7th Grade Math · Unit 2
Add and subtract integers, decimals, and mixed forms.
Integers
Same signs: add the distances from 0 and keep the sign.
Different signs: subtract the distances and keep the sign of the number farther from 0.
Subtract the opposite
Subtracting a number is the same as adding its opposite.
4 − (−3) = 4 + 3.
Decimals
Line up the decimal points. Use the same sign rules as for integers.
Decimals here stop at the thousandths place.
Mixed forms
Write decimals and mixed numbers as fractions, then add.
Simplify the fraction at the end.
Two integers. Watch the signs.
Add the signed numbers from left to right.
−8 + 5
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
8 − 5 = 3
−8 is farther from 0, so the sum is negative.
−8 + 5 = −3
Answer: −3
Subtracting a number is the same as adding its opposite.
−7 − 4 = −7 + (−4)
The signs match. Add the distances from 0 and keep the sign.
7 + 4 = 11
−7 + (−4) = −11
Answer: −11
Add the signed numbers from left to right.
6 + (−9)
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
9 − 6 = 3
−9 is farther from 0, so the sum is negative.
6 + (−9) = −3
Answer: −3
Add the signed numbers from left to right.
−12 + 12
The signs are different, and the distances from 0 match.
−12 + 12 = 0
Answer: 0
Subtracting a number is the same as adding its opposite.
4 − (−3) = 4 + 3
The signs match. Add the distances from 0 and keep the sign.
4 + 3 = 7
4 + 3 = 7
Answer: 7
Add the signed numbers from left to right.
−15 + 8
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
15 − 8 = 7
−15 is farther from 0, so the sum is negative.
−15 + 8 = −7
Answer: −7
Subtracting a number is the same as adding its opposite.
9 − 14 = 9 + (−14)
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
14 − 9 = 5
−14 is farther from 0, so the sum is negative.
9 + (−14) = −5
Answer: −5
Add the signed numbers from left to right.
−2 + (−6)
The signs match. Add the distances from 0 and keep the sign.
2 + 6 = 8
−2 + (−6) = −8
Answer: −8
Subtracting a number is the same as adding its opposite.
−20 − (−5) = −20 + 5
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
20 − 5 = 15
−20 is farther from 0, so the sum is negative.
−20 + 5 = −15
Answer: −15
Add the signed numbers from left to right.
−6 + 10
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
10 − 6 = 4
10 is farther from 0, so the sum is positive.
−6 + 10 = 4
Answer: 4
Add the signed numbers from left to right.
18 + (−25)
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
25 − 18 = 7
−25 is farther from 0, so the sum is negative.
18 + (−25) = −7
Answer: −7
Decimals through thousandths.
Add the signed decimals from left to right.
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
3.4 − 1.2 = 2.2
−3.4 is farther from 0, so the sum is negative.
−3.4 + 1.2 = −2.2
Answer: −2.2
Add the signed decimals from left to right.
The signs match. Add the distances from 0 and keep the sign.
1.25 + 0.4 = 1.65
−1.25 + (−0.4) = −1.65
Answer: −1.65
Subtracting a number is the same as adding its opposite.
2.5 − 3.75 = 2.5 + (−3.75)
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
3.75 − 2.5 = 1.25
−3.75 is farther from 0, so the sum is negative.
2.5 + (−3.75) = −1.25
Answer: −1.25
Add the signed decimals from left to right.
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
0.2 − 0.08 = 0.12
0.2 is farther from 0, so the sum is positive.
−0.08 + 0.2 = 0.12
Answer: 0.12
Subtracting a number is the same as adding its opposite.
4.05 − 6.5 = 4.05 + (−6.5)
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
6.5 − 4.05 = 2.45
−6.5 is farther from 0, so the sum is negative.
4.05 + (−6.5) = −2.45
Answer: −2.45
Subtracting a number is the same as adding its opposite.
−2.4 − 1.05 = −2.4 + (−1.05)
The signs match. Add the distances from 0 and keep the sign.
2.4 + 1.05 = 3.45
−2.4 + (−1.05) = −3.45
Answer: −3.45
Add the signed decimals from left to right.
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
0.6 − 0.45 = 0.15
0.6 is farther from 0, so the sum is positive.
0.6 + (−0.45) = 0.15
Answer: 0.15
Add the signed decimals from left to right.
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
7.2 − 3.15 = 4.05
−7.2 is farther from 0, so the sum is negative.
−7.2 + 3.15 = −4.05
Answer: −4.05
Subtracting a number is the same as adding its opposite.
8.5 − (−1.2) = 8.5 + 1.2
The signs match. Add the distances from 0 and keep the sign.
8.5 + 1.2 = 9.7
8.5 + 1.2 = 9.7
Answer: 9.7
Add the signed decimals from left to right.
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
0.2 − 0.075 = 0.125
0.2 is farther from 0, so the sum is positive.
−0.075 + 0.2 = 0.125
Answer: 0.125
Add the signed decimals from left to right.
The signs are different. Subtract the distances from 0. Keep the sign of the number farther from 0.
12.5 − 9.25 = 3.25
−12.5 is farther from 0, so the sum is negative.
−12.5 + 9.25 = −3.25
Answer: −3.25
A decimal, a fraction, or a mixed number in the same problem.
Add the signed fractions.
−3 + 12
The common denominator is 2.
−3 = −62
Add the numerators. Keep the denominator.
−6 + 1 = −5
= −52
= −212
Answer: −52, which is −212
Write the mixed number as an improper fraction.
212 = 52
Write the decimal as a fraction.
0.75 = 75100
Divide the numerator and the denominator by 25.
= 34
Subtracting a number is the same as adding its opposite.
52 − 34 = 52 + (−34)
The common denominator is 4.
52 = 104
Add the numerators. Keep the denominator.
10 + (−3) = 7
= 74
= 134
Answer: 74, which is 134
Write the decimal as a fraction.
−0.3 = −310
Add the signed fractions.
12 + (−310)
The common denominator is 10.
12 = 510
Add the numerators. Keep the denominator.
5 + (−3) = 2
= 210
Divide the numerator and the denominator by 2.
= 15
Answer: 15
Write the decimal as a fraction.
−1.2 = −1210
Divide the numerator and the denominator by 2.
= −65
Add the signed fractions.
−65 + 34
The common denominator is 20.
−65 = −2420
34 = 1520
Add the numerators. Keep the denominator.
−24 + 15 = −9
= −920
Answer: −920
Write the mixed number as an improper fraction.
−214 = −94
Write the decimal as a fraction.
1.5 = 1510
Divide the numerator and the denominator by 5.
= 32
Add the signed fractions.
−94 + 32
The common denominator is 4.
32 = 64
Add the numerators. Keep the denominator.
−9 + 6 = −3
= −34
Answer: −34
Write the decimal as a fraction.
0.4 = 410
Divide the numerator and the denominator by 2.
= 25
Subtracting a number is the same as adding its opposite.
25 − 35 = 25 + (−35)
The denominators already match.
Add the numerators. Keep the denominator.
2 + (−3) = −1
= −15
Answer: −15
Write the decimal as a fraction.
−0.125 = −1251000
Divide the numerator and the denominator by 125.
= −18
Write the mixed number as an improper fraction.
(−18) = −18
Add the signed fractions.
−18 + (−18)
The denominators already match.
Add the numerators. Keep the denominator.
−1 + (−1) = −2
= −28
Divide the numerator and the denominator by 2.
= −14
Answer: −14
Write the mixed number as an improper fraction.
115 = 65
Write the decimal as a fraction.
0.5 = 510
Divide the numerator and the denominator by 5.
= 12
Subtracting a number is the same as adding its opposite.
65 − 12 = 65 + (−12)
The common denominator is 10.
65 = 1210
−12 = −510
Add the numerators. Keep the denominator.
12 + (−5) = 7
= 710
Answer: 710
Write the decimal as a fraction.
0.2 = 210
Divide the numerator and the denominator by 2.
= 15
Subtracting a number is the same as adding its opposite.
−34 − 15 = −34 + (−15)
The common denominator is 20.
−34 = −1520
−15 = −420
Add the numerators. Keep the denominator.
−15 + (−4) = −19
= −1920
Answer: −1920
Write the decimal as a fraction.
2.25 = 225100
Divide the numerator and the denominator by 25.
= 94
Write the mixed number as an improper fraction.
−112 = −32
Add the signed fractions.
94 + (−32)
The common denominator is 4.
−32 = −64
Add the numerators. Keep the denominator.
9 + (−6) = 3
= 34
Answer: 34
Write the decimal as a fraction.
−0.6 = −610
Divide the numerator and the denominator by 2.
= −35
Add the signed fractions.
−35 + 23
The common denominator is 15.
−35 = −915
23 = 1015
Add the numerators. Keep the denominator.
−9 + 10 = 1
= 115
Answer: 115
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