Comparing Fractions with the Same Denominator

Show your work for each problem.

1.
Which fraction is larger: $\frac{3}{5}$ or $\frac{4}{5}$ ?
1. a) $\frac{4}{5}$
2. b)They are equal
3. c) $\frac{3}{5}$
4. d)Cannot compare
Answer: $\frac{4}{5}$
$\frac{4}{5} > \frac{3}{5}$ because both have the same denominator, and $4 > 3$ . More pieces of the same size means a larger fraction.
2.
Which symbol goes in the blank? $\frac{2}{7}$ ___ $\frac{5}{7}$
1. a) $<$
2. b)None of these
3. c) $=$
4. d) $>$
Answer: $<$
$\frac{2}{7} < \frac{5}{7}$ because $2 < 5$ . When denominators are equal, the fraction with the smaller numerator is smaller.
3.
Is $\frac{6}{9}$ greater than, less than, or equal to $\frac{4}{9}$ ?
1. a)greater than
2. b)less than
3. c)equal to
4. d)You cannot tell
Answer: greater than
$\frac{6}{9} > \frac{4}{9}$ because $6 > 4$ . Six ninths is more than four ninths.
4.
What is the numerator of the larger fraction? $\frac{3}{8}$ or $\frac{7}{8}$
Answer: 7
$\frac{7}{8}$ is larger because $7 > 3$ . The numerator of the larger fraction is 7.
5.
Sarah and Tom each have a pie of the same size, cut into 6 equal slices. Sarah ate $\frac{2}{6}$ of her pie and Tom ate $\frac{5}{6}$ of his. Who ate more?
1. a)Sarah
2. b)They ate the same amount
3. c)Cannot determine
4. d)Tom
Answer: Tom
Tom ate more because $\frac{5}{6} > \frac{2}{6}$ . Since $5 > 2$ and the denominators are equal, Tom's portion is larger.
6.
Order from least to greatest: $\frac{5}{10}$ , $\frac{2}{10}$ , $\frac{8}{10}$ , $\frac{1}{10}$
Answer: 1/10, 2/10, 5/10, 8/10
1. What is the smallest numerator? 1
2. What is the next smallest numerator? 2
3. What comes next? 5
4. What is the largest numerator? 8
7.
Find the fraction with denominator 8 that lies between $\frac{3}{8}$ and $\frac{5}{8}$ . Write it as a fraction (e.g., 1/8).
Answer: 4/8
The only numerator between 3 and 5 is 4, so the answer is $\frac{4}{8}$ : $\frac{3}{8} < \frac{4}{8} < \frac{5}{8}$ .
8.
Which fraction is the smallest? $\frac{9}{12}$ , $\frac{4}{12}$ , $\frac{7}{12}$ , $\frac{11}{12}$
1. a) $\frac{7}{12}$
2. b) $\frac{4}{12}$
3. c) $\frac{11}{12}$
4. d) $\frac{9}{12}$
Answer: $\frac{4}{12}$
$\frac{4}{12}$ is the smallest because 4 is the smallest numerator among 9, 4, 7, and 11.
9.
Maya, Leo and Zoe each have the same chocolate bar with 8 equal pieces. Maya ate $\frac{3}{8}$ of her bar, Leo ate $\frac{5}{8}$ and Zoe ate $\frac{2}{8}$ . Order them from who ate the least to who ate the most.
Answer: Zoe, Maya, Leo
1. Who has the smallest numerator? Zoe
2. Who has the next smallest numerator? Maya
3. Who ate the most (largest numerator)? Leo
10.
How many fractions with denominator 6 are greater than $\frac{2}{6}$ but less than $\frac{5}{6}$ ?
Answer: 2
Numerators between 2 and 5 are 3 and 4. So there are 2 fractions: $\frac{3}{6}$ and $\frac{4}{6}$ .
11.
A race track is divided into 10 equal sections. Anna completed $\frac{7}{10}$ of the track and Ben completed $\frac{9}{10}$ . Who is closer to finishing?
Answer: Ben
1. What fraction did Anna complete? 7/10
2. What fraction did Ben complete? 9/10
3. Which numerator is larger: 7 or 9? 9
4. Who completed more and is closer to finishing? Ben
12.
If $\frac{x}{9} > \frac{5}{9}$ and $x$ is a whole number less than 9, how many possible values can $x$ have?
Answer: 3
For $\frac{x}{9} > \frac{5}{9}$ , we need $x > 5$ . Since $x$ must be less than 9, the possible values are 6, 7, and 8. That's 3 values.
13.
A water tank is $\frac{11}{15}$ full. Water is added until it becomes $\frac{14}{15}$ full. What fraction of the tank was added?
Answer: 3/15
1. What fraction was the tank initially? 11/15
2. What fraction is the tank after adding water? 14/15
3. What is the difference? Subtract: 14 - 11 = ? 3
4. What is the fraction added (with denominator 15)? 3/15
14.
Which statement is TRUE?
1. a) $\frac{3}{11} > \frac{6}{11} > \frac{8}{11}$
2. b) $\frac{8}{11} > \frac{6}{11} > \frac{3}{11}$
3. c) $\frac{6}{11} > \frac{8}{11} > \frac{3}{11}$
4. d) $\frac{8}{11} > \frac{3}{11} > \frac{6}{11}$
Answer: $\frac{8}{11} > \frac{6}{11} > \frac{3}{11}$
Since $8 > 6 > 3$ , we have $\frac{8}{11} > \frac{6}{11} > \frac{3}{11}$ . This is the correct ordering from greatest to least.
15.
Three students are reading the same book. After one week: Amy read $\frac{5}{12}$ , Ben read $\frac{8}{12}$ , and Cara read $\frac{3}{12}$ . How much more of the book has Ben read compared to Cara?
Answer: 5/12
1. How much did Ben read? 8/12
2. How much did Cara read? 3/12
3. To find how much more, subtract: 8 - 3 = ? 5
4. What is the difference as a fraction? 5/12