Order of Operations
How do you know what to do first in this expression? |
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2 × 3 + 3 = x |
Maybe it’s addition first, then multiplication. Adding first gets you . . . |
2 × 3 + 3 = 12 WRONG! |
Or, maybe it’s multiplication first, then addition. Multiplying first gets you . . . |
2 × 3 + 3 = 9 Right! |
And then you set fire to your math book before it gets more complicated, like . . . |
7 + (2 × 3^{2} + 3) = x |
Learn this word to help you: PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction |
Perform the operations in parentheses first. Of course, that means you have to do other operations. Start with exponents. |
7 + (2 × 3^{2} + 3) = x |
7 + (2 × 9 + 3) = x |
Then multiplication/division |
7 + (18 + 3) = x |
Then addition/subtraction |
7 + (21) = x |
Finally, add the parentheses to the remainder of the expression. |
28 = x |
Most importantly, remember Exponents, Multiplication/Division, Addition/Subtraction
- 2 × 3 + 3 =2 × 3 + 3 = 9
- 2 + 3 × 3 =2 + 3 × 3 = 11
- 3 × 4 + 2 =3 × 4 + 2 = 14
- 3 + 4 × 2 =3 + 4 × 2 = 11
- 2 + 3^{2} × 2 =2 + 3^{2} × 2 = 20
- 3^{2} × 2 - 2 =3^{2} × 2 - 2 = 16
You may have heard that you should go from left to right. This is true within multiplication/division, for example. |
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12 ÷ 3 × 4 = 16 Right! |
If you go right to left, you get |
12 ÷ 3 × 4 = 1 WRONG! |