Fraction Benchmarks

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Answer Key & Explanations

Fraction Benchmarks · Grade 3 · Worksheet 2

1. Noah baked a rectangular pan of brownies and cut it into 6 equal pieces. He ate 1 piece after school. Is the fraction of brownies Noah ate closer to 0, 1/2, or 1? Answer: 0 Solution: The pan is cut into 6 equal pieces, so each piece is 1/6 of the whole. Noah ate 1 piece, which is 1/6 of the brownies. Compare 1/6 to the benchmarks 0, 1/2, and 1.
   Full step-by-step solution

   Step 1: The pan is cut into 6 equal pieces, so each piece is 1/6 of the whole. Noah ate 1 piece, which is 1/6 of the brownies. Step 2: Compare 1/6 to the benchmarks 0, 1/2, and 1. 1/2 of the pan would be 3 pieces (since 6 x 1/2 = 3). 1 whole would be 6 pieces (6/6). Step 3: 1 piece is very small compared to 3 pieces (1/2) or 6 pieces (1). It is much closer to 0 pieces. Step 4: So 1/6 is closer to 0. The answer is 0.

2. Tane is organizing a large collection of seashells. He has a display board divided into 16 equal sections. He fills 13 sections with seashells. Is the fraction of the board that is filled closer to 0, 1/2, or 1? Answer: 1 Solution: The board has 16 equal sections, so the whole is 16/16. Tane fills 13 sections, so the fraction filled is 13/16. Compare 13/16 to the benchmarks 0, 1/2, and 1.
   Full step-by-step solution

   Step 1: The board has 16 equal sections, so the whole is 16/16. Tane fills 13 sections, so the fraction filled is 13/16. Step 2: Compare 13/16 to the benchmarks 0, 1/2, and 1. - 0 would mean 0 sections filled, but 13 sections are filled, so it is not close to 0. - 1/2 of 16 is 8 sections (since 16 divided by 2 equals 8). 13 is much more than 8, so 13/16 is much larger than 1/2. - 1 would mean all 16 sections filled. 13 is only 3 sections away from 16, so 13/16 is very close to 1. Step 3: Decide which benchmark is closest. 13/16 is only 3/16 away from 1, but it is 5/16 away from 1/2 and 13/16 away from 0. So 13/16 is closest to 1. The answer is 1.

3. Ava is reading a book for her book report. The book has 16 chapters. She has already read 6 chapters. Is the fraction of the book Ava has read closer to 0, 1/2, or 1? Answer: closer to 1/2 Solution: The book has 16 chapters, so the whole book is 16/16. Ava has read 6 chapters, so the fraction read is 6/16. Compare 6/16 to the benchmarks 0, 1/2, and 1.
   Full step-by-step solution

   Step 1: The book has 16 chapters, so the whole book is 16/16. Ava has read 6 chapters, so the fraction read is 6/16. Step 2: Compare 6/16 to the benchmarks 0, 1/2, and 1. - 0 would mean 0 chapters read, but Ava has read 6 chapters, so it is not close to 0. - 1 would mean all 16 chapters read, but only 6 have been read, so it is not close to 1. - 1/2 of 16 is 8 chapters (since 16 divided by 2 equals 8). 6 is only 2 less than 8, so 6/16 is just a little less than half. Step 3: Decide which benchmark is closest. 6/16 is 2/16 away from 1/2, 6/16 away from 0, and 10/16 away from 1. The smallest distance is to 1/2. The answer is closer to 1/2.

4. 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.

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. 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

7. Aroha is painting a large wooden fence. She has painted 9 out of 20 equal sections. Has she painted more than half of the fence or less than half? Answer: less than half Solution: Find what half of the fence is. The fence has 20 equal sections, so half would be 20 divided by 2 = 10 sections. Aroha painted 9 sections.
   Full step-by-step solution

   Step 1: Find what half of the fence is. The fence has 20 equal sections, so half would be 20 divided by 2 = 10 sections. Step 2: Aroha painted 9 sections. Step 3: Compare 9 to 10. Since 9 is less than 10, she painted less than half of the fence. The answer is: less than half.

8. A rectangular community garden is divided into 20 equal plots. The gardeners plant tomatoes in 8 plots, carrots in 5 plots, and peppers in 3 plots. If you draw a diagram showing the garden with colored sections for each vegetable, what fraction of the garden is planted with vegetables? Write your answer in simplest form. Answer: 4/5 Solution: Find the total number of plots planted with vegetables Tomatoes: 8 plots Carrots: 5 plots Peppers: 3 plots Total planted = 8 + 5 + 3 = 16 plots Total garden plots = 20 Planted plots = 16 Fraction = 16/20 Find the greatest common factor of 16 and 20 Factors of 16: 1, 2, 4, 8, 16 Factors of 20: 1,…
   Full step-by-step solution

   Step 1: Find the total number of plots planted with vegetables Tomatoes: 8 plots Carrots: 5 plots Peppers: 3 plots Total planted = 8 + 5 + 3 = 16 plots Step 2: Write the fraction of garden planted Total garden plots = 20 Planted plots = 16 Fraction = 16/20 Step 3: Simplify the fraction Find the greatest common factor of 16 and 20 Factors of 16: 1, 2, 4, 8, 16 Factors of 20: 1, 2, 4, 5, 10, 20 Greatest common factor = 4 Divide numerator and denominator by 4: 16 ÷ 4 = 4, 20 ÷ 4 = 5 Simplified fraction = 4/5 The answer is 4/5.

9. 3/4 + 1/8 = ? Answer: 7/8 Solution: The fractions are 3/4 and 1/8. They have different denominators (4 and 8). Find a common denominator.
   Full step-by-step solution

   Step 1: The fractions are 3/4 and 1/8. They have different denominators (4 and 8). Step 2: Find a common denominator. The smallest number that both 4 and 8 divide into is 8. Step 3: Convert 3/4 to have denominator 8. Multiply numerator and denominator by 2: (3 × 2)/(4 × 2) = 6/8. Step 4: Now add the fractions: 6/8 + 1/8 = 7/8. Step 5: The fraction 7/8 is already in simplest form. The answer is 7/8.