7th Grade Math · Unit 2
Add and subtract fractions, including negatives, and simplify the result.
Same denominator
Add the numerators. Keep the denominator.
−38 + (−18) = −12 = −12.
Subtract by adding the opposite
Subtracting a number is the same as adding its opposite.
56 − (−16) = 56 + 16.
Unlike denominators
Rewrite both fractions with a common denominator before you add.
12 = 12 and 13 = 13.
Simplify
Divide the numerator and the denominator by the same whole number when you can.
If the absolute value is greater than 1, you can also write a mixed number.
The denominators already match.
Add the signed fractions.
−38 + (−18)
The denominators already match.
Add the numerators. Keep the denominator.
−3 + (−1) = −4
= −48
Divide the numerator and the denominator by 4.
= −12
Answer: −12
Add the signed fractions.
−25 + (−15)
The denominators already match.
Add the numerators. Keep the denominator.
−2 + (−1) = −3
= −35
Answer: −35
Subtracting a number is the same as adding its opposite.
56 − 76 = 56 + (−76)
The denominators already match.
Add the numerators. Keep the denominator.
5 + (−7) = −2
= −26
Divide the numerator and the denominator by 2.
= −13
Answer: −13
Subtracting a number is the same as adding its opposite.
−49 − 29 = −49 + (−29)
The denominators already match.
Add the numerators. Keep the denominator.
−4 + (−2) = −6
= −69
Divide the numerator and the denominator by 3.
= −23
Answer: −23
Add the signed fractions.
310 + (−710)
The denominators already match.
Add the numerators. Keep the denominator.
3 + (−7) = −4
= −410
Divide the numerator and the denominator by 2.
= −25
Answer: −25
Add the signed fractions.
−14 + 34
The denominators already match.
Add the numerators. Keep the denominator.
−1 + 3 = 2
= 24
Divide the numerator and the denominator by 2.
= 12
Answer: 12
Subtracting a number is the same as adding its opposite.
78 − (−18) = 78 + 18
The denominators already match.
Add the numerators. Keep the denominator.
7 + 1 = 8
= 88
Divide the numerator and the denominator by 8.
= 1
Answer: 1
Add the signed fractions.
−512 + (−112)
The denominators already match.
Add the numerators. Keep the denominator.
−5 + (−1) = −6
= −612
Divide the numerator and the denominator by 6.
= −12
Answer: −12
Subtracting a number is the same as adding its opposite.
27 − 57 = 27 + (−57)
The denominators already match.
Add the numerators. Keep the denominator.
2 + (−5) = −3
= −37
Answer: −37
Add the signed fractions.
−1112 + 512
The denominators already match.
Add the numerators. Keep the denominator.
−11 + 5 = −6
= −612
Divide the numerator and the denominator by 6.
= −12
Answer: −12
Subtracting a number is the same as adding its opposite.
415 − 35 = 415 + (−35)
The common denominator is 15.
−35 = −915
Add the numerators. Keep the denominator.
4 + (−9) = −5
= −515
Divide the numerator and the denominator by 5.
= −13
Answer: −13
Find a common denominator first.
Add the signed fractions.
12 + (−13)
The common denominator is 6.
12 = 36
−13 = −26
Add the numerators. Keep the denominator.
3 + (−2) = 1
= 16
Answer: 16
Add the signed fractions.
−12 + 15
The common denominator is 10.
−12 = −510
15 = 210
Add the numerators. Keep the denominator.
−5 + 2 = −3
= −310
Answer: −310
Subtracting a number is the same as adding its opposite.
34 − 16 = 34 + (−16)
The common denominator is 12.
34 = 912
−16 = −212
Add the numerators. Keep the denominator.
9 + (−2) = 7
= 712
Answer: 712
Add the signed fractions.
−23 + (−14)
The common denominator is 12.
−23 = −812
−14 = −312
Add the numerators. Keep the denominator.
−8 + (−3) = −11
= −1112
Answer: −1112
Add the signed fractions.
56 + (−12)
The common denominator is 6.
−12 = −36
Add the numerators. Keep the denominator.
5 + (−3) = 2
= 26
Divide the numerator and the denominator by 2.
= 13
Answer: 13
Subtracting a number is the same as adding its opposite.
−35 − 12 = −35 + (−12)
The common denominator is 10.
−35 = −610
−12 = −510
Add the numerators. Keep the denominator.
−6 + (−5) = −11
= −1110
= −1110
Answer: −1110, which is −1110
Subtracting a number is the same as adding its opposite.
29 − (−13) = 29 + 13
The common denominator is 9.
13 = 39
Add the numerators. Keep the denominator.
2 + 3 = 5
= 59
Answer: 59
Add the signed fractions.
−14 + 56
The common denominator is 12.
−14 = −312
56 = 1012
Add the numerators. Keep the denominator.
−3 + 10 = 7
= 712
Answer: 712
Subtracting a number is the same as adding its opposite.
710 − 45 = 710 + (−45)
The common denominator is 10.
−45 = −810
Add the numerators. Keep the denominator.
7 + (−8) = −1
= −110
Answer: −110
Add the signed fractions.
−58 + 12
The common denominator is 8.
12 = 48
Add the numerators. Keep the denominator.
−5 + 4 = −1
= −18
Answer: −18
Subtracting a number is the same as adding its opposite.
13 − 34 = 13 + (−34)
The common denominator is 12.
13 = 412
−34 = −912
Add the numerators. Keep the denominator.
4 + (−9) = −5
= −512
Answer: −512
Three fractions, or a mixed number.
Subtracting a number is the same as adding its opposite.
−12 + 34 − (−14) = −12 + 34 + 14
The common denominator is 4.
−12 = −24
Add the numerators. Keep the denominator.
−2 + 3 + 1 = 2
= 24
Divide the numerator and the denominator by 2.
= 12
Answer: 12
Subtracting a number is the same as adding its opposite.
23 − 16 − 12 = 23 + (−16) + (−12)
The common denominator is 6.
23 = 46
−12 = −36
Add the numerators. Keep the denominator.
4 + (−1) + (−3) = 0
= 0
Answer: 0
Subtracting a number is the same as adding its opposite.
−34 + 12 − 18 = −34 + 12 + (−18)
The common denominator is 8.
−34 = −68
12 = 48
Add the numerators. Keep the denominator.
−6 + 4 + (−1) = −3
= −38
Answer: −38
Subtracting a number is the same as adding its opposite.
56 − 13 − (−12) = 56 + (−13) + 12
The common denominator is 6.
−13 = −26
12 = 36
Add the numerators. Keep the denominator.
5 + (−2) + 3 = 6
= 66
Divide the numerator and the denominator by 6.
= 1
Answer: 1
Add the signed fractions.
310 + (−12) + 15
The common denominator is 10.
−12 = −510
15 = 210
Add the numerators. Keep the denominator.
3 + (−5) + 2 = 0
= 0
Answer: 0
Subtracting a number is the same as adding its opposite.
−78 + 14 − (−12) = −78 + 14 + 12
The common denominator is 8.
14 = 28
12 = 48
Add the numerators. Keep the denominator.
−7 + 2 + 4 = −1
= −18
Answer: −18
Write each mixed number as an improper fraction.
112 = 32
Add the signed fractions.
32 + (−34)
The common denominator is 4.
32 = 64
Add the numerators. Keep the denominator.
6 + (−3) = 3
= 34
Answer: 34
Write each mixed number as an improper fraction.
−213 = −73
Add the signed fractions.
−73 + 12
The common denominator is 6.
−73 = −146
12 = 36
Add the numerators. Keep the denominator.
−14 + 3 = −11
= −116
= −156
Answer: −116, which is −156
Write each mixed number as an improper fraction.
−114 = −54
Subtracting a number is the same as adding its opposite.
−54 − 38 = −54 + (−38)
The common denominator is 8.
−54 = −108
Add the numerators. Keep the denominator.
−10 + (−3) = −13
= −138
= −158
Answer: −138, which is −158
Write each mixed number as an improper fraction.
215 = 115
Subtracting a number is the same as adding its opposite.
115 − 34 = 115 + (−34)
The common denominator is 20.
115 = 4420
−34 = −1520
Add the numerators. Keep the denominator.
44 + (−15) = 29
= 2920
= 1920
Answer: 2920, which is 1920
Write each mixed number as an improper fraction.
123 = 53
Add the signed fractions.
53 + (−56)
The common denominator is 6.
53 = 106
Add the numerators. Keep the denominator.
10 + (−5) = 5
= 56
Answer: 56
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