Numbers and Their Applications: Get Stronger Answer Key

Name Decimals

In the following exercises, name each decimal.

  1. five and five tenths
  2. five and one hundredth
  3. eight and seventy-one hundredths
  4. two thousandths
  5. three hundred eighty-one thousandths
  6. negative seventeen and nine tenths

Write Decimals

In the following exercises, translate the name into a decimal number.

  1. [latex]8.03[/latex]
  2. [latex]29.81[/latex]
  3. [latex]0.7[/latex]
  4. [latex]0.001[/latex]
  5. [latex]0.029[/latex]
  6. [latex]−11.0009[/latex]
  7. [latex]13.0395[/latex]

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

  1. [latex]1 \frac{99}{100}[/latex]
  2. [latex]15 \frac{7}{10}[/latex]
  3. [latex]\frac{239}{1000}[/latex]
  4. [latex]\frac{13}{100}[/latex]
  5. [latex]\frac{11}{1000}[/latex]
  6. [latex]- \frac{7}{100000}[/latex]
  7. [latex]6 \frac{2}{5}[/latex]
  8. [latex]7 \frac{1}{20}[/latex]
  9. [latex]4 \frac{3}{500}[/latex]
  10. [latex]10 \frac{1}{4}[/latex]
  11. [latex]1 \frac{81}{250}[/latex]
  12. [latex]14 \frac{1}{8}[/latex]

Locate Decimals on the Number Line

  1. There is a number line shown with integers from negative 4 to 4. There is a red dot between 0 and 1 labeled 0.8.
  2. There is a number line shown with integers from negative 4 to 4. There is a red dot between negative 1 and 0 labeled negative 0.2.
  3. This is an image of a number line. It spans from negative 5 on the left to 5 on the right. To the right of 0 are tick marks with the numbers 1, 2, 3, 4, 5 on the number line. To the left of the zero are tick marks with the numbers negative 1, negative 2, negative 3, negative 4, and negative 5. A point is plotted at 3.1.
  4. There is a number line shown with integers from negative 4 to 4. There is a red dot between negative 3 and negative 2 labeled negative 2.5.

Order Decimals

In the following exercises, order each of the following pairs of numbers, using [latex]< or >[/latex].

  1. [latex]>[/latex]
  2. [latex]<[/latex]
  3. [latex]>[/latex]
  4. [latex]>[/latex]
  5. [latex]<[/latex]
  6. [latex]<[/latex]

Round Decimals

In the following exercises, round each number to the nearest tenth.

  1. [latex]0.7[/latex]
  2. [latex]2.8[/latex]

In the following exercises, round each number to the nearest hundredth.

  1. [latex]0.85[/latex]
  2. [latex]5.79[/latex]
  3. [latex]0.30[/latex]
  4. [latex]4.10[/latex]

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

  1. ⓐ [latex]5.78[/latex] ⓑ [latex]5.8[/latex] ⓒ [latex]6[/latex]
  2. ⓐ [latex]63.48[/latex] ⓑ [latex]63.5[/latex] ⓒ [latex]63[/latex]

Operations on Decimals

Add and Subtract Decimals

In the following exercises, add or subtract.

  1. [latex]24.48[/latex]
  2. [latex]170.88[/latex]
  3. [latex]−9.23[/latex]
  4. [latex]49.73[/latex]
  5. [latex]−40.91[/latex]
  6. [latex]−7.22[/latex]
  7. [latex]−13.5[/latex]
  8. [latex]35.8[/latex]
  9. [latex]−27.5[/latex]
  10. [latex]15.73[/latex]
  11. [latex]42.51[/latex]
  12. [latex]102.212[/latex]
  13. [latex]51.31[/latex]
  14. [latex]−4.89[/latex]

Multiply Decimals

In the following exercises, multiply.

  1. [latex]0.12[/latex]
  2. [latex]0.144[/latex]
  3. [latex]42.008[/latex]
  4. [latex]26.7528[/latex]
  5. [latex]−11.653[/latex]
  6. [latex]337.8914[/latex]
  7. [latex]2.2302[/latex]
  8. [latex]1.305[/latex]
  9. [latex]92.4[/latex]
  10. [latex]55,200[/latex]

Divide Decimals

In the following exercises, divide.

  1. [latex]0.03[/latex]
  2. [latex]0.19[/latex]
  3. [latex]$0.71[/latex]
  4. [latex]$2.44[/latex]
  5. [latex]3[/latex]
  6. [latex]−4.8[/latex]
  7. [latex]35[/latex]
  8. [latex]2.08[/latex]
  9. [latex]150[/latex]
  10. [latex]20[/latex]

Mixed Practice

In the following exercises, simplify.

  1. [latex]19.2[/latex]
  2. [latex]12.09[/latex]
  3. [latex]32.706[/latex]
  4. [latex]$48.60[/latex]
  5. [latex]20[/latex]
  6. [latex]2[/latex]
  7. [latex]$17.80[/latex]

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

  1. [latex]$24.89[/latex]
  2. [latex]$29.06[/latex]
  3. [latex]$3.19[/latex]
  4. [latex]181.7 pounds[/latex]
  5. [latex]$15.00[/latex]
  6. [latex]$296.00[/latex]
  7. [latex]$12.75[/latex]
    • [latex]$3[/latex]
    • [latex]$1.50[/latex]
    • [latex]$1[/latex]
  8. [latex]$18.64[/latex]
  9. [latex]$259.45[/latex]

Exploring The Relationship Between Decimals and Fractions

Convert Fractions to Decimals

  1. [latex]0.4[/latex]
  2. [latex]−0.375[/latex]
  3. [latex]0.85[/latex]
  4. [latex]2.75[/latex]
  5. [latex]−12.4[/latex]
  6. [latex]-0.5[/latex]
  7. [latex]-1.36[/latex]
  8. [latex]-0.135[/latex]

Convert Fractions to Decimals and Simplify

In the following exercises, simplify the expression.

  1. [latex]7[/latex]
  2. [latex]3.025[/latex]
  3. [latex]10.58[/latex]

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using [latex]< or >[/latex].

  1. [latex]<[/latex]
  2. [latex]>[/latex]
  3. [latex]<[/latex]
  4. [latex]<[/latex]
  5. [latex]>[/latex]
  6. [latex]>[/latex]
  7. [latex]0.55, \frac{9}{16}, \frac{3}{5}[/latex]
  8. [latex]\frac{5}{8}, \frac{13}{20}, 0.702[/latex]
  9. [latex]- \frac{7}{20}, - \frac{1}{3}, -0.3[/latex]
  10. [latex]- \frac{7}{9}, - \frac{3}{4}, -0.7[/latex]
  11. [latex]−187[/latex]
  12. [latex]295.12[/latex]
  13. [latex]6.15[/latex]
  14. [latex]20.2[/latex]
  15. [latex]107.11[/latex]
  16. [latex]449[/latex]
  17. [latex]9.14[/latex]
  18. [latex]−0.23[/latex]
  19. [latex]−3.25[/latex]
  20. [latex]16.29[/latex]
  21. [latex]632.045[/latex]
  22. [latex]−5.742[/latex]

Find the Circumference and Area of Circles

  1. [latex]31.4[/latex] in ⓑ [latex]78.5[/latex] sq. in
  2. [latex]56.52[/latex] ft ⓑ [latex]254.34[/latex] sq. ft
  3. [latex]288.88[/latex] cm ⓑ [latex]6644.24[/latex] sq. cm
  4. [latex]116.808/latex] m ⓑ [latex]1086.3144/latex] sq. ml
  5. ⓐ [latex]\frac{22}{5}[/latex] mile ⓑ [latex]frac{77}{50}[/latex] sq. mile
  6. ⓐ [latex]\frac{33}{14}[/latex] yard ⓑ[latex]\frac{99}{224}[/latex] sq. yard
  7. ⓐ no ⓑ no ⓒ yes
  8. ⓐ no ⓑ yes ⓒ no
  9. [latex]y = 2.8[/latex]
  10. [latex]f = −0.85[/latex]
  11. [latex]a = −7.9[/latex]
  12. [latex]c = −4.65[/latex]
  13. [latex]n = 4.4[/latex]
  14. [latex]x = −3.5[/latex]
  15. [latex]j = −4.68[/latex]
  16. [latex]m = −1.42[/latex]
  17. [latex]x = 7[/latex]
  18. [latex]c = −5[/latex]
  19. [latex]p = 3[/latex]
  20. [latex]q = −80[/latex]
  21. [latex]x = 20[/latex]
  22. [latex]z = 2.7[/latex]
  23. [latex]a = −8[/latex]
  24. [latex]x = −0.28[/latex]
  25. [latex]p = 8.25[/latex]
  26. [latex]r = 7.2[/latex]

Mixed Practice

  1. [latex]x = −6[/latex]
  2. [latex]p = −10[/latex]
  3. [latex]m = 8[/latex]
  4. [latex]q = - \frac{3}{4}[/latex]
  5. [latex]n-1.9 = 3.4; 5.3[/latex]
  6. [latex]−6.2x = −4.96; 0.8[/latex]
  7. [latex]\frac{y}{-1.7} = -5; 8.5[/latex]
  8. [latex]n + (−7.3) = 2.4; 9.7[/latex]

Name Decimals

  1. three hundred seventy-five thousandths
  2. five and twenty-four hundredths
  3. negative four and nine hundredths
  4. [latex]0.09[/latex]
  5. [latex]10.035[/latex]
  6. [latex]−0.05[/latex]
  7. [latex]\frac{33}{40}[/latex]
  8. [latex]3 \frac{16}{25}[/latex]
  9. [latex]<[/latex]
  10. [latex]<[/latex]
  11. ⓐ [latex]12.53[/latex] ⓑ [latex]12.5[/latex] ⓒ [latex]13[/latex]
  12. ⓐ [latex]5.90[/latex] ⓑ [latex]5.9[/latex] ⓒ [latex]6[/latex]
  13. [latex]24.67[/latex]
  14. [latex]24.831[/latex]
  15. [latex]−2.37[/latex]

Multiply Decimals

  1. [latex]−1.6[/latex]
  2. [latex]15,400[/latex]
  3. [latex]0.18[/latex]
  4. [latex]4[/latex]
  5. [latex]200[/latex]
  6. [latex]$28.22[/latex]
  7. [latex]$1.79[/latex]
  8. [latex]0.875[/latex]
  9. [latex]−5.25[/latex]
  10. [latex]−0.54[/latex]

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using [latex]< or >[/latex]

  1. [latex]>[/latex]
  2. [latex]>[/latex]
  3. [latex]>[/latex]
  4. [latex]\frac{11}{15}, 0.75, \frac{7}{9}[/latex]
  5. [latex]6.03[/latex]
  6. [latex]1.975[/latex]
  7. [latex]−0.22[/latex]
  8. ⓐ [latex]21.98[/latex] ft. ⓑ [latex]38.465[/latex] sq. ft.
  9. ⓐ [latex]34.54[/latex] cm ⓑ [latex]379.94[/latex] sq. cm

Use the Definition of Percents

  1. [latex]\frac{6}{100}[/latex]
  2. [latex]\frac{32}{1000}[/latex]
  3. ⓐ [latex]\frac{57}{100}[/latex] ⓑ [latex]57\%[/latex]
  4. ⓐ [latex]\frac{42}{100}[/latex] ⓑ [latex]42\%[/latex]
  5. [latex]\frac{1}{25}[/latex]
  6. [latex]\frac{17}{100}[/latex]
  7. [latex]\frac{13}{25}[/latex]
  8. [latex]\frac{5}{4}[/latex]
  9. [latex]\frac{3}{8}[/latex]
  10. [latex]\frac{23}{125}[/latex]
  11. [latex]0.05[/latex]
  12. [latex]0.01[/latex]
  13. [latex]0.63[/latex]
  14. [latex]0.4[/latex]
  15. [latex]1.15[/latex]
  16. [latex]1.5[/latex]
  17. [latex]0.214[/latex]
  18. [latex]0.078[/latex]
  19. ⓐ [latex]\frac{3}{200}[/latex] ⓑ [latex]0.015[/latex]
  20. ⓐ [latex]\frac{7023}{10000}[/latex] ⓑ [latex]0.7023[/latex]
  21. ⓐ [latex]\frac{1}{4}[/latex] ⓑ[latex]0.25[/latex]
  22. ⓐ [latex]\frac{3}{5}[/latex] ⓑ[latex]0.6[/latex]
  23. [latex]1\%[/latex]
  24. [latex]18\%[/latex]
  25. [latex]135\%[/latex]
  26. [latex]300\%[/latex]
  27. [latex]0.9\%[/latex]
  28. [latex]8.75\%[/latex]
  29. [latex]150\%[/latex]
  30. [latex]225.4\%[/latex]
  31. [latex]25\%[/latex]
  32. [latex]37.5\%[/latex]
  33. [latex]175\%[/latex]
  34. [latex]680\%[/latex]
  35. [latex]41.7\%[/latex]
  36. [latex]266.6\%[/latex]
  37. [latex]42.9\%[/latex]
  38. [latex]55.6\%[/latex]
  39. [latex]25\%[/latex]
  40. [latex]35\%[/latex]

Translate and Solve Basic Percent Equations

  1. [latex]54[/latex]
  2. [latex]26.88[/latex]
  3. [latex]162.5[/latex]
  4. [latex]18,000[/latex]
  5. [latex]112[/latex]
  6. [latex]108[/latex]
  7. [latex]$35[/latex]
  8. [latex]$940[/latex]
  9. [latex]30\%[/latex]
  10. [latex]36\%[/latex]
  11. [latex]150%[/latex]
  12. [latex]175%[/latex]

Solve Applications of Percents

  1. [latex]$11.88[/latex]
  2. [latex]$259.80[/latex]
  3. [latex]24.2[/latex] grams
  4. [latex]2,407[/latex] grams
  5. [latex]45\%[/latex]
  6. [latex]25\%[/latex]

Find Percent Increase and Percent Decrease

  1. [latex]13.2\%[/latex]
  2. [latex]125\%[/latex]
  3. [latex]72.7\%[/latex]
  4. [latex]2.5\%[/latex]
  5. [latex]11\%[/latex]
  6. [latex]5.5\%[/latex]
  7. ⓐ [latex]$4.20[/latex] ⓑ [latex]$88.20[/latex]
  8. ⓐ [latex]$9.68[/latex] ⓑ [latex]$138.68[/latex]
  9. ⓐ [latex]$17.13[/latex] ⓑ [latex]$267.13[/latex]
  10. ⓐ [latex]$61.45[/latex] ⓑ [latex]$1,260.45[/latex]
  11. [latex]6.5\%[/latex]
  12. [latex]6.85\%[/latex]
  13. [latex]$20.25[/latex]
  14. [latex]$975[/latex]
  15. [latex]$859.25[/latex]
  16. [latex]3\%[/latex]
  17. [latex]16\%[/latex]
  18. [latex]15.5\%[/latex]
  19. [latex]$139[/latex]
  20. [latex]$125[/latex]
  21. ⓐ [latex]$26.97[/latex] ⓑ [latex]$17.98[/latex]
  22. ⓐ [latex]$128.37[/latex] ⓑ [latex]$260.63[/latex]
  23. ⓐ [latex]$332.48[/latex] ⓑ [latex]$617.50[/latex]
  24. ⓐ[latex]$576[/latex] ⓑ [latex]30\%[/latex]
  25. ⓐ [latex]$53.25[/latex] ⓑ [latex]15\%[/latex]
  26. ⓐ [latex]$370[/latex] ⓑ [latex]43.5\%[/latex]

Solve Mark-up Applications

  1. ⓐ [latex]$7.20[/latex] ⓑ [latex]$23.20[/latex]
  2. ⓐ $[latex]0.20[/latex] ⓑ [latex]$0.80[/latex]
  3. ⓐ [latex]$258.75[/latex] ⓑ [latex]$373.75[/latex]
  4. [latex]$90[/latex]
  5. [latex]$579.96[/latex]
  6. [latex]$14,167[/latex]
  7. [latex]$3,280[/latex]
  8. [latex]$860[/latex]
  9. [latex]$24,679.91[/latex]
  10. [latex]4\%[/latex]
  11. [latex]5.5\%[/latex]
  12. [latex]$116[/latex]
  13. [latex]$4,836[/latex]
  14. [latex]3\%[/latex]
  15. [latex]3.75\%[/latex]
  16. [latex]$35,000[/latex]
  17. [latex]$3,345[/latex]
  18. [latex]$332.10[/latex]
  19. [latex]$195.00[/latex]

Solving Proportions and their Applications

  1. [latex]\frac{4}{15} = \frac{36}{135}[/latex]
  2. [latex]\frac{12}{5} = \frac{96}{40}[/latex]
  3. [latex]\frac{5}{7} = \frac{115}{161}[/latex]
  4. [latex]\frac{8}{1} = \frac{48}{6}[/latex]
  5. [latex]\frac{9.36}{18} = \frac{2.6}{5}[/latex]
  6. [latex]\frac{18.04}{11} = \frac{4.92}{3}[/latex]
  7. yes
  8. no
  9. no
  10. yes
  11. [latex]x = 49[/latex]
  12. [latex]z = 7[/latex]
  13. [latex]a = 9[/latex]
  14. [latex]p = -11[/latex]
  15. [latex]a = 7[/latex]
  16. [latex]c = 2[/latex]
  17. [latex]j = 0.6[/latex]
  18. [latex]m = 4[/latex]
  19. [latex]9[/latex] ml
  20. [latex]114[/latex], no
  21. [latex]159[/latex] cal
  22. [latex]\frac{3}{4}[/latex] cup
  23. [latex]$252.50[/latex]
  24. [latex]1.25[/latex]
  25. [latex]48[/latex] quarters
  26. [latex]19, $58.71[/latex]
  27. [latex]12.8[/latex] hours
  28. [latex]4[/latex] bags
  29. [latex]\frac{n}{250} = \frac{35}{100}[/latex]
  30. [latex]\frac{n}{47} = \frac{110}{100}[/latex]
  31. [latex]\frac{45}{n} = \frac{30}{100}[/latex]
  32. [latex]\frac{90}{n} = \frac{150}{100}[/latex]
  33. [latex]\frac{17}{85} = \frac{p}{100}[/latex]
  34. [latex]\frac{340}{260} = \frac{p}{100}[/latex]
  35. [latex]117[/latex]
  36. [latex]16.56[/latex]
  37. [latex]45.5[/latex]
  38. [latex]1464[/latex]
  39. [latex]$45[/latex]
  40. [latex]$164[/latex]
  41. [latex]25\%[/latex]
  42. [latex]12.5\%[/latex]

Using the Language of Algebra

Use Variables and Algebraic Symbols

  1. [latex]16[/latex] minus [latex]9[/latex], the difference of sixteen and nine
  2. [latex]5[/latex] times [latex]6[/latex], the product of five and six
  3. [latex]28[/latex] divided by [latex]4[/latex], the quotient of twenty-eight and four
  4. [latex]x[/latex] plus [latex]8[/latex], the sum of [latex]x[/latex] and eight
  5. [latex]2[/latex] times [latex]7[/latex], the product of two and seven
  6. fourteen is less than twenty-one
  7. thirty-six is greater than or equal to nineteen
  8. [latex]3[/latex] times [latex]n[/latex] equals [latex]24[/latex], the product of three and [latex]n[/latex] equals twenty-four
  9. [latex]y[/latex] minus [latex]1[/latex] is greater than [latex]6[/latex], the difference of [latex]y[/latex] and one is greater than six
  10. [latex]2[/latex] is less than or equal to [latex]18[/latex] divided by [latex]6[/latex]; [latex]2[/latex] is less than or equal to the quotient of eighteen and six
  11. [latex]2[/latex] is less than or equal to [latex]18[/latex] divided by [latex]6[/latex]; [latex]2[/latex] is less than or equal to the quotient of eighteen and six

Identify Expressions and Equations

In the following exercises, determine if each is an expression or an equation.

  1. equation
  2. expression
  3. expression
  4. equation

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

  1. [latex]3^{7}[/latex]
  2. [latex]x^{5}[/latex]

Simplify Expressions with Exponents

In the following exercises, write in expanded form.

  1. [latex]125[/latex]
  2. [latex]256[/latex]

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

  1. [latex]43[/latex]
  2. [latex]55[/latex]
  3. [latex]5[/latex]
  4. [latex]34[/latex]
  5. [latex]58[/latex]
  6. [latex]6[/latex]
  7. [latex]13[/latex]
  8. [latex]4[/latex]
  9. [latex]35[/latex]
  10. [latex]10[/latex]
  11. [latex]41[/latex]
  12. [latex]81[/latex]
  13. [latex]149[/latex]
  14. [latex]50[/latex]

Evaluating, Simplifying, and Translating Algebraic Expressions

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

  1. [latex]22[/latex]
  2. [latex]26[/latex]
  3. [latex]144[/latex]
  4. [latex]32[/latex]
  5. [latex]27[/latex]
  6. [latex]21[/latex]
  7. [latex]41[/latex]
  8. [latex]9[/latex]
  9. [latex]73[/latex]
  10. [latex]73[/latex]
  11. [latex]54[/latex]

Identify Terms, Coefficients, and Like Terms

In the following exercises, list the terms in the given expression.

  1. [latex]15x^{2}, 6x, 2[/latex]
  2. [latex]10y^{3}, y, 2[/latex]
  3. [latex]8[/latex]
  4. [latex]5[/latex]
  5. [latex]x^{3}[/latex], [latex]8x^{3}[/latex] and [latex]14, 5[/latex]
  6. [latex]16ab[/latex] and [latex]4ab[/latex]; [latex]16b^{2}[/latex] and [latex]9b^{2}[/latex]

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

  1. [latex]13x[/latex]
  2. [latex]26a[/latex]
  3. [latex]7c[/latex]
  4. [latex]12x + 8[/latex]
  5. [latex]10u + 3[/latex]
  6. [latex]12p + 10[/latex]
  7. [latex]22a + 1[/latex]
  8. [latex]17x^{2} + 20x + 16[/latex]

Translate English Phrases into Algebraic Expressions

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

  1. [latex]8 + 12[/latex]
  2. [latex]14 − 9[/latex]
  3. [latex]9 ⋅ 7[/latex]
  4. [latex]36 ÷ 9[/latex]
  5. [latex]x − 4[/latex]
  6. [latex]6y[/latex]
  7. [latex]8x + 3x[/latex]
  8. [latex]\frac{y}{3}[/latex]
  9. [latex]8 (y − 9)[/latex]
  10. [latex]5 (x + y)[/latex]

Translate English Phrases into Algebraic Expressions

In the following exercises, write an algebraic expression.

  1. [latex]b + 15[/latex]
  2. [latex]b − 4[/latex]
  3. [latex]2n − 7[/latex]