Comparing Fractions with the Same Numerator

Show your work for each problem.

1.
Which fraction is larger: or ?
1. a)
2. b)Cannot be determined
3. c)
4. d)They are equal
Answer:
is larger because when numerators are equal, the fraction with the smaller denominator is larger. Since , thirds are bigger pieces than fifths.
2.
Which symbol goes in the blank? ___
1. a)
2. b)Cannot compare
3. c)
4. d)
Answer:
because . With the same numerator, larger denominator means smaller pieces, so is less than .
3.
Which is smaller: or ? Enter the smaller fraction (e.g., 1/8).
Answer: 1/8
is smaller because . When you cut something into 8 pieces instead of 4, each piece is smaller.
4.
If you have of a cake and your friend has , who has more?
1. a)You ()
2. b)Your friend ()
3. c)Equal amounts
4. d)Not enough information
Answer: You ()
You have more! Both fractions have numerator 3, so compare denominators. Since , sixths are bigger pieces than tenths. .
5.
Order from smallest to largest: , , . Enter as: 2/9, 2/5, 2/3
Answer: 2/9, 2/5, 2/3
Denominators: . Larger denominator = smaller fraction. So: .
6.
A store offers off all items. Another store offers off. Which is a better deal?
1. a)Both are equal
2. b)Cannot determine without prices
3. c) off (second store)
4. d) off (first store)
Answer: off (first store)
is a better deal because . Both have numerator 1, and , so fourths are larger than sixths.
7.
Compare and . Which is larger?
Answer: 4/7
1. What is the numerator of both fractions? 4
2. Are the numerators the same? (yes/no) yes
3. Which denominator is larger: 7 or 11? 11
4. Larger denominator means smaller or larger fraction? smaller
5. So which fraction is larger? (enter as 4/7 or 4/11) 4/7
8.
Fill in the blank with <, >, or =: ___
Answer: >
because . Eighths are bigger pieces than twelfths, so 5 eighths is more than 5 twelfths.
9.
Order from largest to smallest: , ,
Answer: 3/4, 3/6, 3/8
1. What is the common numerator? 3
2. List the denominators in order from smallest to largest 4, 6, 8
3. Which fraction has the smallest denominator? 3/4
4. The smallest denominator gives the _____ fraction largest
5. Write the order from largest to smallest (use commas) 3/4, 3/6, 3/8
10.
Which statement is TRUE?
1. a)
2. b)
3. c)Cannot compare these fractions
4. d)
Answer:
is true. Both have numerator 7. Since , ninths are larger pieces than fifteenths.
11.
Order from smallest to largest: , , ,
Answer: 6/13, 6/11, 6/9, 6/7
1. What is the common numerator? 6
2. Order the denominators from largest to smallest 13, 11, 9, 7
3. Which fraction is smallest (largest denominator)? 6/13
4. Which fraction is largest (smallest denominator)? 6/7
5. Write all four from smallest to largest 6/13, 6/11, 6/9, 6/7
12.
Find a fraction with numerator 4 that is between and . Enter as 4/n.
Answer: 4/7
(or or ) works. Since , we have . The denominator 7 is between 5 and 9.
13.
Compare the improper fractions: and . Which is larger?
Answer: 8/3
1. What type of fractions are these (proper or improper)? improper
2. Does the same-numerator rule still apply? (yes/no) yes
3. What is the common numerator? 8
4. Which denominator is smaller: 3 or 5? 3
5. Which fraction is larger? (enter as 8/3 or 8/5) 8/3
14.
Which list shows fractions in order from largest to smallest?
1. a)
2. b)
3. c)
4. d)
Answer:
Correct order: . Denominators from smallest to largest (6, 8, 10, 12) give fractions from largest to smallest.
15.
Emma ate of a pie. Jake ate of an identical pie. Who ate more?
Answer: Jake
1. What fraction did Emma eat? 2/5
2. What fraction did Jake eat? 2/3
3. Do both fractions have the same numerator? (yes/no) yes
4. Which denominator is smaller: 5 or 3? 3
5. Who ate the larger fraction (Emma or Jake)? Jake