Expressions, Equations, and Functions

The simplified form of $\frac{1}{3}-\frac{2}{9}$.

The simplified form of $\frac{1}{2}+\frac{1}{4}$.

The simplified form of $\frac{1}{2}-\frac{1}{3}$.

The simplified form of $\frac{3}{7}+\frac{5}{14}$.

The simplified form of $\frac{7}{10}-\frac{2}{15}$.

The simplified form of $\frac{3}{8}+\frac{1}{6}$.

The simplified form of $\frac{13}{20}-\frac{2}{5}$.

The simplified form of $-1.6+\left(-3.8\right)$.

The simplified form of $-32.4+\left(-4.5\right)$.

The simplified form of $-38.9+24.2$.

The simplified form of $-9.16-10.17$.

The simplified form of $26.37+\left(-61.1\right)$.

The simplified form of $72.5-\left(-81.3\right)$.

The simplified form of $43.2+\left(-27.9\right)$.

The simplified form of $79.3-\left(-14\right)$.

The simplified form of $1.34-\left(-0.458\right)$.

The simplified form of $-\frac{1}{6}-\frac{2}{3}$.

The simplified form of $\frac{1}{2}-\frac{4}{5}$.

The simplified form of $-\frac{2}{5}+\frac{17}{20}$.

The simplified form of $-\frac{4}{5}+\left(-\frac{1}{3}\right)$.

The simplified form of $-\frac{1}{12}-\left(-\frac{3}{4}\right)$.

The simplified form of $-\frac{7}{8}-\left(-\frac{3}{16}\right)$.

The amount of Earth’s surface is covered by land.

SHORT RESPONSE

Simplify: $\left[10+15\left(2^3\right)\right]÷\left[7\left(2^2\right)-2\right]$

Step 1: $[10+15(8\left)\right]÷\left[7\right(4)-2]$

Step 2: $[10+120]÷[28-2]$

Step 3: $130÷26$

Step 4: $\frac{1}{5}$

Which is the first incorrect step? Explain the error.

Name the property used in each step:

$\begin{array}{c}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{+}\left(4\cdot 2-8\right)\mathbf{=}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{+}\left(8-8\right)\mathbf{\text{ \_\_\_\_\_\_}}\\ \mathbf{=}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{+}\left(0\right)\mathbf{\text{ \_\_\_\_\_\_}}\\ \mathbf{=}\mathbf{6}\mathbf{+}\mathbf{0}\mathbf{\text{ \_\_\_\_\_\_}}\\ \mathbf{=}\mathbf{6}\mathbf{\text{ \_\_\_\_\_\_}}\end{array}$

Name the property used in each step:

$\begin{array}{c}7\cdot \frac{1}{7}+6\left(15÷3-5\right)=7\cdot \frac{1}{7}+6\left(5-5\right)\text{ \_\_\_\_\_\_\_}\\ =7\cdot \frac{1}{7}+6\left(0\right)\text{ \_\_\_\_\_\_\_}\\ =1+6\left(0\right)\text{ \_\_\_\_\_\_\_}\\ =1+0\text{ \_\_\_\_\_\_\_}\\ =1\text{ \_\_\_\_\_\_\_}\end{array}$

The simplified value of the expression $6.5\left(0.13\right)$.

The simplified value of the expression $-5.8\left(2.3\right)$.

Furniture Rafael is buying furnishings for his first apartment. He buys a  couch for \( 300, lamps for \) 30.50, a rug for \( 25.50, and a table for \) 50 . Find the total cost of these items.

Evaluate the following expression. Name the property used in each step:

$\mathbf{6}\mathbf{+}\mathbf{4}\left(19-15\right)$

The simplified value of the expression $42.3÷\left(-6\right)$.

Evaluate each expression using the properties of numbers. Name the property used in each step.

3A. $\mathbf{2}\mathbf{.9}\mathbf{\cdot }\mathbf{4}\mathbf{\cdot }\mathbf{10}$

Evaluate the following expression. Name the property used in each step:

$\mathbf{5}\left(14-5\right)\mathbf{+}\mathbf{6}\left(3+7\right)$

Evaluate each expression using the properties of numbers. Name the property used in each step.

3B. $\frac{\mathbf{5}}{\mathbf{3}}\mathbf{\cdot }\mathbf{25}\mathbf{\cdot }\mathbf{3}\mathbf{\cdot }\mathbf{2}$

The simplified value of the expression $-14.1\left(-2.9\right)$.

Carolyn has 9 quarters, 4 dimes, 7 nickels and 2 pennies, which can be represented as in below:

$\mathbf{9}\left(25\right)\mathbf{+}\mathbf{4}\left(10\right)\mathbf{+}\mathbf{7}\left(5\right)\mathbf{+}\mathbf{2}$

Evaluate the above expression to find how much money she has. Name the property used in each step:

The simplified value of the expression $-78÷\left(-1.3\right)$.

Evaluate the following expression. Name the property used in each step:

$\mathbf{23}\mathbf{+}\mathbf{42}\mathbf{+}\mathbf{37}$

The simplified value of the expression $108÷\left(-0.9\right)$.

Evaluate the following expression. Name the property used in each step:

$\mathbf{2}\mathbf{.75}\mathbf{+}\mathbf{3}\mathbf{.5}\mathbf{+}\mathbf{4}\mathbf{.25}\mathbf{+}\mathbf{1}\mathbf{.5}$

The simplified value of the expression $0.75\left(-6.4\right)$.

Evaluate the following expression. Name the property used in each step:

$\mathbf{3}\mathbf{\cdot }\mathbf{7}\mathbf{\cdot }\mathbf{10}\mathbf{\cdot }\mathbf{2}$

The simplified value of the expression $-23.94÷\left(10.5\right)$.

Evaluate the following expression. Name the property used in each step:

$\frac{1}{4}\cdot 24\cdot \frac{2}{3}$

The simplified value of the expression $-32.4÷\left(21.3\right)$.

The simplified value of the expression $\frac{3}{4}.\frac{1}{5}$.

The simplified value of the expression $\frac{2}{5}.\frac{3}{7}$.

The simplified value of the expression $-\frac{1}{3}.\frac{2}{5}$.

Example 1  Evaluate each expression. Name the property used in each step.

12. $\left[3÷\left(2\cdot 1\right)\right]\frac{\mathbf{2}}{\mathbf{3}}$

The simplified value of the expression $-\frac{2}{3}.\left(-\frac{1}{11}\right)$.