Integers

Multiplying and Dividing Integers

Multiply and divide integers using sign rules: same signs give a positive result, different signs give a negative result.

Example

Use magnitude arithmetic and sign rules for integer products and quotients.

highlighted = computed this step

Step 1 — Multiply setup

Set up the expression.

(−4)(−3)( -4 )( -3 )
Separate signs from magnitudes: (-4)(-3).-magnitude 4-magnitude 3+magnitude 12x=Keep the signs visible before multiplying 4 and 3.

Step 2 — Multiplication sign

Like signs give a positive result.

like signs⇒positive\text{like signs} \Rightarrow \hl{positive}
Sign pair: - with - gives +.-magnitude 4-magnitude 3+magnitude 12x=Like signs give the positive sign used by the product.

Step 3 — Multiply magnitudes

Multiply magnitudes: 4 x 3 = 12.

4×3=124 \times 3 = \hl{12}
Multiply magnitudes: 4 x 3 = 12.4 rows of 3 make 12 units.positive sign + magnitude 12 gives 12

Step 4 — Divide setup

Set up the expression.

(−12)÷4( -12 ) \div 4
Separate signs from magnitudes: (-12) div 4.-magnitude 12+magnitude 4-magnitude 3div=Keep the signs visible before dividing 12 by 4.

Step 5 — Division sign

Unlike signs give a negative result.

unlike signs⇒negative\text{unlike signs} \Rightarrow \hl{negative}
Sign pair: - with + gives -.-magnitude 12+magnitude 4-magnitude 3div=Unlike signs give the negative sign used by the quotient.

Step 6 — Divide magnitudes

Divide magnitudes: 12 ÷ 4 = 3, then use the sign: -3.

12÷4=3⇒-312 \div 4 = 3 \Rightarrow \hl{-3}
Divide magnitudes: 12 div 4 = 3.group 1group 2group 3group 412 split into 4 groups gives 3 in each group.negative sign + magnitude 3 gives -3

Step 7 — Result

Read the final result.

12−312 \quad -3
Combine each sign with its magnitude.product 12quotient -3The signs and magnitudes match the two pinned examples.
multiply-divide-integers Sign rules for multiplication and division: - Positive x Positive = Positive - Negative x Negative = Positive - Positive x Negative = Negative - Negative x Positive = Negative Same rule applies to division.