Problem Set 5: Decimals

Practice Makes Perfect

Everyday Math

Writing Exercises

Self Check

Practice Makes Perfect

Everyday Math

Writing Exercises

Self Check

Practice Makes Perfect

Everyday Math

Writing Exercises

Self Check

Practice Makes Perfect

Everyday Math

Writing Exercises

Self Check

Practice Makes Perfect

Everyday Math

Writing Exercises

Self Check

Practice Makes Perfect

Everyday Math

Writing Exercises

Self Check

Chapter Review Exercises

Decimals

Decimal Operations

Decimals and Fractions

Solve Equations with Decimals

Solving Equations With Decimals

Determine Whether a Decimal is a Solution of an Equation In the following exercises, determine whether each number is a solution of the given equation.

[latex]x - 0.8=2.3[/latex]

ⓐ [latex]x=2[/latex] ⓑ [latex]x=-1.5[/latex] ⓒ [latex]x=3.1[/latex]

ⓐ no ⓑ no ⓒ yes

[latex]y+0.6=-3.4[/latex]

ⓐ [latex]y=-4[/latex] ⓑ [latex]y=-2.8[/latex] ⓒ [latex]y=2.6[/latex]

[latex]\frac{h}{1.5}=-4.3[/latex]

ⓐ [latex]h=6.45[/latex] ⓑ [latex]h=-6.45[/latex] ⓒ [latex]h=-2.1[/latex]

ⓐ no ⓑ yes ⓒ no

[latex]0.75k=-3.6[/latex]

ⓐ [latex]k=-0.48[/latex] ⓑ [latex]k=-4.8[/latex] ⓒ [latex]k=-2.7[/latex]

Solve Equations with Decimals In the following exercises, solve the equation.

[latex]y+2.9=5.7[/latex]

y = 2.8

[latex]m+4.6=6.5[/latex]

[latex]f+3.45=2.6[/latex]

f = −0.85

[latex]h+4.37=3.5[/latex]

[latex]a+6.2=-1.7[/latex]

a = −7.9

[latex]b+5.8=-2.3[/latex]

[latex]c+1.15=-3.5[/latex]

c = −4.65

[latex]d+2.35=-4.8[/latex]

[latex]n - 2.6=1.8[/latex]

n = 4.4

[latex]p - 3.6=1.7[/latex]

[latex]x - 0.4=-3.9[/latex]

x = −3.5

[latex]y - 0.6=-4.5[/latex]

[latex]j - 1.82=-6.5[/latex]

j = −4.68

[latex]k - 3.19=-4.6[/latex]

[latex]m - 0.25=-1.67[/latex]

m = −1.42

[latex]q - 0.47=-1.53[/latex]

[latex]0.5x=3.5[/latex]

x = 7

[latex]0.4p=9.2[/latex]

[latex]-1.7c=8.5[/latex]

c = −5

[latex]-2.9x=5.8[/latex]

[latex]-1.4p=-4.2[/latex]

p = 3

[latex]-2.8m=-8.4[/latex]

[latex]-120=1.5q[/latex]

q = −80

[latex]-75=1.5y[/latex]

[latex]0.24x=4.8[/latex]

x = 20

[latex]0.18n=5.4[/latex]

[latex]-3.4z=-9.18[/latex]

z = 2.7

[latex]-2.7u=-9.72[/latex]

[latex]\frac{a}{0.4}=-20[/latex]

a = −8

[latex]\frac{b}{0.3}=-9[/latex]

[latex]\frac{x}{0.7}=-0.4[/latex]

x = −0.28

[latex]\frac{y}{0.8}=-0.7[/latex]

[latex]\frac{p}{-5}=-1.65[/latex]

p = 8.25

[latex]\frac{q}{-4}=-5.92[/latex]

[latex]\frac{r}{-1.2}=-6[/latex]

r = 7.2

[latex]\frac{s}{-1.5}=-3[/latex]

Mixed Practice In the following exercises, solve the equation. Then check your solution.

[latex]x - 5=-11[/latex]

x = −6

[latex]-\frac{2}{5}=x+\frac{3}{4}[/latex]

[latex]p+8=-2[/latex]

p = −10

[latex]p+\frac{2}{3}=\frac{1}{12}[/latex]

[latex]-4.2m=-33.6[/latex]

m = 8

[latex]q+9.5=-14[/latex]

[latex]q+\frac{5}{6}=\frac{1}{12}[/latex]

[latex]q=-\frac{3}{4}[/latex]

[latex]\frac{8.6}{15}=-d[/latex]

[latex]\frac{7}{8}m=\frac{1}{10}[/latex]

[latex]m=\frac{4}{35}[/latex]

[latex]\frac{j}{-6.2}=-3[/latex]

[latex]-\frac{2}{3}=y+\frac{3}{8}[/latex]

[latex]y=-\frac{25}{24}[/latex]

[latex]s - 1.75=-3.2[/latex]

[latex]\frac{11}{20}=-f[/latex]

[latex]f=-\frac{11}{20}[/latex]

[latex]-3.6b=2.52[/latex]

[latex]-4.2a=3.36[/latex]

a = −0.8

[latex]-9.1n=-63.7[/latex]

[latex]r - 1.25=-2.7[/latex]

r = −1.45

[latex]\frac{1}{4}n=\frac{7}{10}[/latex]

[latex]\frac{h}{-3}=-8[/latex]

h = 24

[latex]y - 7.82=-16[/latex]

Translate to an Equation and Solve In the following exercises, translate and solve.

The difference of [latex]n[/latex] and [latex]1.9[/latex] is [latex]3.4[/latex].

[latex]n - 1.9=3.4;5.3[/latex]

The difference [latex]n[/latex] and [latex]1.5[/latex] is [latex]0.8[/latex].

The product of [latex]-6.2[/latex] and [latex]x[/latex] is [latex]-4.96[/latex].

−6.2x = −4.96; 0.8

The product of [latex]-4.6[/latex] and [latex]x[/latex] is [latex]-3.22[/latex].

The quotient of [latex]y[/latex] and [latex]-1.7[/latex] is [latex]-5[/latex].

[latex]\frac{y}{-1.7}=-5;8.5[/latex]

The quotient of [latex]z[/latex] and [latex]-3.6[/latex] is [latex]3[/latex].

The sum of [latex]n[/latex] and [latex]-7.3[/latex] is [latex]2.4[/latex].

n + (−7.3) = 2.4; 9.7

The sum of [latex]n[/latex] and [latex]-5.1[/latex] is [latex]3.8[/latex].

Everyday Math

Shawn bought a pair of shoes on sale for [latex]$78[/latex] . Solve the equation [latex]0.75p=78[/latex] to find the original price of the shoes, [latex]p[/latex].

$104

Mary bought a new refrigerator. The total price including sales tax was [latex]\text{$1,350}[/latex]. Find the retail price, [latex]r[/latex], of the refrigerator before tax by solving the equation [latex]1.08r=1,350[/latex].

Writing Exercises

Think about solving the equation [latex]1.2y=60[/latex], but do not actually solve it. Do you think the solution should be greater than [latex]60[/latex] or less than [latex]60?[/latex] Explain your reasoning. Then solve the equation to see if your thinking was correct.

Answers will vary.

Think about solving the equation [latex]0.8x=200[/latex], but do not actually solve it. Do you think the solution should be greater than [latex]200[/latex] or less than [latex]200?[/latex] Explain your reasoning. Then solve the equation to see if your thinking was correct.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Ratios and Rate

Simplify and Use Square Roots

Chapter Practice Test

Licenses & Attributions