Comparing Fractions by Cross Multiplication

Show your work for each problem.

1.
Which fraction is greater: or ?
1. a)
2. b)Cannot be determined
3. c)They are equal
4. d)
Answer:
Cross multiply: and . Since , we have .
2.
When comparing and by cross multiplication, what is the left cross product ()?
Answer: 20
The left cross product is . This corresponds to .
3.
Are and equal?
1. a)Cannot compare
2. b)No, is greater
3. c)No, is greater
4. d)Yes, they are equal
Answer: Yes, they are equal
Cross multiply: and . Since , the fractions are equal. Both simplify to .
4.
Compare and using cross multiplication.
Answer: 5/8 > 7/12
1. Calculate the left cross product: 60
2. Calculate the right cross product: 56
3. Which is larger: 60 or 56? 60
4. So which fraction is greater? 5/8
5.
When comparing and , what is the right cross product ()?
Answer: 20
The right cross product is . The left cross product is . Since , we have .
6.
Which fraction is smaller: or ?
1. a)
2. b)Cannot be determined
3. c)They are equal
4. d)
Answer:
Cross multiply: and . Since , we have , so is smaller.
7.
A recipe needs cup of sugar. Another needs cup. Which recipe uses more sugar?
Answer: 2/5
1. Calculate 16
2. Calculate 15
3. Which is larger: 16 or 15? 16
4. Which fraction is greater: or ? 2/5
8.
If , and the cross products are vs , what is the smallest whole number value of ?
Answer: 4
For , we need , so . The smallest whole number greater than is .
9.
Order these fractions from least to greatest: , ,
Answer: 3/5, 5/8, 2/3
1. Compare and : 24
2. And 25
3. So is _____ than less
4. Compare and : 15
5. And 16
6. So is _____ than less
10.
A store sells 5 apples for 3 euros or 8 apples for 5 euros. Which deal gives more apples per euro?
1. a)8 apples for 5 euros
2. b)Cannot determine
3. c)They are equal
4. d)5 apples for 3 euros
Answer: 5 apples for 3 euros
Compare vs : and . Since , . The first deal gives more apples per euro.
11.
What symbol (<, >, or =) goes between and ?
Answer: >
and . Since , we have .
12.
Compare and .
Answer: 11/15 > 13/18
1. Calculate the left cross product: 198
2. Calculate the right cross product: 195
3. Which is larger: 198 or 195? 198
4. So is _____ greater than
13.
Which fraction is closest to : , , or ?
1. a)
2. b)
3. c)They are all equally close
4. d)
Answer:
Compare to : vs : vs (diff ). vs : vs (diff ). vs : vs (diff ). All differ by , but while and . is closest to .
14.
Find a value of such that (the fractions are equal).
Answer: 7.5
For equal fractions: , so , giving . Check: .
15.
Three students completed different portions of a test. Anna finished , Ben finished , and Cara finished . Who completed the most?
Answer: Ben
1. Compare Anna and Ben: 105
2. And 110
3. Who has more between Anna and Ben? Ben
4. Compare Ben and Cara: 77
5. And 75
6. Who completed the most overall? Ben
16.
If , which inequality must be true?
1. a)
2. b)
3. c)
4. d)
Answer:
By the cross multiplication rule, if , then . The product using the smaller fraction's numerator is smaller.