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Grades 5-8 / GED Foundation

Simplifying and Comparing Fractions

Simplify each fraction. For comparison problems, write <, >, or =.

Fractions
  1. Simplify 12/18.
  2. Simplify 21/28.
  3. Simplify 45/60.
  4. Compare 3/4 and 5/8.
  5. Compare 7/12 and 2/3.
  6. Order from least to greatest: 1/2, 3/8, 5/6.
  7. Write 0.4 as a simplified fraction.
  8. Write 75% as a simplified fraction.
  9. A ribbon is 18 inches long. Maria uses 2/3 of it. How many inches does she use?
  10. A recipe needs 3/4 cup sugar. Jamal has 6/8 cup. Does he have enough?
Answer key
  1. 2/3
  2. 3/4
  3. 3/4
  4. 3/4 > 5/8
  5. 7/12 < 2/3
  6. 3/8, 1/2, 5/6
  7. 2/5
  8. 3/4
  9. 12 inches
  10. Yes

Grades 5-8 / GED / HiSET

Adding and Subtracting Fractions

Find a common denominator when needed. Simplify every final answer.

Fraction operations
  1. 1/4 + 3/8
  2. 5/6 - 1/3
  3. 2/5 + 1/10
  4. 7/9 - 2/9
  5. 3/4 + 2/3
  6. 1 1/2 + 2 1/4
  7. 4 2/3 - 1 5/6
  8. A runner completes 3/8 mile, rests, then runs 1/4 mile. How far did the runner go?
  9. A tank is 5/6 full. After using 1/4 of the tank, what fraction remains?
  10. A board is 7 1/2 feet long. If 2 3/4 feet are cut off, how much remains?
Answer key
  1. 5/8
  2. 1/2
  3. 1/2
  4. 5/9
  5. 1 5/12
  6. 3 3/4
  7. 2 5/6
  8. 5/8 mile
  9. 7/12
  10. 4 3/4 feet

Grades 6-8 / TEAS / ASVAB

Multiplying and Dividing Fractions

Multiply across. To divide fractions, multiply by the reciprocal. Reduce answers.

Fraction fluency
  1. 2/3 x 9/10
  2. 5/8 x 4/15
  3. 3/4 x 8/9
  4. 2 1/2 x 3/5
  5. 5/6 divided by 10/12
  6. 7/8 divided by 1/4
  7. A garden uses 3/5 of a bag of soil per row. How many bags are needed for 6 rows?
  8. One serving is 2/3 cup. How many servings are in 4 cups?
  9. A board is 9/10 meter long. It is cut into pieces that are 3/10 meter each. How many pieces?
  10. A recipe is cut in half. It originally calls for 3/4 cup oil. How much oil is needed?
Answer key
  1. 3/5
  2. 1/6
  3. 2/3
  4. 1 1/2
  5. 1
  6. 3 1/2
  7. 3 3/5 bags
  8. 6 servings
  9. 3 pieces
  10. 3/8 cup

Grades 6-9 / TEAS / GED

Decimals, Percents, and Money

Convert carefully between decimals and percents. Round money answers to the nearest cent.

Percent calculations
  1. Write 0.37 as a percent.
  2. Write 85% as a decimal.
  3. Find 15% of 240.
  4. Find 6% of 750.
  5. A jacket costs $64 and is discounted 25%. What is the sale price?
  6. A $42 meal has an 18% tip. What is the tip?
  7. Increase 80 by 12%.
  8. A score rose from 40 to 50. What is the percent increase?
  9. A $120 item is marked up by 30%. What is the new price?
  10. A class has 18 girls and 12 boys. What percent of the class are boys?
Answer key
  1. 37%
  2. 0.85
  3. 36
  4. 45
  5. $48.00
  6. $7.56
  7. 89.6
  8. 25%
  9. $156.00
  10. 40%

Grades 6-9 / Praxis / SAT Foundation

Ratios, Rates, and Proportions

Write each ratio in simplest form. Use cross-products or unit rates when helpful.

Proportional reasoning
  1. Simplify the ratio 18:24.
  2. A car travels 210 miles on 7 gallons. Find miles per gallon.
  3. Solve x/12 = 5/8.
  4. A map scale is 1 inch = 25 miles. How many miles are represented by 3.5 inches?
  5. A recipe uses 2 cups rice for 5 people. How many cups are needed for 20 people?
  6. If 4 notebooks cost $7.20, what is the cost of 1 notebook?
  7. A team wins 9 games and loses 6. What is the win-to-loss ratio in simplest form?
  8. Solve 6/15 = y/40.
  9. A printer makes 36 pages in 3 minutes. How many pages in 10 minutes?
  10. A 12-ounce bottle costs $1.80. What is the cost per ounce?
Answer key
  1. 3:4
  2. 30 mpg
  3. 7.5
  4. 87.5 miles
  5. 8 cups
  6. $1.80
  7. 3:2
  8. 16
  9. 120 pages
  10. $0.15

Grades 6-8 / Pre-Algebra

Order of Operations and Integers

Use the correct order of operations. For integer problems, watch the signs.

Number sense
  1. 8 + 3 x 4
  2. (8 + 3) x 4
  3. 24 divided by 3 + 5
  4. 7^2 - 6 x 5
  5. -8 + 13
  6. -6 - 9
  7. -4 x 7
  8. -36 divided by -6
  9. 5 - (-11)
  10. The temperature is -3 degrees and rises 12 degrees. What is the new temperature?
Answer key
  1. 20
  2. 44
  3. 13
  4. 19
  5. 5
  6. -15
  7. -28
  8. 6
  9. 16
  10. 9 degrees

Pre-Algebra / Algebra I

Expressions and Equations

Simplify expressions first. Then solve for the variable and check your answer.

Solving equations
  1. Simplify 4x + 7x.
  2. Simplify 3(a + 5).
  3. Evaluate 2x + 9 when x = 6.
  4. x + 9 = 24
  5. 7p = 63
  6. y / 5 = 11
  7. 2x + 7 = 31
  8. 5a - 8 = 42
  9. 3(n + 4) = 30
  10. 18 - 2k = 6
Answer key
  1. 11x
  2. 3a + 15
  3. 21
  4. x = 15
  5. p = 9
  6. y = 55
  7. x = 12
  8. a = 10
  9. n = 6
  10. k = 6

Algebra I / SAT / ACT Foundation

Linear Equations and Slope

Use slope = rise/run. For slope-intercept form, identify m and b in y = mx + b.

Lines and graphs
  1. Find the slope through (2, 5) and (6, 13).
  2. Find the slope through (-1, 4) and (3, -4).
  3. What is the y-intercept of y = 3x - 8?
  4. Write the slope of y = -2x + 7.
  5. Does the point (2, 9) lie on y = 4x + 1?
  6. Find y when x = 5 in y = 2x - 3.
  7. A line has slope 3 and y-intercept -2. Write its equation.
  8. Find the x-intercept of y = x - 6.
  9. A taxi charges $4 plus $2 per mile. Write a cost equation.
  10. Using the taxi equation, find the cost for 9 miles.
Answer key
  1. 2
  2. -2
  3. -8
  4. -2
  5. Yes
  6. 7
  7. y = 3x - 2
  8. 6
  9. C = 2m + 4
  10. $22

Grades 6-10 / GED / SAT Foundation

Geometry: Area, Perimeter, and Angles

Use the correct formula. Include square or cubic units when measurement is requested.

Geometry formulas
  1. Find the perimeter of a rectangle with length 12 cm and width 5 cm.
  2. Find the area of a triangle with base 14 in and height 9 in.
  3. A circle has radius 6. Find the circumference in terms of pi.
  4. A right angle is split into angles of x and 35 degrees. Find x.
  5. Find the volume of a box that is 8 ft by 3 ft by 5 ft.
  6. A square has area 81 square inches. What is its side length?
  7. Two angles are supplementary. One is 118 degrees. Find the other.
  8. Find the area of a parallelogram with base 11 m and height 7 m.
  9. A triangle has angles 42 degrees and 68 degrees. Find the third angle.
  10. Find the area of a circle with radius 4 in terms of pi.
Answer key
  1. 34 cm
  2. 63 square inches
  3. 12 pi
  4. 55 degrees
  5. 120 cubic feet
  6. 9 inches
  7. 62 degrees
  8. 77 square meters
  9. 70 degrees
  10. 16 pi

Grades 6-10 / Praxis / ACT Foundation

Statistics and Probability

For probability, write answers as simplified fractions unless the problem asks for a percent.

Data analysis
  1. Find the mean of 6, 8, 10, 14, and 17.
  2. Find the median of 12, 4, 9, 18, 7.
  3. Find the range of 3, 15, 9, 22, 10.
  4. A bag has 5 red marbles and 7 blue marbles. What is P(red)?
  5. A number cube is rolled. What is P(rolling an even number)?
  6. A test score set is 80, 84, 84, 90, 92. What is the mode?
  7. A spinner has 8 equal sections, 3 green. What is P(not green)?
  8. If the mean of 4 numbers is 12, what is their total?
  9. A coin is flipped twice. What is the probability of two heads?
  10. A survey has 30 yes answers and 20 no answers. What percent answered yes?
Answer key
  1. 11
  2. 9
  3. 19
  4. 5/12
  5. 1/2
  6. 84
  7. 5/8
  8. 48
  9. 1/4
  10. 60%

Exam prep

GED, TEAS, and ASVAB Mixed Review

Use this as a short readiness check. Review missed problems with the topic worksheets above.

Mixed readiness
  1. A score of 42 out of 50 is what percent?
  2. Solve 4x - 9 = 27.
  3. Convert 3.6 liters to milliliters.
  4. A car travels 315 miles in 7 hours. What is its average speed?
  5. Find 2/5 of 85.
  6. A rectangle has area 96 and width 8. Find the length.
  7. Simplify 3(2x + 5) - x.
  8. A $75 item is discounted 20%. What is the sale price?
  9. Find the mean of 10, 12, 18, and 20.
  10. A rope is 9 feet long. It is cut into 3 equal pieces. How long is each piece?
Answer key
  1. 84%
  2. x = 9
  3. 3,600 mL
  4. 45 mph
  5. 34
  6. 12
  7. 5x + 15
  8. $60
  9. 15
  10. 3 feet