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Negative numbers

Negative numbers

Japanese school year: Junior high 1

What you learn

Arithmetic with negative numbers - watch the signs.

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Key points

This rule shows that subtracting a negative number −b-b is equivalent to adding the positive number bb. Reverse the sign of the subtracted number and perform addition.

a−(−b)=a+ba - (-b) = a + b

This formula shows that multiplying two negative numbers yields a positive product. The product of two numbers with the same negative sign is always positive.

(−a)×(−b)=ab(-a) \times (-b) = ab

This formula shows that multiplying a negative number by a positive number yields a negative product. The product of numbers with opposite signs is always negative.

(−a)×b=−ab(-a) \times b = -ab

This rule shows that dividing two negative numbers yields a positive quotient. Dividing numbers with matching negative signs results in the positive fraction ab\frac{a}{b}.

(−a)÷(−b)=ab(b≠0)(-a) \div (-b) = \frac{a}{b} \quad (b \neq 0)
Worked example
(−6)×4−(−18)÷3(-6) \times 4 - (-18) \div 3
Expression: (−6)×4−(−18)÷3=−18(-6) \times 4 - (-18) \div 3 = -18

Choose a set to practice.