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4.E: Fractions (Exercises)

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4.1 - Visualize Fractions

In the following exercises, name the fraction of each figure that is shaded.

  1. A circle is shown. It is divided into 8 equal pieces. 5 pieces are shaded.
  2. A square is shown. It is divided into 9 equal pieces. 5 pieces are shaded.

In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.

  1. Two squares are shown. Both are divided into four equal pieces. The square on the left has all 4 pieces shaded. The square on the right has one piece shaded.
  2. Two circles are shown. Both are divided into two equal pieces. The circle on the left has both pieces shaded. The circle on the right has one piece shaded.

In the following exercises, convert the improper fraction to a mixed number.

  1. 5815
  2. 6311

In the following exercises, convert the mixed number to an improper fraction.

  1. 1214
  2. 945
  3. Find three fractions equivalent to 25. Show your work, using figures or algebra.
  4. Find three fractions equivalent to 43. Show your work, using figures or algebra.

In the following exercises, locate the numbers on a number line.

  1. 58,43,334, 4
  2. 14,14,113,113,72,72

In the following exercises, order each pair of numbers, using < or >.

  1. −1___25
  2. 212___−3

4.2 - Multiply and Divide Fractions

In the following exercises, simplify.

  1. 6384
  2. 90120
  3. 14a14b
  4. 8x8y

In the following exercises, multiply.

  1. 25813
  2. 13127
  3. 29(4532)
  4. 6m 411
  5. 14 (−32)
  6. 315178

In the following exercises, find the reciprocal.

  1. 29
  2. 154
  3. 3
  4. 14
  5. Fill in the chart.
Opposite Absolute Value Reciprocal
513      
310      
94      
-12      

In the following exercises, divide.

  1. 23÷16
  2. (3x5)÷(2y3)
  3. 45÷ 3
  4. 8 ÷223
  5. 823÷1112

4.3 - Multiply and Divide Mixed Numbers and Complex Fractions

In the following exercises, perform the indicated operation.

  1. 315178
  2. 57124411
  3. 8 ÷223
  4. 823÷1112

In the following exercises, translate the English phrase into an algebraic expression.

  1. the quotient of 8 and y
  2. the quotient of V and the difference of h and 6

In the following exercises, simplify the complex fraction.

  1. 5845
  2. 894
  3. n438
  4. 156112

In the following exercises, simplify.

  1. 5+165
  2. 8452312
  3. 87+5(810)9364

4.4 - Add and Subtract Fractions with Common Denominators

In the following exercises, add.

  1. 38+28
  2. 45+15
  3. 25+15
  4. 1532+932
  5. x10+710

In the following exercises, subtract.

  1. 811611
  2. 1112512
  3. 45y5
  4. 3130730
  5. 32(32)
  6. 1115515(215)

4.5 - Add and Subtract Fractions with Different Denominators

In the following exercises, find the least common denominator.

  1. 13 and 112
  2. 13 and 45
  3. 815 and 1120
  4. 34,16, and 510

In the following exercises, change to equivalent fractions using the given LCD.

  1. 13 and 15, LCD = 15
  2. 38 and 56, LCD = 24
  3. 916 and 512, LCD = 48
  4. 13,34 and 45, LCD = 60

In the following exercises, perform the indicated operations and simplify.

  1. 15+23
  2. 111223
  3. 91034
  4. 11361120
  5. 2225+940
  6. y1013
  7. 25+(59)
  8. 411÷27d
  9. 25+(3n8)(29n)
  10. (23)2(58)2
  11. (1112+38)÷(56110)

In the following exercises, evaluate.

  1. y − 45 when (a) y = 45 (b) y = 14
  2. 6mn2 when m = 34 and n = 13

4.6 - Add and Subtract Mixed Numbers

In the following exercises, perform the indicated operation.

  1. 413+913
  2. 625+735
  3. 5811+2411
  4. 358+378
  5. 9132041120
  6. 23101910
  7. 211121712
  8. 86112911

4.7 - Solve Equations with Fractions

In the following exercises, determine whether the each number is a solution of the given equation.

  1. x − 12 = 16:
    1. x = 1
    2. x = 23
    3. x = 13
  2. y + 35 = 59:
    1. y = 12
    2. y = 5245
    3. y = 245

In the following exercises, solve the equation.

  1. n + 911 = 411
  2. x − 16 = 76
  3. h − (78) = 25
  4. x5 = −10
  5. −z = 23

In the following exercises, translate and solve.

  1. The sum of two-thirds and n is 35.
  2. The difference of q and one-tenth is 12.
  3. The quotient of p and −4 is −8.
  4. Three-eighths of y is 24.

PRACTICE TEST

Convert the improper fraction to a mixed number.

  1. 195

Convert the mixed number to an improper fraction.

  1. 327

Locate the numbers on a number line.

  1. 12,123,234, and 94

In the following exercises, simplify.

  1. 520
  2. 18r27s
  3. 1334
  4. 35 15
  5. −36u(49)
  6. 57124411
  7. 56÷512
  8. 711÷(711)
  9. 9a10÷15a8
  10. 625÷ 4
  11. (1556)÷(316)
  12. 6611
  13. p2q5
  14. 415223
  15. 924294
  16. 2d+9d
  17. 313+(413)
  18. 2225+940
  19. 25+(75)
  20. 310+(58)
  21. 34÷x3
  22. 2322(34)2
  23. 514+18956

Evaluate.

  1. x + 13 when (a) x = 23 (b) x = 56

In the following exercises, solve the equation.

  1. y + 35 = 75
  2. a − 310 = 910
  3. f + (23) = 512
  4. m2 = −16
  5. 23c = 18
  6. Translate and solve: The quotient of p and −4 is −8. Solve for p.

Contributors and Attributions


This page titled 4.E: Fractions (Exercises) is shared under a not declared license and was authored, remixed, and/or curated by OpenStax.

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