so the whole pizza is 8/8. Find how many slices Liam ate. He ate 3 slices for dinner and 2 slices later as a snack.
   Full step-by-step solution

   Step 1: Understand the problem. The pizza is cut into 8 equal slices, so the whole pizza is 8/8. Step 2: Find how many slices Liam ate. He ate 3 slices for dinner and 2 slices later as a snack. Total slices eaten = 3 + 2 = 5 slices. Step 3: Write the fraction of the pizza eaten. Since each slice is 1/8 of the pizza, 5 slices = 5 × (1/8) = 5/8 of the pizza. Step 4: Conclusion. Liam ate 5/8 of the whole pizza in total.

4. Isabella is making a large batch of lemonade for her family picnic. She needs to fill a big pitcher that holds 12 cups of lemonade. So far, she has poured in 5 cups of lemonade. Has Isabella filled more than half of the pitcher yet? Answer: no Solution: Find half of the pitcher's capacity. The pitcher holds 12 cups. Half of 12 is 12 divided by 2, which equals 6 cups.
   Full step-by-step solution

   Step 1: Find half of the pitcher's capacity. The pitcher holds 12 cups. Half of 12 is 12 divided by 2, which equals 6 cups. So, 1/2 of the pitcher is 6 cups. Step 2: Compare the amount poured to half. Isabella poured 5 cups. Since 5 is less than 6, she has not filled half of the pitcher. Step 3: Answer the question. The question asks if she has filled more than half. Since 5 cups is less than 6 cups, the answer is no. The answer is no.

5. Liam is baking cookies and needs 3/4 cup of sugar. His measuring cup is divided into eighths. What fraction of the cup should he fill to get the correct amount of sugar? Answer: 6/8 Solution: Liam needs 3/4 cup of sugar, but his measuring cup is divided into eighths. That means each cup marking is 1/8 of a cup. We need to find how many eighths equal 3/4.
   Full step-by-step solution

   Step 1: Understand the problem. Liam needs 3/4 cup of sugar, but his measuring cup is divided into eighths. That means each cup marking is 1/8 of a cup. We need to find how many eighths equal 3/4. Step 2: Compare the fractions. We have 3/4 and want to express it in eighths. Since 1/4 is the same as 2/8, we can convert 3/4 into eighths. Step 3: Convert 3/4 to eighths. Multiply both the numerator and denominator of 3/4 by 2 so that the denominator becomes 8. 3/4 = (3 × 2)/(4 × 2) = 6/8. Step 4: Interpret the result. 6/8 means 6 parts out of 8 parts of the cup. Since the cup is divided into eighths, Liam should fill 6 of those eighths. Step 5: Final answer. He should fill 6/8 of the cup to get 3/4 cup of sugar.

6. Is 7/9 closer to 0, 1/2, or 1? Answer: 1 Solution: The fraction is 7/9. The denominator is 9, so the whole is divided into 9 equal parts. Half of 9 is 4.5.
   Full step-by-step solution

   Step 1: The fraction is 7/9. The denominator is 9, so the whole is divided into 9 equal parts. Half of 9 is 4.5. Step 2: Compare the numerator 7 to 4.5. Since 7 is greater than 4.5, the fraction is greater than 1/2. Step 3: Compare 7/9 to 1 (or 9/9). Since 7 is close to 9, and 7/9 is only 2 parts away from 9/9, it is much closer to 1 than to 1/2. Step 4: Therefore, 7/9 is closest to 1. The answer is 1.

7. A rectangular garden is divided into 8 equal sections. 5 sections are planted with tomatoes and the rest are planted with carrots. What fraction of the garden is planted with carrots? Answer: 3/8 Solution: The garden is divided into 8 equal sections. Find how many sections are carrots. 5 sections are tomatoes.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. So, the whole garden is represented by 8 sections. Step 2: Find how many sections are carrots. 5 sections are tomatoes. Total sections = 8. Carrot sections = Total sections − Tomato sections Carrot sections = 8 − 5 = 3. Step 3: Write the fraction for carrots. The fraction is the number of carrot sections over the total number of sections. So, fraction = 3/8. Step 4: Conclusion. 3/8 of the garden is planted with carrots.

8. A rectangular field is divided into 12 equal sections. The farmer plants corn in 5 sections, wheat in 4 sections, and leaves the rest empty. If you draw a diagram showing the field with colored sections for each crop, what fraction of the field is planted with corn? Write your answer in simplest form. Answer: 5/12 Solution: The field is divided into 12 equal sections, so the whole field is represented by 12/12. The farmer plants corn in 5 of these sections.
   Full step-by-step solution

   Step 1: The field is divided into 12 equal sections, so the whole field is represented by 12/12. Step 2: The farmer plants corn in 5 of these sections. Step 3: The fraction of the field planted with corn is the number of corn sections divided by the total number of sections: 5/12. Step 4: Check if the fraction 5/12 can be simplified. Since 5 and 12 have no common factors other than 1, the fraction is already in simplest form. The answer is 5/12.

9. Is 3/8 closer to 0, 1/2, or 1? Answer: 1/2 Solution: The fraction is 3/8. The whole is cut into 8 equal pieces, and we have 3 of them. Compare to 0: 3/8 is greater than 0 because 3 pieces is more than 0 pieces.
   Full step-by-step solution

   Step 1: The fraction is 3/8. The whole is cut into 8 equal pieces, and we have 3 of them. Step 2: Compare to 0: 3/8 is greater than 0 because 3 pieces is more than 0 pieces. Step 3: Compare to 1/2: 1/2 of 8 pieces is 4 pieces (because 8 ÷ 2 = 4). So 1/2 = 4/8. Since 3/8 is less than 4/8, it is less than 1/2. Step 4: Compare to 1: 1 whole would be 8/8. 3/8 is much less than 8/8. Step 5: Now decide which benchmark is closest. The distance from 3/8 to 0 is 3/8. The distance from 3/8 to 1/2 (4/8) is 1/8. The distance from 3/8 to 1 (8/8) is 5/8. The smallest distance is 1/8, so 3/8 is closest to 1/2. The answer is 1/2.