Student 1 | Student 2 |
3 + 4 x 2 | 3 + 4 x 2 |
= 7 x 2 | = 3 + 8 |
= 14 | = 11 |
Order of Operations | ||
Expression | Evaluation | Operation |
6 + 7 x 8 | = 6 + 7 x 8 | Multiplication |
= 6 + 56 | Addition | |
= 62 | ||
16 ÷ 8 - 2 | = 16 ÷ 8 - 2 | Division |
= 2 - 2 | Subtraction | |
= 0 | ||
(25 - 11) x 3 | = (25 - 11) x 3 | Parentheses |
= 14 x 3 | Multiplication | |
= 42 |
Step 1: | 3 + 6 x (5 + 4)÷ 3 - 7 | = | 3 + 6 x 9 ÷ 3 - 7 | Parentheses |
Step 2: | 3 + 6 x 9÷ 3 - 7 | = | 3 + 54 ÷ 3 - 7 | Multiplication |
Step 3: | 3 + 54 ÷ 3 - 7 | = | 3 + 18 - 7 | Division |
Step 4: | 3 + 18 - 7 | = | 21 - 7 | Addition |
Step 5: | 21 - 7 | = | 14 | Subtraction |
Step 1: | 9 - 5 ÷(8 - 3) x 2 + 6 | = | 9 - 5 ÷ 5 x 2 + 6 | Parentheses |
Step 2: | 9 - 5 ÷ 5 x 2 + 6 | = | 9 - 1 x 2 + 6 | Division |
Step 3: | 9 - 1 x 2 + 6 | = | 9 - 2 + 6 | Multiplication |
Step 4: | 9 - 2 + 6 | = | 7 + 6 | Subtraction |
Step 5: | 7 + 6 | = | 13 | Addition |
Step 1: | 150 ÷ (6 + 3 x 8) - 5 | = | 150 ÷ (6 + 24) - 5 | Multiplication inside Parentheses |
Step 2: | 150 ÷(6 + 24) - 5 | = | 150 ÷ 30 - 5 | Addition inside Parentheses |
Step 3: | 150 ÷ 30 - 5 | = | 5 - 5 | Division |
Step 4: | 5 - 5 | = | 0 | Subtraction |
1. | 9 + 6 x (8 - 5) |
2. | (14 - 5) ÷ (9 - 6) |
3. | 5 x 8 + 6 ÷ 6 - 12 x 2 |
4. |
5. | A caterer charges a setup fee of $50, plus $20 per person. How much will the caterer charge if 35 people attend the party, and the customer has a coupon for $100 off the total? |
Order of Operations | |
---|---|
Please | Parentheses |
Excuse | Exponents |
My Dear | Multiplication and Division |
Aunt Sally | Addition and Subtraction |
1. | |
[latex]4+3cdot 7[/latex] | |
Are there any parentheses? No. | |
Are there any exponents? No. | |
Is there any multiplication or division? Yes. | |
Multiply first. | [latex]4+color{red}{3cdot 7}[/latex] |
Add. | [latex]4+21[/latex] |
[latex]25[/latex] |
2. | |
[latex](4+3)cdot 7[/latex] | |
Are there any parentheses? Yes. | [latex]color{red}{(4+3)}cdot 7[/latex] |
Simplify inside the parentheses. | [latex](7)7[/latex] |
Are there any exponents? No. | |
Is there any multiplication or division? Yes. | |
Multiply. | [latex]49[/latex] |
1. | |
[latex]18div 9cdot 2[/latex] | |
Are there any parentheses? No. | |
Are there any exponents? No. | |
Is there any multiplication or division? Yes. | |
Multiply and divide from left to right. Divide. | [latex]color{red}{2}cdot 2[/latex] |
Multiply. | [latex]4[/latex] |
2. | |
[latex]18cdot 9div 2[/latex] | |
Are there any parentheses? No. | |
Are there any exponents? No. | |
Is there any multiplication or division? Yes. | |
Multiply and divide from left to right. | |
Multiply. | [latex]color{red}{162}div 2[/latex] |
Divide. | [latex]81[/latex] |
[latex]18div 6+4(5-2)[/latex] | |
Parentheses? Yes, subtract first. | [latex]18div 6+4(color{red}{3})[/latex] |
Exponents? No. | |
Multiplication or division? Yes. | |
Divide first because we multiply and divide left to right. | [latex]color{red}{3}+4(3)[/latex] |
Any other multiplication or division? Yes. | |
Multiply. | [latex]3+color{red}{12}[/latex] |
Any other multiplication or division? No. | |
Any addition or subtraction? Yes. | [latex]15[/latex] |
[latex]5+{2}^{3}+ 3[6-3(4-2)][/latex] | |
Are there any parentheses (or other grouping symbol)? Yes. | |
Focus on the parentheses that are inside the brackets. | [latex]5+{2}^{3}+ 3[6-3color{red}{(4-2)}][/latex] |
Subtract. | [latex]5+{2}^{3}+3[6-color{red}{3(2)}][/latex] |
Continue inside the brackets and multiply. | [latex]5+{2}^{3}+3[6-color{red}{6}][/latex] |
Continue inside the brackets and subtract. | [latex]5+{2}^{3}+3[color{red}{0}][/latex] |
The expression inside the brackets requires no further simplification. | |
Are there any exponents? Yes. | |
Simplify exponents. | [latex]5+color{red}{{2}^{3}}+3[0][/latex] |
Is there any multiplication or division? Yes. | |
Multiply. | [latex]5+8+color{red}{3[0]}[/latex] |
Is there any addition or subtraction? Yes. | |
Add. | [latex]color{red}{5+8}+0[/latex] |
Add. | [latex]color{red}{13+0}[/latex] |
[latex]13[/latex] |
[latex]{2}^{3}+{3}^{4}div 3-{5}^{2}[/latex] | |
If an expression has several exponents, they may be simplified in the same step. | |
Simplify exponents. | [latex]color{red}{{2}^{3}}+color{red}{{3}^{4}}div 3-color{red}{{5}^{2}}[/latex] |
Divide. | [latex]8+color{red}{81div 3}-25[/latex] |
Add. | [latex]color{red}{8+27}-25[/latex] |
Subtract. | [latex]color{red}{35-25}[/latex] |
[latex]10[/latex] |