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$37.5+12.23$
$\mathrm{-8.6}+\left(\mathrm{-8.6}\right)$
$100-65.83$
$9.38+60$
Multiply and Divide Decimals
In the following exercises, multiply.
$\left(0.6\right)\left(0.7\right)$
$\left(5.32\right)\left(4.86\right)$
$\left(0.04\right)\left(36.89\right)$
In the following exercises, divide.
$0.27\xf73$
$\mathrm{\$16.99}\xf79$
$5\xf70.04$
Convert Decimals, Fractions, and Percents
In the following exercises, write each decimal as a fraction.
In the following exercises, convert each fraction to a decimal.
$\frac{4}{5}$
$-\phantom{\rule{0.2em}{0ex}}\frac{5}{8}$
$\frac{2}{9}$
$\frac{1}{4}+10.75$
In the following exercises, convert each percent to a decimal.
In the following exercises, convert each decimal to a percent.
Simplify Expressions with Square Roots
In the following exercises, simplify.
$\sqrt{144}$
$\text{\u2212}\sqrt{81}$
Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers
In the following exercises, write as the ratio of two integers.
ⓐ $\mathrm{-15}$ ⓑ 3.591
In the following exercises, list the ⓐ rational numbers, ⓑ irrational numbers.
$0.84,0.79132\text{\u2026},1.\stackrel{\text{\u2013}}{3}$
ⓐ $0.84,1.\stackrel{\text{\u2013}}{3}$ ⓑ $0.79132\text{\u2026},$
$2.3\stackrel{\text{\u2013}}{8},0.572,4.93814\text{\u2026}$
In the following exercises, identify whether each number is rational or irrational.
ⓐ $\sqrt{56}$ ⓑ $\sqrt{16}$
In the following exercises, identify whether each number is a real number or not a real number.
ⓐ $\sqrt{\mathrm{-9}}$ ⓑ $\text{\u2212}\sqrt{169}$
ⓐ not a real number ⓑ real number
ⓐ $\sqrt{\mathrm{-64}}$ ⓑ $\text{\u2212}\sqrt{81}$
In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.
$\mathrm{-4},0,\frac{5}{6},\sqrt{16},\sqrt{18},5.2537\text{\u2026}$
ⓐ $0,\sqrt{16}$ ⓑ $\mathrm{-4},0,\sqrt{16}$ ⓒ $\mathrm{-4},0,\frac{5}{6},\sqrt{16}$ ⓓ $\sqrt{18},5.2537\text{\u2026}$ ⓔ $\mathrm{-4},0,\frac{5}{6},\sqrt{16},\sqrt{18},5.2537\text{\u2026}$
$\text{\u2212}\sqrt{4},0.\stackrel{\text{\u2014}}{36},\frac{13}{3},6.9152\text{\u2026},\sqrt{48},10\frac{1}{2}$
Locate Fractions on the Number Line
In the following exercises, locate the numbers on a number line.
$\frac{1}{3},\frac{7}{4},\frac{13}{5}$
$1\frac{3}{5},\mathrm{-1}\frac{3}{5}$
In the following exercises, order each of the following pairs of numbers, using<or>.
$\mathrm{-1}\_\_\_-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}$
<
$\mathrm{-3}\frac{1}{4}\_\_\_\mathrm{-4}$
$-\phantom{\rule{0.2em}{0ex}}\frac{7}{9}\_\_\_-\phantom{\rule{0.2em}{0ex}}\frac{4}{9}$
>
$\mathrm{-2}\_\_\_-\phantom{\rule{0.2em}{0ex}}\frac{19}{8}$
Locate Decimals on the Number Line
In the following exercises, locate on the number line.
$\mathrm{-0.2}$
In the following exercises, order each of the following pairs of numbers, using<or>.
$0.7\_\_\_0.8$
$\mathrm{-0.27}\_\_\_\mathrm{-0.3}$
Use the Commutative and Associative Properties
In the following exercises, use the Associative Property to simplify.
$30\left(\frac{5}{6}q\right)$
$\left(c+0.2\right)+0.7$
In the following exercises, simplify.
$\frac{1}{4}+\frac{11}{15}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}\right)$
$\frac{14}{11}\xb7\frac{35}{9}\xb7\frac{14}{11}$
$\frac{35}{9}$
$\mathrm{-18}\xb715\xb7\frac{2}{9}$
$\left(\frac{7}{12}+\frac{4}{5}\right)+\frac{1}{5}$
$1\frac{7}{12}$
$\left(3.98d+0.75d\right)+1.25d$
$52m+\left(\mathrm{-20}n\right)+\left(\mathrm{-18}m\right)+\left(\mathrm{-5}n\right)$
Use the Identity and Inverse Properties of Addition and Multiplication
In the following exercises, find the additive inverse of each number.
ⓐ
$\frac{1}{3}$
ⓑ
$5.1$
ⓒ
$\mathrm{-14}$
ⓓ
$-\phantom{\rule{0.2em}{0ex}}\frac{8}{5}$
ⓐ $-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}$ ⓑ $\mathrm{-5.1}$ ⓒ 14 ⓓ $\frac{8}{5}$
ⓐ
$-\phantom{\rule{0.2em}{0ex}}\frac{7}{8}$
ⓑ
$\mathrm{-0.03}$
ⓒ
$17$
ⓓ
$\frac{12}{5}$
In the following exercises, find the multiplicative inverse of each number.
ⓐ 10 ⓑ $-\phantom{\rule{0.2em}{0ex}}\frac{4}{9}$ ⓒ 0.6
ⓐ $\frac{1}{10}$ ⓑ $-\phantom{\rule{0.2em}{0ex}}\frac{9}{4}$ ⓒ $\frac{5}{3}$
ⓐ $-\phantom{\rule{0.2em}{0ex}}\frac{9}{2}$ ⓑ $\mathrm{-7}$ ⓒ 2.1
Use the Properties of Zero
In the following exercises, simplify.
$\frac{0}{9}$
$0\xf7\frac{2}{3}$
In the following exercises, simplify.
$\left(n+6.75\right)+0.25$
$\frac{1}{6}\xb717\xb712$
$9\left(6x-11\right)+15$
Simplify Expressions Using the Distributive Property
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