Order of Operations
Exercise  Problem  Solution  
1.  9 + 6 x (8  5)  9 + 6 x (8  5) = 9 + 6 x 3 = 9 + 18 = 27 

2.  (14  5) ÷ (9  6)  (14  5) ÷ (9  6) = 9 ÷ (9  6) = 9 ÷ 3 = 3 

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 

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?  50 + 20 x 35  100 = 50 + 700  100 = 750  100 = 650 Answer: $650 
Order of Operations With Exponents
Exercise  Problem  Solution 
1.  3^{2} x 4^{3}  3^{2} x 4^{3} = 9 x 4^{3} = 9 x 64 = 576 
2.  27  256 ÷ 4^{3}  27  256 ÷ 4^{3} = 27  256 ÷ 64 = 27  4 = 23 
3.  9 x (5 + 3)^{2}  144  9 x (5 + 3)^{2}  144 = 9 x 8^{2}  144 = 9 x 64  144 = 576  144 = 432 
4.  7 + 3 x 2^{4} ÷ 6  7 + 3 x 2^{4} ÷ 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 squareshaped 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 6^{2}  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 

2.  [49 + 3(49)] ÷ ^{}17  [49 + 3(49)] ÷ ^{}17 = [49 + 3(^{}5)] ÷ ^{}17 = [49 + ^{}15] ÷ ^{}17 = 34 ÷ ^{}17 = ^{}2 

3.  5^{3} + (^{}9)(^{+}2) ÷ 6  5^{3} + (^{}9)(^{+}2) ÷ 6 = 125 + (^{}9)(^{+}2) ÷ 6 = 125 + ^{}18 ÷ 6 = 125 + ^{}3 = 122 or ^{+}122 

4. 


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 twentyeight.  2x = 28 
2.  The quotient of thirtynine and a number is three.  
3.  Five less than three times a number is fortysix.  3t  5 = 46 
4.  Three is twentyone 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 

2.  Evaluate this arithmetic expression:

Answer: 5 or ^{+}5 

3.  Evaluate this arithmetic expression: 15  2 x 3^{2} ÷ 6 
15  2 x 3^{2} ÷ 6 = 15  2 x 9 ÷ 6 = 15  18 ÷ 6 = 15  3 = 12 Answer: 12 or ^{+}12 

4.  Evaluate this arithmetic expression: 36 ÷ (74)^{2} + 21 
36 ÷ (74)^{2} + 21 = 36 ÷ 3^{2} + 21 = 36 ÷ 9 + 21 = 4 + 21 = 25 Answer: 25 or ^{+}25 

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 

6.  Evaluate this arithmetic expression:

Answer: ^{}3 

7.  Which algebraic expression correctly represents this phrase? Twentyfive 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. 

9.  Which sentence correctly represents this algebraic equation? 2w  9 = 32 
Nine less than twice a number is thirtytwo.  
10.  Which sentence correctly represents this algebraic equation? 
The quotient of fortytwo 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 

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 7^{2} = 8 x 49 = 392 Answer: $392 

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 

4.  Evaluate the following expression:



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 

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? Twentyfive 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. 