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Signs and Multiplication/Division of Signed Numbers in Algebra, Lecture notes of Algebra

San Joaquin Valley College - AtascaderoAlgebra

The rules for multiplying and dividing signed numbers in algebra. It covers the cases where the signs are the same or different, and provides examples for both multiplication and division. The document also includes exercises for practice.

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

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Section 1.3: Multiplication and division with signed numbers Chapter 1: Introduction to Algebra
Multiplication with negative numbers
โ€ข When you multiply two integers with the same signs, the result is always positive. Just
multiply the absolute values and make the answer positive.
๐‘ƒ๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ ๐‘ฅ ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ 3 ๐‘ฅ 2 = 6
๐‘๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ ๐‘ฅ ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ (โˆ’3)(โˆ’2) = 6
โ€ข When you multiply two integers with different signs, the result is always negative. Just
multiply the absolute values and make the answer negative.
๐‘ƒ๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ ๐‘ฅ ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ (3)(โˆ’2) = โˆ’6
๐‘๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ ๐‘ฅ ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ (โˆ’3)(2) = โˆ’6
Division with negative numbers
โ€ข When you divide two integers with the same sign, the result is always positive. Just divide the
absolute values and make the answer positive.
๐‘ƒ๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ รท ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ 8 รท 4 = 2 ๐‘œ๐‘Ÿ 8
4= 2
๐‘๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ รท ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ (โˆ’8)รท(โˆ’2)= 4 ๐‘œ๐‘Ÿ โˆ’8
โˆ’2 = 4
โ€ข When you divide two integers with different signs, the result is always negative. Just divide
the absolute values and make the answer negative.
๐‘ƒ๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ รท ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ 8 รท (โˆ’4)= โˆ’2 ๐‘œ๐‘Ÿ 8
โˆ’4 = โˆ’2
๐‘๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ รท ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ (โˆ’8)รท 4 = โˆ’2 ๐‘œ๐‘Ÿ โˆ’8
4= โˆ’2
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Multiplication with negative numbers

  • When you multiply two integers with the same signs , the result is always positive. Just

multiply the absolute values and make the answer positive.

  • When you multiply two integers with different signs , the result is always negative. Just

multiply the absolute values and make the answer negative.

Division with negative numbers

  • When you divide two integers with the same sign , the result is always positive. Just divide the

absolute values and make the answer positive.

๐‘ƒ๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ รท ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ 8 รท 4 = 2 ๐‘œ๐‘Ÿ

๐‘๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ รท ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’

รท

  • When you divide two integers with different signs , the result is always negative. Just divide

the absolute values and make the answer negative.

๐‘ƒ๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ รท ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ 8 รท

๐‘๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’ รท ๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘’ = ๐‘›๐‘’๐‘”๐‘Ž๐‘ก๐‘–๐‘ฃ๐‘’

รท 4 = โˆ’ 2 ๐‘œ๐‘Ÿ

#1 โ€“ 24: Simplify

5) (โˆ’ 6 )(โˆ’ 7 ) 6) (โˆ’ 4 )(โˆ’ 3 ) 7) โˆ’ 2 ร— โˆ’ 4 8) โˆ’ 7 ร— โˆ’ 8

24

โˆ’ 6

36

โˆ’ 3

โˆ’ 14

2

โˆ’ 40

8

โˆ’ 10

โˆ’ 2

โˆ’ 55

โˆ’ 11

โˆ’ 16

โˆ’ 8

โˆ’ 60

โˆ’ 10

17) โˆ’ 20 รท 4 18) โˆ’ 14 รท 7 19) โˆ’ 28 รท โˆ’ 7 20) โˆ’ 64 รท โˆ’ 8

21) 6 รท โˆ’ 2 22) 42 รท โˆ’ 7 23) โˆ’

10

2

34

17

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