7th Grade Math · Unit 2
Compare and order integers, fractions, mixed numbers, decimals, and percents.
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Same number, different form
12 = 0.5 = 50%.
Change the numbers into one form before you compare them. Decimals to the thousandths place work well.
Benchmarks
Use 0, 12, and 1 as landmarks.
0.4 is less than 12 because 12 = 0.5.
A positive number is greater than 0. A negative number is less than 0.
Number line
Farther right is greater. Farther left is smaller.
−3 is to the left of −1, so −3 < −1.
Symbols
< means less than. > means greater than. = means the same value.
For more than two numbers, write the chain in the order the problem asks: least to greatest, or greatest to least.
Compare two numbers. Use a benchmark, a number line, or an equivalent form.
The benchmark is 12 = 0.5.
0.3 is less than 0.5.
0.3 = 0.300 and 12 = 0.500.
0.3 < 12
Answer: 0.3 < 12
The benchmark is 12 = 0.5.
0.4 is less than 0.5, so 0.4 is less than 12.
0.4 = 0.400 and 12 = 0.500.
0.4 < 12
Answer: 0.4 < 12
50% = 50100 = 0.50.
12 = 0.50.
The decimals match, so the numbers are equal.
50% = 12
Answer: 50% = 12
● Teal: −3 ● Blue: −1
−3 is farther left than −1.
Both are negative. The one farther from 0 is smaller.
−3 < −1
Answer: −3 < −1
14 = 0.25.
0.25 = 0.250 and 14 = 0.250.
0.25 = 14
Answer: 0.25 = 14
1.9 is less than the benchmark 2.
2 = 2.000 and 1.9 = 1.900.
2 > 1.9
Answer: 2 > 1.9
−0.5 = −0.500.
−12 = −0.500.
−0.5 = −12
Answer: −0.5 = −12
75% = 75100 = 0.750.
0.8 = 0.800.
0.750 is less than 0.800.
75% < 0.8
Answer: 75% < 0.8
112 = 1 + 12 = 1.500.
1.5 = 1.500.
112 = 1.5
Answer: 112 = 1.5
34 is a proper fraction, so it is less than 1.
34 = 0.750 and 1 = 1.000.
34 < 1
Answer: 34 < 1
● Teal: −2 ● Blue: −2.5
−2.5 is farther left than −2.
−2 = −2.000 and −2.5 = −2.500.
−2 > −2.5
Answer: −2 > −2.5
Order three numbers.
How to convert each number to a decimal:
0.5 is already a decimal.
Add zeros to the thousandths place.
0.5 = 0.500
40% means 40 out of 100.
40% = 40100
40 ÷ 100 = 0.4
Add zeros to the thousandths place.
0.4 = 0.400
12 means 1 ÷ 2.
1 ÷ 2 = 0.5
Add zeros to the thousandths place.
0.5 = 0.500
Least to greatest:
40% < 0.5 = 12
Answer: 40% < 0.5 = 12
How to convert each number to a decimal:
0.2 is already a decimal.
Add zeros to the thousandths place.
0.2 = 0.200
14 means 1 ÷ 4.
1 ÷ 4 = 0.25
Add zeros to the thousandths place.
0.25 = 0.250
30% means 30 out of 100.
30% = 30100
30 ÷ 100 = 0.3
Add zeros to the thousandths place.
0.3 = 0.300
Least to greatest:
0.2 < 14 < 30%
Answer: 0.2 < 14 < 30%
How to convert each number to a decimal:
−1 is a whole number.
Write zeros in the tenths, hundredths, and thousandths places.
−1 = −1.000
−0.5 is already a decimal.
Add zeros to the thousandths place.
−0.5 = −0.500
−1.5 is already a decimal.
Add zeros to the thousandths place.
−1.5 = −1.500
● Teal: −1 ● Blue: −0.5 ● Amber: −1.5
Farther left is smaller. Farther right is greater.
A negative number is less than a positive number. Between two negatives, the one farther from 0 is smaller.
Least to greatest:
−1.5 < −1 < −0.5
Answer: −1.5 < −1 < −0.5
How to convert each number to a decimal:
0.75 is already a decimal.
Add zeros to the thousandths place.
0.75 = 0.750
45 means 4 ÷ 5.
4 ÷ 5 = 0.8
Add zeros to the thousandths place.
0.8 = 0.800
70% means 70 out of 100.
70% = 70100
70 ÷ 100 = 0.7
Add zeros to the thousandths place.
0.7 = 0.700
Greatest to least:
45 > 0.75 > 70%
Answer: 45 > 0.75 > 70%
How to convert each number to a decimal:
1.25 is already a decimal.
Add zeros to the thousandths place.
1.25 = 1.250
115 = 1 + 15
1 ÷ 5 = 0.2
1 + 0.2 = 1.2
Add zeros to the thousandths place.
1.2 = 1.200
130% means 130 out of 100.
130% = 130100
130 ÷ 100 = 1.3
Add zeros to the thousandths place.
1.3 = 1.300
Least to greatest:
115 < 1.25 < 130%
Answer: 115 < 1.25 < 130%
How to convert each number to a decimal:
−0.4 is already a decimal.
Add zeros to the thousandths place.
−0.4 = −0.400
0.1 is already a decimal.
Add zeros to the thousandths place.
0.1 = 0.100
−0.1 is already a decimal.
Add zeros to the thousandths place.
−0.1 = −0.100
● Teal: −0.4 ● Blue: 0.1 ● Amber: −0.1
Farther left is smaller. Farther right is greater.
A negative number is less than a positive number. Between two negatives, the one farther from 0 is smaller.
Least to greatest:
−0.4 < −0.1 < 0.1
Answer: −0.4 < −0.1 < 0.1
How to convert each number to a decimal:
−34 means −3 ÷ 4.
−3 ÷ 4 = −0.75
Add zeros to the thousandths place.
−0.75 = −0.750
0.2 is already a decimal.
Add zeros to the thousandths place.
0.2 = 0.200
−0.1 is already a decimal.
Add zeros to the thousandths place.
−0.1 = −0.100
Use 0 as a benchmark. Negative numbers are left of 0. Positive numbers are right of 0.
A negative number is less than a positive number. Between two negatives, the one farther from 0 is smaller.
Least to greatest:
−34 < −0.1 < 0.2
Answer: −34 < −0.1 < 0.2
How to convert each number to a decimal:
25 means 2 ÷ 5.
2 ÷ 5 = 0.4
Add zeros to the thousandths place.
0.4 = 0.400
0.4 is already a decimal.
Add zeros to the thousandths place.
0.4 = 0.400
45% means 45 out of 100.
45% = 45100
45 ÷ 100 = 0.45
Add zeros to the thousandths place.
0.45 = 0.450
Least to greatest:
25 = 0.4 < 45%
Answer: 25 = 0.4 < 45%
How to convert each number to a decimal:
−2.5 is already a decimal.
Add zeros to the thousandths place.
−2.5 = −2.500
−214 = −(2 + 14)
1 ÷ 4 = 0.25
−(2 + 0.25) = −2.25
Add zeros to the thousandths place.
−2.25 = −2.250
−2 is a whole number.
Write zeros in the tenths, hundredths, and thousandths places.
−2 = −2.000
● Teal: −2.5 ● Blue: −214 ● Amber: −2
Farther left is smaller. Farther right is greater.
A negative number is less than a positive number. Between two negatives, the one farther from 0 is smaller.
Least to greatest:
−2.5 < −214 < −2
Answer: −2.5 < −214 < −2
How to convert each number to a decimal:
1 is a whole number.
Write zeros in the tenths, hundredths, and thousandths places.
1 = 1.000
0.99 is already a decimal.
Add zeros to the thousandths place.
0.99 = 0.990
100% means 100 out of 100.
100% = 100100
100 ÷ 100 = 1
Add zeros to the thousandths place.
1 = 1.000
Greatest to least:
1 = 100% > 0.99
Answer: 1 = 100% > 0.99
How to convert each number to a decimal:
0.08 is already a decimal.
Add zeros to the thousandths place.
0.08 = 0.080
110 means 1 ÷ 10.
1 ÷ 10 = 0.1
Add zeros to the thousandths place.
0.1 = 0.100
9% means 9 out of 100.
9% = 9100
9 ÷ 100 = 0.09
Add zeros to the thousandths place.
0.09 = 0.090
Least to greatest:
0.08 < 9% < 110
Answer: 0.08 < 9% < 110
Order four numbers. Decimals go to the thousandths place.
How to convert each number to a decimal:
0.4 is already a decimal.
Add zeros to the thousandths place.
0.4 = 0.400
0.45 is already a decimal.
Add zeros to the thousandths place.
0.45 = 0.450
25 means 2 ÷ 5.
2 ÷ 5 = 0.4
Add zeros to the thousandths place.
0.4 = 0.400
41% means 41 out of 100.
41% = 41100
41 ÷ 100 = 0.41
Add zeros to the thousandths place.
0.41 = 0.410
Least to greatest:
0.4 = 25 < 41% < 0.45
Answer: 0.4 = 25 < 41% < 0.45
How to convert each number to a decimal:
−0.5 is already a decimal.
Add zeros to the thousandths place.
−0.5 = −0.500
−0.55 is already a decimal.
Add zeros to the thousandths place.
−0.55 = −0.550
−12 means −1 ÷ 2.
−1 ÷ 2 = −0.5
Add zeros to the thousandths place.
−0.5 = −0.500
−48% means −48 out of 100.
−48% = −48100
−48 ÷ 100 = −0.48
Add zeros to the thousandths place.
−0.48 = −0.480
A negative number is less than a positive number. Between two negatives, the one farther from 0 is smaller.
Least to greatest:
−0.55 < −0.5 = −12 < −48%
Answer: −0.55 < −0.5 = −12 < −48%
How to convert each number to a decimal:
0.125 is already a decimal.
It already shows the thousandths place.
18 means 1 ÷ 8.
1 ÷ 8 = 0.125
13% means 13 out of 100.
13% = 13100
13 ÷ 100 = 0.13
Add zeros to the thousandths place.
0.13 = 0.130
0.12 is already a decimal.
Add zeros to the thousandths place.
0.12 = 0.120
Least to greatest:
0.12 < 0.125 = 18 < 13%
Answer: 0.12 < 0.125 = 18 < 13%
How to convert each number to a decimal:
2.5 is already a decimal.
Add zeros to the thousandths place.
2.5 = 2.500
225 = 2 + 25
2 ÷ 5 = 0.4
2 + 0.4 = 2.4
Add zeros to the thousandths place.
2.4 = 2.400
251% means 251 out of 100.
251% = 251100
251 ÷ 100 = 2.51
Add zeros to the thousandths place.
2.51 = 2.510
2.45 is already a decimal.
Add zeros to the thousandths place.
2.45 = 2.450
● Teal: 2.5 ● Blue: 225 ● Amber: 251% ● Rose: 2.45
Farther left is smaller. Farther right is greater.
Greatest to least:
251% > 2.5 > 2.45 > 225
Answer: 251% > 2.5 > 2.45 > 225
How to convert each number to a decimal:
−1.2 is already a decimal.
Add zeros to the thousandths place.
−1.2 = −1.200
−114 = −(1 + 14)
1 ÷ 4 = 0.25
−(1 + 0.25) = −1.25
Add zeros to the thousandths place.
−1.25 = −1.250
−1.25 is already a decimal.
Add zeros to the thousandths place.
−1.25 = −1.250
−1.205 is already a decimal.
It already shows the thousandths place.
A negative number is less than a positive number. Between two negatives, the one farther from 0 is smaller.
Least to greatest:
−114 = −1.25 < −1.205 < −1.2
Answer: −114 = −1.25 < −1.205 < −1.2
How to convert each number to a decimal:
−0.001 is already a decimal.
It already shows the thousandths place.
0 is a whole number.
Write zeros in the tenths, hundredths, and thousandths places.
0 = 0.000
0.001 is already a decimal.
It already shows the thousandths place.
−0.01 is already a decimal.
Add zeros to the thousandths place.
−0.01 = −0.010
● Teal: −0.001 ● Blue: 0 ● Amber: 0.001 ● Rose: −0.01
Farther left is smaller. Farther right is greater.
A negative number is less than a positive number. Between two negatives, the one farther from 0 is smaller.
Least to greatest:
−0.01 < −0.001 < 0 < 0.001
Answer: −0.01 < −0.001 < 0 < 0.001
How to convert each number to a decimal:
35 means 3 ÷ 5.
3 ÷ 5 = 0.6
Add zeros to the thousandths place.
0.6 = 0.600
0.6 is already a decimal.
Add zeros to the thousandths place.
0.6 = 0.600
62% means 62 out of 100.
62% = 62100
62 ÷ 100 = 0.62
Add zeros to the thousandths place.
0.62 = 0.620
0.599 is already a decimal.
It already shows the thousandths place.
Least to greatest:
0.599 < 35 = 0.6 < 62%
Answer: 0.599 < 35 = 0.6 < 62%
How to convert each number to a decimal:
−34 means −3 ÷ 4.
−3 ÷ 4 = −0.75
Add zeros to the thousandths place.
−0.75 = −0.750
−0.7 is already a decimal.
Add zeros to the thousandths place.
−0.7 = −0.700
−80% means −80 out of 100.
−80% = −80100
−80 ÷ 100 = −0.8
Add zeros to the thousandths place.
−0.8 = −0.800
−0.75 is already a decimal.
Add zeros to the thousandths place.
−0.75 = −0.750
Use 0 and −34 as benchmarks. −0.75 should match that fraction if they are equal.
A negative number is less than a positive number. Between two negatives, the one farther from 0 is smaller.
Greatest to least:
−0.7 > −34 = −0.75 > −80%
Answer: −0.7 > −34 = −0.75 > −80%
How to convert each number to a decimal:
1.005 is already a decimal.
It already shows the thousandths place.
1 is a whole number.
Write zeros in the tenths, hundredths, and thousandths places.
1 = 1.000
101% means 101 out of 100.
101% = 101100
101 ÷ 100 = 1.01
Add zeros to the thousandths place.
1.01 = 1.010
11100 = 1 + 1100
1 ÷ 100 = 0.01
1 + 0.01 = 1.01
Add zeros to the thousandths place.
1.01 = 1.010
Least to greatest:
1 < 1.005 < 101% = 11100
Answer: 1 < 1.005 < 101% = 11100
How to convert each number to a decimal:
−2 is a whole number.
Write zeros in the tenths, hundredths, and thousandths places.
−2 = −2.000
−1.999 is already a decimal.
It already shows the thousandths place.
−200% means −200 out of 100.
−200% = −200100
−200 ÷ 100 = −2
Add zeros to the thousandths place.
−2 = −2.000
−1910 = −(1 + 910)
9 ÷ 10 = 0.9
−(1 + 0.9) = −1.9
Add zeros to the thousandths place.
−1.9 = −1.900
A negative number is less than a positive number. Between two negatives, the one farther from 0 is smaller.
Least to greatest:
−2 = −200% < −1.999 < −1910
Answer: −2 = −200% < −1.999 < −1910
How to convert each number to a decimal:
0.875 is already a decimal.
It already shows the thousandths place.
78 means 7 ÷ 8.
7 ÷ 8 = 0.875
88% means 88 out of 100.
88% = 88100
88 ÷ 100 = 0.88
Add zeros to the thousandths place.
0.88 = 0.880
0.87 is already a decimal.
Add zeros to the thousandths place.
0.87 = 0.870
● Teal: 0.875 ● Blue: 78 ● Amber: 88% ● Rose: 0.87
Farther left is smaller. Farther right is greater.
Equal numbers land on the same point.
Greatest to least:
88% > 0.875 = 78 > 0.87
Answer: 88% > 0.875 = 78 > 0.87
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