T1_LO7 · lo-yr9-gema-bedmas
GEMA tells you the order to work in: \textbf{G
rouping symbols first, then \textbf{E}xponents, then \textbf{M}ultiplication and \textbf{D}ivision from left to right, then \textbf{A}ddition and \textbf{S}ubtraction from left to right.}
Steps
Do anything inside brackets first.
Work out powers such as $3^2$.
Multiply and divide from left to right.
Add and subtract from left to right.
If two versions look similar, brackets can completely change the value.
Key facts
$3+4\times2=11$, not $14$.
$(3+4)\times2=14$.
$18\div3\times2=6\times2=12$.
$2^3+5=8+5=13$.
Multiplication and division have equal priority.
Addition and subtraction have equal priority.
Doing addition before multiplication. In $5+2\times3$, you must do $2\times3$ first, so the answer is $11$, not $21$.
Evaluate $6+3\times4$.
Evaluate $(6+3)\times4$.
Evaluate $20\div(2+3)$.
Example 1: no brackets
Evaluate $7+3\times2$.$$ 7+3\times2=7+6=13 $$Multiply first, then add.
Example 2: brackets
Evaluate $(7+3)\times2$.$$ (7+3)\times2=10\times2=20 $$Brackets make the addition happen first.
Example 3: left to right
Evaluate $18\div3\times2$.$$ 18\div3\times2=6\times2=12 $$Do division and multiplication left to right.
Example 4: powers
Evaluate $2^3+4$.$$ 2^3+4=8+4=12 $$Work out the exponent before adding.