Comparing Fractions with the Same Denominator

Show your work for each problem.

1.
Which fraction is larger: or ?
1. a)
2. b)They are equal
3. c)
4. d)Cannot compare
Answer:
because both have the same denominator, and . More pieces of the same size means a larger fraction.
2.
Which symbol goes in the blank? ___
1. a)
2. b)None of these
3. c)
4. d)
Answer:
because . When denominators are equal, the fraction with the smaller numerator is smaller.
3.
Compare: Is greater than, less than, or equal to ? Type: greater, less, or equal
Answer: greater
because . Six ninths is more than four ninths.
4.
What is the numerator of the larger fraction? or
Answer: 7
is larger because . The numerator of the larger fraction is 7.
5.
Sarah ate of a pie and Tom ate . Who ate more?
1. a)Tom
2. b)Sarah
3. c)Cannot determine
4. d)They ate the same amount
Answer: Tom
Tom ate more because . Since and the denominators are equal, Tom's portion is larger.
6.
Order from least to greatest: , , ,
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 a fraction between and . Write your answer as a fraction (e.g., 4/8).
Answer: 4/8
Possible answers include or . Any fraction with denominator 8 and numerator between 3 and 6 works: and .
8.
Which fraction is the smallest? , , ,
1. a)
2. b)
3. c)
4. d)
Answer:
is the smallest because 4 is the smallest numerator among 9, 4, 7, and 11.
9.
A chocolate bar has 8 pieces. Maya ate , Leo ate , and Zoe ate . Who ate the most? Order them from least to greatest.
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 but less than ?
Answer: 2
Numerators between 2 and 5 are 3 and 4. So there are 2 fractions: and .
11.
A race track is divided into 10 equal sections. Anna completed of the track and Ben completed . 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 and is a whole number less than 9, how many possible values can have?
Answer: 3
For , we need . Since must be less than 9, the possible values are 6, 7, and 8. That's 3 values.
13.
A water tank is full. Water is added until it becomes 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)
2. b)
3. c)
4. d)
Answer:
Since , we have . This is the correct ordering from greatest to least.
15.
Three students are reading the same book. After one week: Amy read , Ben read , and Cara read . 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