7th Grade Math · Unit 2
Place the sign of a fraction, then multiply or divide and simplify.
Where the sign sits
The sign can sit on the numerator, on the denominator, or in front of the fraction.
Those three forms are equal.
Two negatives
A negative over a negative is positive.
−2−5 = 25.
Multiply
Multiply the numerators and multiply the denominators.
Then simplify. A negative times a negative is positive.
Divide
Dividing by a fraction is multiplying by its reciprocal.
Write a mixed number as an improper fraction first.
Move the sign, or simplify two negatives.
A negative fraction can show the sign on the numerator, on the denominator, or in front.
−25 = 2−5 = −(25)
All three name the same number.
Answer: 2−5 and −(25)
A negative fraction can show the sign on the numerator, on the denominator, or in front.
−35 = 3−5 = −(35)
All three name the same number.
Answer: 3−5 and −(35)
A negative fraction can show the sign on the numerator, on the denominator, or in front.
−47 = 4−7 = −(47)
All three name the same number.
Answer: 4−7 and −(47)
A negative fraction can show the sign on the numerator, on the denominator, or in front.
−14 = 1−4 = −(14)
All three name the same number.
Answer: 1−4 and −(14)
A negative fraction can show the sign on the numerator, on the denominator, or in front.
−611 = 6−11 = −(611)
All three name the same number.
Answer: 6−11 and −(611)
A negative fraction can show the sign on the numerator, on the denominator, or in front.
−58 = 5−8 = −(58)
All three name the same number.
Answer: 5−8 and −(58)
A negative fraction can show the sign on the numerator, on the denominator, or in front.
−29 = 2−9 = −(29)
All three name the same number.
Answer: 2−9 and −(29)
A negative divided by a negative is positive.
−2−9 = 29
Answer: 29
A negative divided by a negative is positive.
−3−4 = 34
Answer: 34
A negative divided by a positive is negative.
9 ÷ 3 = 3
−93 = −3
Answer: −3
A negative divided by a positive is negative.
12 ÷ 4 = 3
−124 = −3
Answer: −3
Multiply. Then simplify.
To multiply fractions, multiply the numerators and multiply the denominators.
A positive times a negative is a negative.
(−12) × (35)
= −1 × 32 × 5
= −310
Answer: −310
To multiply fractions, multiply the numerators and multiply the denominators.
A positive times a negative is a negative.
(−23) × (45)
= −2 × 43 × 5
= −815
Answer: −815
To multiply fractions, multiply the numerators and multiply the denominators.
A negative times a negative is a positive.
(−34) × (−25)
= −3 × −24 × 5
= 620
Divide the numerator and the denominator by 2.
= 310
Answer: 310
To multiply fractions, multiply the numerators and multiply the denominators.
A positive times a negative is a negative.
(56) × (−310)
= 5 × −36 × 10
= −1560
Divide the numerator and the denominator by 15.
= −14
Answer: −14
To multiply fractions, multiply the numerators and multiply the denominators.
A positive times a negative is a negative.
(−78) × (47)
= −7 × 48 × 7
= −2856
Divide the numerator and the denominator by 28.
= −12
Answer: −12
To multiply fractions, multiply the numerators and multiply the denominators.
A negative times a negative is a positive.
(−12) × (−12)
= −1 × −12 × 2
= 14
Answer: 14
To multiply fractions, multiply the numerators and multiply the denominators.
A positive times a negative is a negative.
(29) × (−34)
= 2 × −39 × 4
= −636
Divide the numerator and the denominator by 6.
= −16
Answer: −16
To multiply fractions, multiply the numerators and multiply the denominators.
A positive times a negative is a negative.
(−53) × (910)
= −5 × 93 × 10
= −4530
Divide the numerator and the denominator by 15.
= −32
= −112
Answer: −32, which is −112
To multiply fractions, multiply the numerators and multiply the denominators.
A negative times a negative is a positive.
(−45) × (−56)
= −4 × −55 × 6
= 2030
Divide the numerator and the denominator by 10.
= 23
Answer: 23
To multiply fractions, multiply the numerators and multiply the denominators.
A positive times a negative is a negative.
(83) × (−14)
= 8 × −13 × 4
= −812
Divide the numerator and the denominator by 4.
= −23
Answer: −23
To multiply fractions, multiply the numerators and multiply the denominators.
A positive times a negative is a negative.
(−67) × (79)
= −6 × 77 × 9
= −4263
Divide the numerator and the denominator by 21.
= −23
Answer: −23
Divide. Write a mixed number as an improper fraction first.
Dividing by a number is multiplying by its reciprocal.
The reciprocal of 34 is 43.
−12 ÷ 34 = −12 × 43
(−12) × (43)
= −1 × 42 × 3
= −46
Divide the numerator and the denominator by 2.
= −23
Answer: −23
Dividing by a number is multiplying by its reciprocal.
The reciprocal of 12 is 2.
−34 ÷ 12 = −34 × 2
(−34) × (2)
= −3 × 24 × 1
= −64
Divide the numerator and the denominator by 2.
= −32
= −112
Answer: −32, which is −112
Dividing by a number is multiplying by its reciprocal.
The reciprocal of −415 is −154.
−25 ÷ −415 = −25 × −154
(−25) × (−154)
= −2 × −155 × 4
= 3020
Divide the numerator and the denominator by 10.
= 32
= 112
Answer: 32, which is 112
Dividing by a number is multiplying by its reciprocal.
The reciprocal of −59 is −95.
56 ÷ −59 = 56 × −95
(56) × (−95)
= 5 × −96 × 5
= −4530
Divide the numerator and the denominator by 15.
= −32
= −112
Answer: −32, which is −112
Write the mixed number as an improper fraction.
−112 = −32
Dividing by a number is multiplying by its reciprocal.
The reciprocal of 14 is 4.
−112 ÷ 14 = −32 × 4
(−32) × (4)
= −3 × 42 × 1
= −122
Divide the numerator and the denominator by 2.
= −6
Answer: −6
Write the mixed number as an improper fraction.
213 = 73
Dividing by a number is multiplying by its reciprocal.
The reciprocal of −13 is −3.
213 ÷ −13 = 73 × −3
(73) × (−3)
= 7 × −33 × 1
= −213
Divide the numerator and the denominator by 3.
= −7
Answer: −7
Dividing by a number is multiplying by its reciprocal.
The reciprocal of 4 is 14.
−83 ÷ 4 = −83 × 14
(−83) × (14)
= −8 × 13 × 4
= −812
Divide the numerator and the denominator by 4.
= −23
Answer: −23
Dividing by a number is multiplying by its reciprocal.
The reciprocal of −34 is −43.
−92 ÷ −34 = −92 × −43
(−92) × (−43)
= −9 × −42 × 3
= 366
Divide the numerator and the denominator by 6.
= 6
Answer: 6
Write the mixed number as an improper fraction.
−134 = −74
Dividing by a number is multiplying by its reciprocal.
The reciprocal of −12 is −2.
−134 ÷ −12 = −74 × −2
(−74) × (−2)
= −7 × −24 × 1
= 144
Divide the numerator and the denominator by 2.
= 72
= 312
Answer: 72, which is 312
Dividing by a number is multiplying by its reciprocal.
The reciprocal of −815 is −158.
45 ÷ −815 = 45 × −158
(45) × (−158)
= 4 × −155 × 8
= −6040
Divide the numerator and the denominator by 20.
= −32
= −112
Answer: −32, which is −112
Write each mixed number as an improper fraction.
−215 = −115
1110 = 1110
Dividing by a number is multiplying by its reciprocal.
The reciprocal of 1110 is 1011.
−215 ÷ 1110 = −115 × 1011
(−115) × (1011)
= −11 × 105 × 11
= −11055
Divide the numerator and the denominator by 55.
= −2
Answer: −2
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