Comparing Mixed Numbers

Show your work for each problem.

1.
Which symbol correctly compares and ?
1. a)
2. b)
3. c)Cannot be determined
4. d)
Answer:
because 5 whole units is more than 4 whole units. The fractional parts don't matter when the whole parts are different.
2.
Which mixed number is smaller: or ?
1. a)
2. b)
3. c)They are equal
4. d)Cannot compare
Answer:
is smaller because the whole parts are equal, so we compare fractions: (a quarter is less than a half).
3.
Compare and . Enter , , or to complete: ___
Answer: <
because . Even though , the whole number part determines the comparison when they differ.
4.
Which is greater: or ? Enter the greater number.
Answer: 4 2/3
is greater because the whole parts are equal (4), and .
5.
Which is greater: or ?
1. a)They are equal
2. b)
3. c)
4. d)Cannot compare
Answer:
because , and .
6.
Compare and . Enter , , or .
Answer: <
because and .
7.
Which is smaller: or ?
1. a)
2. b)
3. c)Cannot determine
4. d)They are equal
Answer:
is smaller because , and .
8.
Compare and using common denominators.
Answer: <
1. What are the whole parts of both numbers? 2
2. What is the LCD of 3 and 8? 24
3. Convert to 24ths: 8/24
4. Convert to 24ths: 9/24
5. Which is greater: or ? 9/24
9.
Convert to an improper fraction.
Answer: 17/5
1. What is the whole number part? 3
2. What is the denominator? 5
3. Multiply: ? 15
4. Add the numerator: ? 17
5. Write as improper fraction (keep same denominator): 17/5
10.
A recipe needs cups of flour. You have cups. Do you have enough? Enter yes or no.
Answer: no
No, you don't have enough. because and , and .
11.
Order from least to greatest: , ,
Answer: 2 1/4, 2 1/3, 2 2/6
1. Are the whole parts all equal? yes
2. Simplify : 1/3
3. What is the LCD of 4, 3, and 3? 12
4. Convert to 12ths: 3/12
5. Convert to 12ths: 4/12
6. Which is smallest: or ? 3/12
12.
Which list shows the mixed numbers in order from greatest to least?
1. a), ,
2. b), ,
3. c), ,
4. d), ,
Answer: , ,
Converting to 12ths: , , . From greatest to least: , so , , .
13.
Compare and by converting to improper fractions.
Answer: >
1. Convert to improper fraction: 15/8
2. Convert to improper fraction: 11/6
3. What is the LCD of 8 and 6? 24
4. Convert to 24ths: 45/24
5. Convert to 24ths: 44/24
6. Which is greater: or ? 45/24
14.
Runner A finished in minutes. Runner B finished in minutes. Who was faster? Enter A or B.
Answer: A
Runner A was faster. and . Since , we have . Less time = faster!
15.
Order these four mixed numbers from least to greatest: , , ,
Answer: 5 5/12, 5 1/2, 5 2/3, 5 3/4
1. Are all whole parts equal? yes
2. What is the LCD of 2, 3, 4, and 12? 12
3. Convert to 12ths: 6/12
4. Convert to 12ths: 8/12
5. Convert to 12ths: 9/12
6. Order the numerators from smallest to largest: 5, 6, 8, 9 5, 6, 8, 9
16.
Is greater than, less than, or equal to ?
1. a)Less than ()
2. b)Greater than ()
3. c)Equal to ()
4. d)Cannot compare
Answer: Less than ()
because 6 is the same as , and . Adding any positive fraction makes the number larger.