Order of operations and substitution with integers

Using the order of operations with negative numbers, including powers and grouping symbols, and substituting negative values into algebraic expressions.

Order of operations

Example 1●●

Evaluate $-2 \times (5 - 8)^2 + 10 \div (-5)$.

Brackets: $5 - 8 = -3$. Index: $(-3)^2 = 9$.

$-2 \times 9 + 10 \div (-5) = -18 + (-2)$

$= -20$

Substitution

Example 2●●

Evaluate $3a^2 - ab$ when $a = -2$ and $b = 5$.

$3(-2)^2 - (-2)(5)$

$= 3(4) + 10 = 22$

Flashcards

BIDMAS

Brackets, Indices, Division/Multiplication, Addition/Subtraction

$a^2$ when $a = -5$

$25$

$-a$ when $a = -5$

$5$

Practice

Evaluate $-2 \times (5 - 8)^2 + 10 \div (-5)$.
Evaluate $3a^2 - ab$ when $a = -2$, $b = 5$.
Find $a^2$ when $a = -5$.
Find $-a$ when $a = -5$.
Evaluate $-3 - 4 \times 2$.
Evaluate $(-3 - 4) \times (-2)$.
Find $\dfrac{x + y}{x - y}$ when $x = 2$ and $y = -6$.
Evaluate $5 + (-12) \div 2 \times 2$.