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GEMA (formerly BEDMAS)

T1_LO7 · lo-yr9-gema-bedmas

Complete
Key idea:

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

  1. Do anything inside brackets first.

  1. Work out powers such as $3^2$.

  1. Multiply and divide from left to right.

  1. Add and subtract from left to right.

  1. 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.

Common mistake

Doing addition before multiplication. In $5+2\times3$, you must do $2\times3$ first, so the answer is $11$, not $21$.

Try these
  1. Evaluate $6+3\times4$.

  2. Evaluate $(6+3)\times4$.

  3. 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.