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2.5 Solve Equations with Fractions or Decimals

Clearing fraction coefficients by multiplying through by the LCD, and handling decimal coefficients by scaling up to whole numbers.

Elementary Algebra 2e, 2.5 Solve Equations with Fractions or Decimals

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52 exercises

2.5 Exercise 1

Before you get started, take this readiness quiz.

Multiply: 8·38.8 \cdot \frac{3}{8} .
If you missed this problem, review the reference.

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2.5 Exercise 2

Find the LCD of 56\frac{5}{6} and 14\frac{1}{4}.
If you missed this problem, review the reference.

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2.5 Exercise 3

Multiply 4.78 by 100.
If you missed this problem, review the reference.

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2.5 Exercise 5

Solve: 14x+12=58\frac{1}{4} x + \frac{1}{2} = \frac{5}{8}.

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2.5 Exercise 6

Solve: 18x+12=14\frac{1}{8} x + \frac{1}{2} = \frac{1}{4}.

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2.5 Exercise 8

Solve: 7=12x+34x−23x7 = \frac{1}{2} x + \frac{3}{4} x - \frac{2}{3} x.

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2.5 Exercise 9

Solve: −1=12u+14u−23u−1 = \frac{1}{2} u + \frac{1}{4} u - \frac{2}{3} u.

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2.5 Exercise 11

Solve: x+13=16x−12x + \frac{1}{3} = \frac{1}{6} x - \frac{1}{2}.

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2.5 Exercise 12

Solve: c+34=12c−14c + \frac{3}{4} = \frac{1}{2} c - \frac{1}{4}.

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2.5 Exercise 14

Solve: −11=12(6p+2)−11 = \frac{1}{2} \left(6 p + 2\right).

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2.5 Exercise 15

Solve: 8=13(9q+6)8 = \frac{1}{3} \left(9 q + 6\right).

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2.5 Exercise 17

Solve: 15(n+3)=14(n+2)\frac{1}{5} \left(n + 3\right) = \frac{1}{4} \left(n + 2\right).

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2.5 Exercise 18

Solve: 12(m−3)=14(m−7)\frac{1}{2} \left(m - 3\right) = \frac{1}{4} \left(m - 7\right).

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2.5 Exercise 20

Solve: 4y−73=y6\frac{4 y - 7}{3} = \frac{y}{6}.

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2.5 Exercise 21

Solve: −2z−54=z8\frac{−2 z - 5}{4} = \frac{z}{8}.

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2.5 Exercise 23

Solve: b10+2=b4+5\frac{b}{10} + 2 = \frac{b}{4} + 5.

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2.5 Exercise 24

Solve: c6+3=c3+4\frac{c}{6} + 3 = \frac{c}{3} + 4.

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2.5 Exercise 26

Solve: 3r+56+1=4r+33\frac{3 r + 5}{6} + 1 = \frac{4 r + 3}{3}.

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2.5 Exercise 27

Solve: 2s+32+1=3s+24\frac{2 s + 3}{2} + 1 = \frac{3 s + 2}{4}.

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2.5 Exercise 29

Solve: 0.14h+0.12=0.35h−2.40.14 h + 0.12 = 0.35 h - 2.4.

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2.5 Exercise 30

Solve: 0.65k−0.1=0.4k−0.350.65 k - 0.1 = 0.4 k - 0.35.

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2.5 Exercise 32

Solve: 0.25n+0.05(n+5)=2.950.25 n + 0.05 \left(n + 5\right) = 2.95.

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2.5 Exercise 33

Solve: 0.10d+0.05(d−5)=2.150.10 d + 0.05 \left(d - 5\right) = 2.15.

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2.5 Exercise 35

Solve each equation with fraction coefficients.

34x−12=14\frac{3}{4} x - \frac{1}{2} = \frac{1}{4}

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2.5 Exercise 37

Solve each equation with fraction coefficients.

56y−13=−76\frac{5}{6} y - \frac{1}{3} = - \frac{7}{6}

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2.5 Exercise 39

Solve each equation with fraction coefficients.

58b+12=−34\frac{5}{8} b + \frac{1}{2} = - \frac{3}{4}

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2.5 Exercise 41

Solve each equation with fraction coefficients.

2=35x−13x+25x2 = \frac{3}{5} x - \frac{1}{3} x + \frac{2}{5} x

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2.5 Exercise 43

Solve each equation with fraction coefficients.

56n−14n−12n=−2\frac{5}{6} n - \frac{1}{4} n - \frac{1}{2} n = −2

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2.5 Exercise 45

Solve each equation with fraction coefficients.

x+34=12x−54x + \frac{3}{4} = \frac{1}{2} x - \frac{5}{4}

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2.5 Exercise 47

Solve each equation with fraction coefficients.

32z+13=z−23\frac{3}{2} z + \frac{1}{3} = z - \frac{2}{3}

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2.5 Exercise 49

Solve each equation with fraction coefficients.

12a−14=16a+112\frac{1}{2} a - \frac{1}{4} = \frac{1}{6} a + \frac{1}{12}

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2.5 Exercise 51

Solve each equation with fraction coefficients.

13x+25=15x−25\frac{1}{3} x + \frac{2}{5} = \frac{1}{5} x - \frac{2}{5}

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2.5 Exercise 53

Solve each equation with fraction coefficients.

1=15(15x−10)1 = \frac{1}{5} \left(15 x - 10\right)

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2.5 Exercise 55

Solve each equation with fraction coefficients.

15(q+3)=12(q−3)\frac{1}{5} \left(q + 3\right) = \frac{1}{2} \left(q - 3\right)

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2.5 Exercise 57

Solve each equation with fraction coefficients.

13(x+5)=56\frac{1}{3} \left(x + 5\right) = \frac{5}{6}

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2.5 Exercise 59

Solve each equation with fraction coefficients.

4m+26=m3\frac{4 m + 2}{6} = \frac{m}{3}

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2.5 Exercise 61

Solve each equation with fraction coefficients.

3p+63=p2\frac{3 p + 6}{3} = \frac{p}{2}

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2.5 Exercise 63

Solve each equation with fraction coefficients.

v10+1=v4−2\frac{v}{10} + 1 = \frac{v}{4} - 2

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2.5 Exercise 65

Solve each equation with fraction coefficients.

d6+3=d8+2\frac{d}{6} + 3 = \frac{d}{8} + 2

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2.5 Exercise 67

Solve each equation with fraction coefficients.

10y−23+3=10y+19\frac{10 y - 2}{3} + 3 = \frac{10 y + 1}{9}

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2.5 Exercise 69

Solve each equation with fraction coefficients.

3v−62+5=11v−45\frac{3 v - 6}{2} + 5 = \frac{11 v - 4}{5}

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2.5 Exercise 71

Solve each equation with decimal coefficients.

0.4y−4=20.4 y - 4 = 2

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2.5 Exercise 73

Solve each equation with decimal coefficients.

2.1k+3=7.22.1 k + 3 = 7.2

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2.5 Exercise 75

Solve each equation with decimal coefficients.

0.7x+0.4=0.6x+2.40.7 x + 0.4 = 0.6 x + 2.4

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2.5 Exercise 77

Solve each equation with decimal coefficients.

0.48x+1.56=0.58x−0.640.48 x + 1.56 = 0.58 x - 0.64

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2.5 Exercise 79

Solve each equation with decimal coefficients.

1.2x−0.91=0.8x+2.291.2 x - 0.91 = 0.8 x + 2.29

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2.5 Exercise 81

Solve each equation with decimal coefficients.

0.05n+0.10(n+7)=3.550.05 n + 0.10 \left(n + 7\right) = 3.55

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2.5 Exercise 83

Solve each equation with decimal coefficients.

0.10d+0.25(d+7)=5.250.10 d + 0.25 \left(d + 7\right) = 5.25

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2.5 Exercise 85

Solve each equation with decimal coefficients.

0.05(q−8)+0.25q=4.100.05 \left(q - 8\right) + 0.25 q = 4.10

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2.5 Exercise 87

Stamps Paula bought $22.82 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 8 less than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−8)=22.820.49 s + 0.21 \left(s - 8\right) = 22.82 for s, to find the number of 49-cent stamps Paula bought.

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2.5 Exercise 89

If an equation has several fractions, how does multiplying both sides by the LCD make it easier to solve?

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2.5 Exercise 91

In the equation 0.35x+2.1=3.850.35 x + 2.1 = 3.85 what is the LCD? How do you know?

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Adapted from Elementary Algebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Elementary Algebra 2e. Imported at revision 77a933c.