Comparing Fractions Using Benchmarks

Show your work for each problem.

1.
Which fraction is greater than ?
1. a)
2. b)
3. c)
4. d)
Answer:
is greater than because (and ). The others are either less than or equal to half.
2.
Which fraction is closest to 0?
1. a)
2. b)
3. c)
4. d)
Answer:
is closest to 0 because 1 is the smallest numerator. It represents only 1 part out of 6.
3.
What is written with a denominator of 10? Write your answer as a fraction (e.g., 3/10).
Answer: 5/10
because . This is essential for comparing fractions with denominator 10 to the benchmark .
4.
Is greater than, less than, or equal to ? Type: greater, less, or equal.
Answer: less
is less than because (and ). So is below the halfway benchmark.
5.
Which fraction is closest to 1?
1. a)
2. b)
3. c)
4. d)
Answer:
is closest to 1 because 7 is only 1 away from 8. It represents 7 out of 8 equal parts - almost the whole!
6.
Which is greater: or ?
1. a)They are equal
2. b)
3. c)
4. d)Cannot determine
Answer:
is less than (since ), but is greater than (since ). Any fraction greater than half beats any fraction less than half, so .
7.
What is written with a denominator of 12? Write your answer as a fraction (e.g., 3/12).
Answer: 6/12
because . Now you can compare any twelfths to half: , but .
8.
Order from least to greatest: , ,
Answer: 1/10, 2/5, 7/10
1. Is close to 0, close to , or close to 1? 0
2. Is greater or less than ? (Half of 5 is 2.5) less
3. Is close to 0, close to , or close to 1? 1
4. Write the fractions in order from least to greatest (use commas) 1/10, 2/5, 7/10
9.
A basketball player made of her free throws. Is this more or less than half?
1. a)Less than half
2. b)Exactly half
3. c)Cannot determine
4. d)More than half
Answer: Less than half
, and , so . The player made less than half her free throws.
10.
Compare and . Which is greater?
Answer: 3/7
1. What is half of 7? 3.5
2. Is greater or less than ? (Compare 3 to 3.5) less
3. What is half of 9? 4.5
4. Is greater or less than ? (Compare 4 to 4.5) less
5. Both are less than half. Which is closer to ? Type the larger fraction. 3/7
11.
A recipe needs cup of milk. Is this close to 0, close to , or close to 1? Type: 0, half, or 1
Answer: 1
is close to 1 because 7 is only 1 less than 8. You need almost a full cup of milk!
12.
Order from least to greatest: , , ,
Answer: 2/6, 5/12, 3/4, 7/8
1. Compare to . Is it greater or less? (Half of 12 is 6) less
2. Compare to . Is it greater or less? (Half of 6 is 3) less
3. Compare to . Is it greater or less? (Half of 4 is 2) greater
4. Is close to 0, , or 1? 1
5. Which is smaller: or ? (Hint: ) 2/6
6. Write all four in order from least to greatest (use commas) 2/6, 5/12, 3/4, 7/8
13.
Which fraction is closest to ?
1. a)
2. b)
3. c)
4. d)
Answer:
is closest to . Here's why: , which is away from . The others: (0.1 away), (0.125 away), (0.083 away). So wins!
14.
Sarah ate of a pizza. Tom ate of an identical pizza. Who ate more? Type: Sarah or Tom
Answer: Tom
Both are greater than . and . Tom ate more because . Another way: needs more to reach 1, but needs only more.
15.
Which is greater: or ? Use benchmarks to decide.
Answer: 5/11
1. What is half of 11? 5.5
2. Is greater or less than ? less
3. What is half of 13? 6.5
4. Is greater or less than ? less
5. Both are less than half. is 0.5 away from half. is also 0.5 away. Which fraction is greater? (Hint: , ) 6/13