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3.8

# Dividing with negative numbers

Division is the inverse operation of multiplication.

If $$3 \times 2 = 6$$, then $$6 \div 3 = 2$$ and $$6 \div 2 = 3$$.

If $$3 \times ({-2}) = ({-6})$$ then $$({-6}) \div 3 = ({-2})$$ and $$({-6}) \div ({-2}) = 3$$.

The logic in this argument shows that the same rules apply to division of positive and negative numbers as apply to multiplication.

When stretching or enlarging shapes, students will be required to link division with fractions. When dividing by 2 this is the same as multiplying by $$\frac{1}{2}$$ hence whereas an enlargement scale factor 2 doubles each length of a shape, a scale factor of $$\frac{1}{2}$$, halves the length of each shape.

a) $$8 \div 2 = 4$$
b) $$({-8}) \div 2 = ({-4})$$
c) $$({-8}) \div ({-2}) = 4$$