Comparing Fractions with the Same Numerator

Show your work for each problem.

1.
Which fraction is larger: $\frac{1}{3}$ or $\frac{1}{5}$ ?
1. a) $\frac{1}{5}$
2. b)Cannot be determined
3. c) $\frac{1}{3}$
4. d)They are equal
Answer: $\frac{1}{3}$
$\frac{1}{3}$ is larger because when numerators are equal, the fraction with the smaller denominator is larger. Since $3 < 5$ , thirds are bigger pieces than fifths.
2.
Which symbol goes in the blank? $\frac{2}{7}$ ___ $\frac{2}{4}$
1. a) $<$
2. b)Cannot compare
3. c) $=$
4. d) $>$
Answer: $<$
$\frac{2}{7} < \frac{2}{4}$ because $7 > 4$ . With the same numerator, larger denominator means smaller pieces, so $\frac{2}{7}$ is less than $\frac{2}{4}$ .
3.
Which is smaller: $\frac{1}{4}$ or $\frac{1}{8}$ ? Type it as a fraction, for example 3/5.
Answer: 1/8
$\frac{1}{8}$ is smaller because $8 > 4$ . When you cut something into 8 pieces instead of 4, each piece is smaller.
4.
If you have $\frac{3}{6}$ of a cake and your friend has $\frac{3}{10}$ , who has more?
1. a)You ( $\frac{3}{6}$ )
2. b)Your friend ( $\frac{3}{10}$ )
3. c)Equal amounts
4. d)Not enough information
Answer: You ( $\frac{3}{6}$ )
You have more! Both fractions have numerator 3, so compare denominators. Since $6 < 10$ , sixths are bigger pieces than tenths. $\frac{3}{6} > \frac{3}{10}$ .
5.
Order from smallest to largest: $\frac{2}{3}$ , $\frac{2}{9}$ , $\frac{2}{5}$ . Which fraction is in the middle? Type it as a fraction, for example 3/7.
Answer: 2/5
Denominators: $9 > 5 > 3$ . Larger denominator = smaller fraction. So: $\frac{2}{9} < \frac{2}{5} < \frac{2}{3}$ . The fraction in the middle is $\frac{2}{5}$ .
6.
A store offers $\frac{1}{4}$ off all items. Another store offers $\frac{1}{6}$ off. Which is a better deal?
1. a)Both are equal
2. b)Cannot determine without prices
3. c) $\frac{1}{6}$ off (second store)
4. d) $\frac{1}{4}$ off (first store)
Answer: $\frac{1}{4}$ off (first store)
$\frac{1}{4}$ is a better deal because $\frac{1}{4} > \frac{1}{6}$ . Both have numerator 1, and $4 < 6$ , so fourths are larger than sixths.
7.
Compare $\frac{4}{7}$ and $\frac{4}{11}$ . Which is larger?
Answer: 4/7
1. What is the numerator of both fractions? 4
2. Are the numerators the same? 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 =: $\frac{5}{8}$ ___ $\frac{5}{12}$
Answer: >
$\frac{5}{8} > \frac{5}{12}$ because $8 < 12$ . Eighths are bigger pieces than twelfths, so 5 eighths is more than 5 twelfths.
9.
Order from largest to smallest: $\frac{3}{4}$ , $\frac{3}{8}$ , $\frac{3}{6}$
Answer: 3/4, 3/6, 3/8
1. What is the common numerator? 3
2. Which denominator is the smallest: 4, 8 or 6? 4
3. Which fraction has the smallest denominator? 3/4
4. The smallest denominator gives the _____ fraction largest
5. In the order from largest to smallest, which fraction comes second? 3/6
10.
Which statement is TRUE?
1. a) $\frac{7}{9} > \frac{7}{15}$
2. b) $\frac{7}{9} < \frac{7}{15}$
3. c)Cannot compare these fractions
4. d) $\frac{7}{9} = \frac{7}{15}$
Answer: $\frac{7}{9} > \frac{7}{15}$
$\frac{7}{9} > \frac{7}{15}$ is true. Both have numerator 7. Since $9 < 15$ , ninths are larger pieces than fifteenths.
11.
Order from smallest to largest: $\frac{6}{7}$ , $\frac{6}{13}$ , $\frac{6}{9}$ , $\frac{6}{11}$
Answer: 6/13, 6/11, 6/9, 6/7
1. What is the common numerator? 6
2. Order the denominators from largest to smallest. Which denominator comes second? 11
3. Which fraction is smallest (largest denominator)? 6/13
4. Which fraction is largest (smallest denominator)? 6/7
5. In the order from smallest to largest, which fraction comes second? 6/11
12.
Which whole number goes in the box? $\frac{4}{9} < \frac{4}{\square} < \frac{4}{7}$
Answer: 8
The answer is $8$ . Since $9 > 8 > 7$ , we get $\frac{4}{9} < \frac{4}{8} < \frac{4}{7}$ : eighths are bigger than ninths but smaller than sevenths.
13.
Compare the improper fractions: $\frac{8}{3}$ and $\frac{8}{5}$ . 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
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) $\frac{5}{6}, \frac{5}{10}, \frac{5}{8}, \frac{5}{12}$
2. b) $\frac{5}{12}, \frac{5}{10}, \frac{5}{8}, \frac{5}{6}$
3. c) $\frac{5}{8}, \frac{5}{6}, \frac{5}{12}, \frac{5}{10}$
4. d) $\frac{5}{6}, \frac{5}{8}, \frac{5}{10}, \frac{5}{12}$
Answer: $\frac{5}{6}, \frac{5}{8}, \frac{5}{10}, \frac{5}{12}$
Correct order: $\frac{5}{6}, \frac{5}{8}, \frac{5}{10}, \frac{5}{12}$ . Denominators from smallest to largest (6, 8, 10, 12) give fractions from largest to smallest.
15.
Emma ate $\frac{2}{5}$ of a pie. Jake ate $\frac{2}{3}$ 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
4. Which denominator is smaller: 5 or 3? 3
5. Who ate the larger fraction (Emma or Jake)? Jake