Order of Operations
| Exercise | Problem | Solution | ||||||
| 1. | 9 + 6 x (8 - 5) | 9 + 6 x (8 - 5) = 9 + 6 x 3 = 9 + 18 = 27 |
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| 2. | (14 - 5) ÷ (9 - 6) | (14 - 5) ÷ (9 - 6) = 9 ÷ (9 - 6) = 9 ÷ 3 = 3 |
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| 3. | 5 x 8 + 6 ÷ 6 - 12 x 2 | 5 x 8 + 6 ÷ 6 - 12 x 2 = 40 + 6 ÷ 6 - 12 x 2 = 40 + 1 - 12 x 2 = 40 + 1 - 24 = 41 - 24 = 17 |
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| 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? | 50 + 20 x 35 - 100 = 50 + 700 - 100 = 750 - 100 = 650 Answer: $650 |
Order of Operations With Exponents
| Exercise | Problem | Solution |
| 1. | 32 x 43 | 32 x 43 = 9 x 43 = 9 x 64 = 576 |
| 2. | 27 - 256 ÷ 43 | 27 - 256 ÷ 43 = 27 - 256 ÷ 64 = 27 - 4 = 23 |
| 3. | 9 x (5 + 3)2 - 144 | 9 x (5 + 3)2 - 144 = 9 x 82 - 144 = 9 x 64 - 144 = 576 - 144 = 432 |
| 4. | 7 + 3 x 24 ÷ 6 | 7 + 3 x 24 ÷ 6 = 7 + 3 x 16 ÷ 6 = 7 + 48 ÷ 6 = 7 + 8 = 15 |
| 5. | A carpenter charges $10 per square foot to lay a floor. If a square-shaped hallway is 6 feet along one side, and the customer has a coupon for $25 off the total, then how much will the floor cost? | 10 x 62 - 25 = 10 x 36 - 25 = 360 - 25 = 335 Answer: $335 |
Order of Operations With Integers
| Exercise | Problem | Solution | ||||||
| 1. | 18 - (-6)2 ÷ 9 | 18 - (-6)2 ÷ 9 = 18 - 36 ÷ 9 = 18 - 4 = 14 or +14 |
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| 2. | [49 + 3(4-9)] ÷ -17 | [49 + 3(4-9)] ÷ -17 = [49 + 3(-5)] ÷ -17 = [49 + -15] ÷ -17 = 34 ÷ -17 = -2 |
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| 3. | 53 + (-9)(+2) ÷ 6 | 53 + (-9)(+2) ÷ 6 = 125 + (-9)(+2) ÷ 6 = 125 + -18 ÷ 6 = 125 + -3 = 122 or +122 |
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| 5. | (-4)(-3) ÷ 6 - 2[5 - -8 + (6 ÷ 2)] | (-4)(-3) ÷ 6 - 2[5 - -8 + (6 ÷ 2)] = (-4)(-3) ÷ 6 - 2[5 - -8 + 3] = (-4)(-3) ÷ 6 - 2[13 + 3] = (-4)(-3) ÷ 6 - 2[16] = (-4)(-3) ÷ 6 - 32 = 12 ÷ 6 - 32 = 2 - 32 = -30 |
Writing Algebraic Expressions
| Exercise | Problem | Solution |
| 1. | Fifteen less than twice a number | 2x - 15 |
| 2. | Three times a number increased by seventeen | 3a + 17 |
| 3. | The product of nine and a number, decreased by six | 9m - 6 |
| 4. | Thirty divided by seven times a number | None of the above. |
| 5. | Jenny earns $30 a day working part time at a supermarket. Write an algebraic expression to represent the amount of money she will earn in d days. | 30d |
Writing Algebraic Equations
| Exercise | Problem | Solution |
| 1. | Twice a number is twenty-eight. | 2x = 28 |
| 2. | The quotient of thirty-nine and a number is three. |  |
| 3. | Five less than three times a number is forty-six. | 3t - 5 = 46 |
| 4. | Three is twenty-one divided by the sum of a number and five. | None of the above. |
| 5. | Eric had $197 in his savings account before he was paid his weekly salary. His current savings balance is $429. How much money does Eric earn each week? | 197 + n = 429 |
Practice Exercises
| Exercise | Problem | Solution | ||||||
| 1. | Evaluate this arithmetic expression: 7 x 8 - 6 ÷ 2 + 18 x 3 |
7 x 8 - 6 ÷ 2 + 18 x 3 = 56 - 6 ÷ 2 + 18 x 3 = 56 - 3 + 18 x 3 = 56 - 3 + 54 = 53 + 54 = 107 Answer: 107 or +107 |
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| 2. | Evaluate this arithmetic expression:
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Answer: 5 or +5 |
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| 3. | Evaluate this arithmetic expression: 15 - 2 x 32 ÷ 6 |
15 - 2 x 32 ÷ 6 = 15 - 2 x 9 ÷ 6 = 15 - 18 ÷ 6 = 15 - 3 = 12 Answer: 12 or +12 |
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| 4. | Evaluate this arithmetic expression: 36 ÷ (7-4)2 + 21 |
36 ÷ (7-4)2 + 21 = 36 ÷ 32 + 21 = 36 ÷ 9 + 21 = 4 + 21 = 25 Answer: 25 or +25 |
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| 5. | Evaluate this arithmetic expression: [54 - 3(2 + 4)] ÷ -9 |
[54 - 3(2 + 4)] ÷ -9 = [54 - 3(6)] ÷ -9 = [54 - 18] ÷ -9 = 36 ÷ -9 = -4 Answer: -4 |
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| 6. | Evaluate this arithmetic expression:
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Answer: -3 |
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| 7. | Which algebraic expression correctly represents this phrase? Twenty-five less than three times a number. |
3x - 25 | ||||||
| 8. | Which algebraic expression correctly represents this phrase? The quotient of a number and seven, decreased by ten. |
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| 9. | Which sentence correctly represents this algebraic equation? 2w - 9 = 32 |
Nine less than twice a number is thirty-two. | ||||||
| 10. | Which sentence correctly represents this algebraic equation? |
The quotient of forty-two and a number is seven. |
Challenge Exercises
| Exercise | Problem | Solution | ||||||||||
| 1. | An agent charges $150 per gig to book a rock band, plus $75 per month for travel expenses. What was his monthly fee if he booked 6 gigs for the band last month? | 150 x 6 + 75 = 900 + 75 = 975 Answer: $975 |
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| 2. | A gardener charges $8 per square foot to lay sod. If a square garden is 7 feet along each side, how much will he charge to lay sod on it? | 8 x 72 = 8 x 49 = 392 Answer: $392 |
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| 3. | Six people in a club will share the expenses of a party that costs $240. How much will Katie pay for her share of the party if the club also credits her $8? | 240 ÷ 6 - 8 = 40 - 8 = 32 Answer: $32 |
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| 4. | Evaluate the following expression:
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| 5. | Jesse spends $5 a day on lunch. Which algebraic expression correctly represents the amount of money he will spend on lunch in x days? | 5x | ||||||||||
| 6. | Which algebraic expression correctly represents this phrase? The quotient of twelve and seven times a number, decreased by five |
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| 7. | Which algebraic equation correctly represents this sentence? A number increased by eight is nineteen. |
y + 8 = 19 | ||||||||||
| 8. | Which algebraic equation correctly represents this sentence? Twenty-five is three times a number, decreased by eight. |
25 = 3w - 8 | ||||||||||
| 9. | Which sentence correctly represents this algebraic equation? 15 = 16y - 3 |
None of the above. | ||||||||||
| 10. | Which sentence correctly represents this algebraic equation? |
The quotient of three times a number and five is thirty. |
