Multiplying and dividing integers; absolute value
Multiply and divide negative numbers with hops on the number line, find the pattern behind the signs, and measure distance from zero.
π Start here: read the steps of the βLessonβ in order (1, 2, 3 β¦) and answer each question. Then continue with βPracticeβ.
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Guide
Adding a negative number is a hop to the left: β3 + (β4) starts at β3 and hops 4 to the left.
Multiplying is repeated hops from zero: 3Γ(β2) is three hops of β2, so it lands on β6.
When a pattern goes down by one each time, the answers change by the same amount each time. Following the pattern past zero shows why a negative number times a negative number is positive.
Division undoes multiplication: (β12) Γ· 3 asks "3 times what makes β12?". The answer is β4, because 3Γ(β4) = β12.
The absolute value (modulus) of a number is its distance from zero, so it is never negative: |β7| = 7 and |7| = 7.