Powers and Exponents
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Write each expression using exponents. 1) 7 • 7 • 7 • 6 • 6 • 6 • 6 2) 2 • 2 • 5 • 5 • 9 • 9 3) 10 • 10 • 8 • 8
Evaluate each expression.
4) 105 5) 25 6) 72 7) 33 • 42
8) 19 • 53 9) 1002 • 62 10) 122 11) 24 • 16
12) 503 13) 72 • 72 14) 42 • 32 • 22 15) 91 • 92
1 Variables, Expressions and Equations
Show all work on the following page. No Calculators. Evaluate each expression. 1) (42 + 4) 4 2) 3) 52 4 10
4) 15 – 2 4 – (6 – 3) 5) [1 +(5 – 2)2] 6 6) (4 5)2
Evaluate each expressions if m = 4, n = 3, and p = 2. 7) 7m – 3p 8) mn – p 9) 2p + p2
10) 5m – 4n + p 11) (m – p)n 12) 5p + m
Find the solution for each equation from the given replacement set. 13) k + 23 = 45, {21, 22, 23} 14) 55 – d = 17, {36, 37, 38}
15) 2p = $19.80, {$9.00, $9.45, $9.90} 16) = 15, {485, 495, 505}
2 Variables, Expressions and Equations Evaluate each expression. 1) (42 + 4) 4 2) 3) 52 4 10
4) 15 – 2 4 – (6 – 3) 5) [1 +(5 – 2)2] 6 6) (4 5)2
Evaluate each expressions if m = 4, n = 3, and p = 2. 7) 7m – 3p 8) mn – p 9) 2p + p2
10) 5m – 4n + p 11) (m – p)n 12) 5p + m
Find the solution for each equation from the given replacement set. 13) k + 23 = 45, {21, 22, 23} 14) 55 – d = 17, {36, 37, 38}
3 15) 2p = $19.80, {$9.00, $9.45, $9.90} 16) = 15, {485, 495, 505}
Solving Addition and Subtraction Equations
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Solve each equation. Check your solution. 1) d + 22 = 60 2) s – 46 = 12 3) t - 71 = 20
4) 1.5 + r = 3 5) g - $2.25 = $1.25 6) x + 140 = 300
7) $5.60 + h = $7.00 8) e – 405 = 325 9) 808 = p + 500
10) 4.09 = 2 + y 11) 11.3 = b – 3.7 12) r – 2.2 = 6
4 Solving Addition and Subtraction Equations Solve each equation. Check your solution. 1) d + 22 = 60 2) s – 46 = 12 3) t - 71 = 20
4) 1.5 + r = 3 5) g - $2.25 = $1.25 6) x + 140 = 300
7) $5.60 + h = $7.00 8) e – 405 = 325 9) 808 = p + 500
5 10) 4.09 = 2 + y 11) 11.3 = b – 3.7 12) r – 2.2 = 6
Solving Multiplication and Division Equations
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Solve each equation. Check your solution. 1) 14k = 84 2) = 12 3) 99 = 3e
4) 15 = 5) $5.00 = 4w 6) 9t = 729
6 7) 3 = 8) 0.5p = 3 9) 2.7 = 0.9r
10) The product of 7 and a number w is 91. Find the number.
Solving Multiplication and Division Equations Solve each equation. Check your solution.
1) 14k = 84 2) = 12 3) 99 = 3e
4) 15 = 5) $5.00 = 4w 6) 9t = 729
7) 3 = 8) 0.5p = 3 9) 2.7 = 0.9r
7 10) The product of 7 and a number w is 91. Find the number.
Greatest Common Factor
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Find the GCF of each set of numbers.
1) 18, 30 2) 36, 90 3) 15, 17
4) 63, 42 5) 36, 12, 72 6) 30, 45, 75 Least Common Multiple
8 Show your work on the following page. No Calculators.
Find the LCM of each set of numbers.
1) 16, 12 2) 6, 10 3) 15, 20
4) 4, 10, 8 5) 30, 21, 7 6) 8, 14, 28
Greatest Common Factor Find the GCF of each set of numbers.
1) 18, 30 2) 36, 90 3) 15, 17
4) 63, 42 5) 36, 12, 72 6) 30, 45, 75
Least Common Multiple Find the LCM of each set of numbers.
1) 16, 12 2) 6, 10 3) 15, 20
9 4) 4, 10, 8 5) 30, 21, 7 6) 8, 14, 28
Ratios and Rates
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1) 12 wins:15 games 2) 8 out of 20 cars 3) 65 to 10
4) 8 out of 10 people 5) 90 men:144 women 6) 81 to 36
7) 180 tickets:60 tickets 8) 4 feet:1 yard 9) 3 out of 24
Express each ratio or rate in simplest form.
Express each rate as a unit rate. 10) $45 for 9 hours 11) 280 kilometers in 5 hours
10 12) $330 for 3 days 13) 432 beats in 6 minutes
14) 77 pounds in 11 weeks 15) 480 miles in 12 hours
Ratios and Rates 1) 12 wins:15 games 2) 8 out of 20 cars 3) 65 to 10
4) 8 out of 10 people 5) 90 men:144 women 6) 81 to 36
7) 180 tickets:60 tickets 8) 4 feet:1 yard 9) 3 out of 24
Express each ratio or rate in simplest form.
Express each rate as a unit rate. 10) $45 for 9 hours 11) 280 kilometers in 5 hours
12) $330 for 3 days 13) 432 beats in 6 minutes
11 14) 77 pounds in 11 weeks 15) 480 miles in 12 hours
Ratios and Percents
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Evaluate each ratio or fraction as a percent. 1) 2) 49 out of 98 3) 91 hundredths
4) 16 out of 25 5) out of 100 6) $18 per $40
Express each percent as a fraction in simplest form. 7) 20% 8) 24% 9) 35%
12 10) 47% 11) 48% 12) 70%
Ratios and Percents Evaluate each ratio or fraction as a percent. 1) 2) 49 out of 98 3) 91 hundredths
4) 16 out of 25 5) out of 100 6) $18 per $40
Express each percent as a fraction in simplest form. 7) 20% 8) 24% 9) 35%
13 10) 47% 11) 48% 12) 70%
Fractions, Decimals, and Percents
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1) 45% 2) 91% 3) 24.5% 4) 8.37%
Express each percent as a decimal.
14 5) 0.13 6) 0.06 7) 0.765 8) 0.0122
Express each decimal as a percent. 9) 10) 11) 12)
Express each fraction as a percent. Solving Inequalities
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Solve each inequality. Graph the solution on a number line. 1) y + 7 < 12
2) t – 1 > 4
3) m – 3 ≤ 8
15 4) 6w ≥ 18
5) 2h < 14
6) > 3
Writing Expressions and Equations
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Write each phrase as an algebraic expression.
1) 12 more than a number
2) the quotient of a number divided by 9
3) 4 times a number
4) 15 less than a number
5) 1 less than the product of 3 and m
6) The product of 4 times a number minus 8
Write each sentence as an algebraic equation.
7) A number minus 6 equals 12.
16 8) A number plus 14 equals 25.
9) 3 more than 5 times the number of dogs is 18 dogs
10) 4 times the number of cows plus 2 times the number of ducks is 20.
11) 2 less than the quotient of 12 divided by a number is 2.
12) The product of 5 and y added to 3 is 33. Multiplying Decimals
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Multiply. 1) 0.5 x 20.2 2) 12. x 2.3 3) 0.055 x 3.2
4) 0.014 x 0.4 5) 12.4 x 12. 4 6) 3.07 x 1.07
17 Evaluate each expression if m = 0.09, n = 1.2, and p = 8.19. 7) mn 8) p(n + m) 9) pm
Dividing Decimals
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Find each quotient. 1) 2.7 40.5 2) 2.1 4.41 3) 0.212 1.696
4) 62.8 87.92 5) 8.652 1.2 6) 17.6 3.2
Zeros in the Quotient
18 Show all work on the following page. No Calculators.
Find each quotient to the nearest hundredth. 1) 14 1.26 2) 7 28.35
3) 19.065 9.3 4) 72.76 6.8 Dividing Decimals Find each quotient.
1) 2.7 40.5 2) 2.1 4.41 3) 0.212 1.696
5) 8.652 1.2 6) 17.6 3.2 4) 62.8 87.92
19 Zeros in the Quotient Find each quotient to the nearest hundredth.
1) 14 1.26 2) 7 28.35
3) 19.065 9.3 4) 72.76 6.8
Adding & Subtracting Fractions - Unlike Denominators
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Add or subtract. Write each answer in simplest form.
20 1) 2) 3)
4) 5) 6)
Adding and Subtracting Mixed Numbers
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Add or subtract. Write each answer in simplest form.
21 1) 2) 3)
4) 5) 6)
Multiplying Fractions
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Find each product. Write each answer in simplest form.
22 1) 2) 3)
4) 5) 6) Multiplying Mixed Numbers
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Find each product. Write each answer in simplest form. 1) 2) 5 3) 9 4)
5) 6) 7) 6) 8 Multiplying Fractions Find each product. Write each answer in simplest form. 1) 2) 3)
4) 5) 6)
23 Multiplying Mixed Numbers Find each product. Write each answer in simplest form. 1) 2) 5 3) 9 4)
5) 6) 7) 6) 8
Dividing Fractions
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Find each quotient. Write each answer in simplest form. 1) 2) 3) 4)
24 5) 6) 7) 6)
Dividing Mixed Numbers
Show all work on the following page. No Calculators. Find each quotient. Write each answer in simplest form. 1) 2) 3) 5 4) 5) 6) Dividing Fractions Find each quotient. Write each answer in simplest form. 1) 2) 3) 4)
5) 6) 7) 6)
25 Dividing Mixed Numbers Find each quotient. Write each answer in simplest form. 1) 2) 3) 5
4) 5) 6)
Adding and Subtracting Fractions Word Problems
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26 1) Adam bought a box of fruit that weighed 2) Emily walked a total of miles in two kilograms. If he bought a second box days. Emily walked miles on the that weighed kilograms, what is the first day, how far did she walk the combined weight of both boxes? second day?
3) A recipe called for cups of flour before 4) Haley’s class recycled boxes of paper baking and another cups of flour after in two months. If they recycled baking. What is the total amount of flour boxes the first month, how many boxes needed in the recipe? did they recycle in the second month?
Multiplying Fractions Word Problems
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27 1) A jumbo bag of M&M’s weighs 3 pounds. 2) A batch of cookies requires 2 cups of If I have 4 jumbo bags of M&M’s, how sugar. Phyllis needs to make 4 batches much would their total weight be? of cookies for the bake sale. How much sugar does Phyllis need?
3) The area of a rectangle can be found by 4) Adam had a lump of Silly Putty that was 4 multiplying the length times the width. inches long. If he stretched it out to 2 Find the area of a rectangle that has a times its current length, how long would length of inches and a width of 7. it be?
Dividing Fractions Word Problems
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28 1) 1) At the end Sarah’s birthday dinner, 2) How many cup servings of ice cream can she had Juan get from 6 cups of ice cream? 2) of her cake left over. Her 5 friends each 3) took home the same amount of leftover 4) cake. How much cake did each friend take 5) home?
6) 3) There are pizzas. Each child will 9) 4) Stan has pounds of M&M’s and he get gives 7) of a pizza. How many children will pound to each friend. How many get friends 8) pizza? will get M&M’s ?
Using Rates Word Problems
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29 1) We paid $40 for 8 hamburgers. How much 2) A machine makes 9 pencils in 3 seconds. did we pay per hamburger? What is the rate of pencils per second?
3) For every 4 miles Vanessa jogged, Cody 4) Amelia uses 8 cups of chocolate chips to jogged 3 miles. If Vanessa jogged 1 make 4 batches of cookies. What is the mile, rate of bags of chocolate chips per how far would Cody have jogged? batch?
5) A computer programmer works for 10 6) Jimena jogged 35 miles in 5 days. What is hours and makes $75. What is their rate the rate of the miles per day? per hour?
30 31