7th Grade Math · Unit 2
Decide when two products or quotients name the same number.
The sign can move
−4 × 6 and 4 × (−6) are the same product.
Both equal −24.
Two negatives
(−7) × (−4) is positive.
It matches 7 × 4, not the negative of that product.
Division
−18 ÷ 6 and 18 ÷ (−6) are the same quotient.
−18 ÷ (−6) is the opposite kind of quotient.
A sign in front
A negative sign in front of a product or quotient flips the value.
−(−5 × 6) = 5 × 6.
Move the sign in a product.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
(−6) × 4 = −24
6 × (−4) = −24
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −24.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
(−4) × 6 = −24
4 × (−6) = −24
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −24.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
(−3) × (−5) = 15
−(3 × 5) = −15
The values do not match, so the expressions are not equivalent.
Answer: No. 15 and −15.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
(−8) × 2 = −16
8 × (−2) = −16
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −16.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
(−7) × (−4) = 28
7 × 4 = 28
The values match, so the expressions are equivalent.
Answer: Yes. Both equal 28.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
−(9 × 3) = −27
9 × (−3) = −27
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −27.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
(−5) × 5 = −25
−(5 × 5) = −25
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −25.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
10 × (−3) = −30
(−10) × 3 = −30
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −30.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
(−1) × 14 = −14
(−14) = −14
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −14.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
(−6) × (−2) = 12
(−6) × 2 = −12
The values do not match, so the expressions are not equivalent.
Answer: No. 12 and −12.
Compute each expression. Same signs give a positive product. Different signs give a negative product.
(−2) × 9 = −18
−(2 × 9) = −18
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −18.
Move the sign in a quotient.
A negative divided by a negative is positive. Different signs give a negative quotient.
(−12) ÷ 3 = −4
12 ÷ (−3) = −4
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −4.
A negative divided by a negative is positive. Different signs give a negative quotient.
(−18) ÷ 6 = −3
18 ÷ (−6) = −3
−(18 ÷ 6) = −3
The values match, so the expressions are equivalent.
Answer: Yes. Each equals −3.
A negative divided by a negative is positive. Different signs give a negative quotient.
(−24) ÷ (−6) = 4
24 ÷ 6 = 4
The values match, so the expressions are equivalent.
Answer: Yes. Both equal 4.
A negative divided by a negative is positive. Different signs give a negative quotient.
(−20) ÷ 4 = −5
20 ÷ 4 = 5
The values do not match, so the expressions are not equivalent.
Answer: No. −5 and 5.
Different signs give a negative quotient.
−32 ÷ 8 = −328 = 32−8
−328 = −4
Answer: −328 and 32−8
A negative divided by a negative is positive. Different signs give a negative quotient.
(−15) ÷ (−3) = 5
−(15 ÷ 3) = −5
The values do not match, so the expressions are not equivalent.
Answer: No. 5 and −5.
A positive divided by a negative is negative.
40 ÷ (−8) = −5
−40 ÷ 8 = −5
Answer: −5. An equivalent quotient is −40 ÷ 8.
A negative divided by a negative is positive. Different signs give a negative quotient.
−(27 ÷ 9) = −3
(−27) ÷ 9 = −3
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −3.
A negative divided by a positive is negative.
−16 ÷ 4 = −4
The values match.
Answer: Yes. Both equal −4.
Zero divided by a nonzero number is zero.
0 ÷ (−5) = 0
Answer: 0
A negative divided by a negative is positive. Different signs give a negative quotient.
(−45) ÷ 9 = −5
45 ÷ (−9) = −5
The values match, so the expressions are equivalent.
Answer: Yes. Both equal −5.
A sign in front, or multiply and divide from left to right.
−4 × 7 = −28
−(−28) = 28
Answer: 28
A negative sign in front flips the value inside.
−5 × 6 = −30
−(−30) = 30
Answer: 30
8 × (−3) = −24
−(−24) = 24
Answer: 24
Multiply and divide from left to right.
(−12) ÷ 4 = −3
−3 × (−2) = 6
Answer: 6
(−2) × (−7) = 14
−(14) = −14
Answer: −14
Multiply and divide from left to right.
−4 × (−9) = 36
36 ÷ 6 = 6
Answer: 6
Divide from left to right.
(−20) ÷ 5 = −4
−4 ÷ (−2) = 2
Answer: 2
−6 × 4 = −24
−24 ÷ (−3) = 8
6 × 4 ÷ 3 = 8
The values match.
Answer: Yes. Both equal 8.
15 ÷ (−5) = −3
−(−3) = 3
Answer: 3
Multiply and divide from left to right.
(−48) ÷ (−6) = 8
8 × (−1) = −8
Answer: −8
Multiply and divide from left to right.
−2 × (−8) = 16
16 ÷ (−4) = −4
Answer: −4
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