Write an expression for the total amount of caffeine using the chart from Figure \(1\).

Find the perimeter and area of the three figures.

Label the points on a number line
\(-3.5, -1\displaystyle\frac{1}{4}, \displaystyle\frac{1}{2}, \displaystyle\frac{3}{4}, 2.5\).

Which are the integers? \(\bigg\{-5, -1.75, 0, \displaystyle\frac{2}{3}, 1, \pi, 3\bigg\}\)

Show why each is rational \(\bigg\{-3, -\displaystyle\frac{2}{3}, 0, 0.333\ldots, 0.75\bigg\}\)

Write each expression without absolute value symbols.

1. \(\lvert5\rvert\)

2. \(\lvert-5\rvert\)

3. \(\left\lvert-\displaystyle\frac{1}{2}\right\rvert\)

Simplify.

1. \(\lvert8-3\rvert\)

2. \(\left\lvert3\cdot 2^3+2\cdot 3^2\right\rvert\)

3. \(\lvert9-2\rvert-\lvert8-6\rvert\)

Give the opposite of each number.

1. \(5\)

2. \(-3\)

3. \(\displaystyle\frac{1}{4}\)

4. \(-2.3\)

Add \(3+(-4)\).

Add \(-3+4\).

Add \(-3+(-4)\).

Show \(-5+(-7)=-12\).

Add all combinations of positive and negative \(10\) and \(13\).

Add all combinations of positive and negative \(12\) and \(17\).

Add \(-3+2+(-4)\).

Add \(-8+[2+(-5)]+(-1)\).

Simplify \(-10+2(-8+11)+(-4)\).

Find the next two numbers for each sequence.

1. \(7, 10, 13, \ldots\)

2. \(9.5, 10, 10.5, \ldots\)

3. \(5, 0, -5, \ldots\)

Subtract all possible combinations of positive and negative \(7\) and \(2\).

Subtract all possible combinations of positive and negative \(8\) and \(13\).

Simplify each expression as much as possible.

1. \(7+(-3)-5\)

2. \(8-(-2)-6\)

3. \(-2-(-3+1)-5\)

Simplify \(2\cdot 5-3\cdot 8-4\cdot 9\).

Simplify \(3\cdot2^3-2\cdot4^2\).

Subtract \(7\) from \(-3\).

Subtract \(-5\) from \(2\).

Find the difference of \(9\) and \(2\).

Find the difference of \(3\) and \(-5\).

Multiply.

1. \(3(5)\)

2. \(3(-5)\)

3. \(-3(5)\)

4. \(-3(-5)\)

Multiply.

\[\begin{aligned} &\text{a.} -8(-3) && \text{b.} -10(-5)&\\ &\text{c.} -4(-7) && \text{d.}\, 5(-7)&\\ &\text{e.} -4(8) && \text{f.} -6(10)\end{aligned}\]

Simplify.

\[\begin{aligned} &\text{a.} -5(-3)(-4) && \text{b.}\, 4(-3)+6(-5)-10&\\ &\text{c.}\, (-2)^3 && \text{d.} -3(-2)^3-5(-4)^2&\\ &\text{e.}\, 6-4(7-2)\end{aligned}\]

Divide.

\[\begin{aligned} &\text{a.}\, \displaystyle\frac{12}{6} && \text{b.}\,\displaystyle\frac{12}{-6}& && \text{c.}\,\displaystyle\frac{-12}{6}& && \text{d.}\,\displaystyle\frac{-12}{-6}&\\ &\text{e.}\,\displaystyle\frac{15}{-3} && \text{f.} \,\displaystyle\frac{-40}{-5}& && \text{g.}\,\displaystyle\frac{-14}{2}&\end{aligned}\]

Simplify as much as possible.

1. \(\displaystyle\frac{-4(5)}{6}\)

2. \(\displaystyle\frac{30}{-4-5}\)

Simplify.

1. \(\displaystyle\frac{2(-3)+4}{12}\)

2. \(\displaystyle\frac{5(-4)+6(-1)}{2(3)-4(1)}\)

Simplify.

1. \(\displaystyle\frac{5^2-3^2}{-5+3}\)

2. \(\displaystyle\frac{(3+2)^2}{-3^2-2^2}\)

Find the net change in calories using the bar graphs from Figure \(1\) and Figure \(2\).

Factor \(60\) into the product of primes.

Factor \(630\) into the product of primes.

Reduce \(\displaystyle\frac{210}{231}\)

Write \(\displaystyle\frac{3}{4}\) with denominator \(20\).

Multiply \(\displaystyle\frac{3}{4}\cdot \displaystyle\frac{5}{7}\)

Multiply \(7\left(\displaystyle\frac{1}{3}\right)\)

Multiply \(\left(\displaystyle\frac{2}{3}\right)^3\)

Multiply.

1. \(-\displaystyle\frac{3}{4}\left(\displaystyle\frac{5}{7}\right)\)

2. \(-6\left(\displaystyle\frac{1}{2}\right)\)

3. \(-\displaystyle\frac{2}{3}\left(-\displaystyle\frac{3}{2}\right)\)

Divide.

1. \(\displaystyle\frac{2}{3}\div \displaystyle\frac{5}{7}\)

2. \(-\displaystyle\frac{3}{4}\div \displaystyle\frac{7}{9}\)

3. \(8\div \left( -\displaystyle\frac{4}{5}\right)\)

Simplify.

1. \(\displaystyle\frac{3}{8}+\displaystyle\frac{1}{8}\)

2. \(\displaystyle\frac{a+5}{8}-\displaystyle\frac{3}{8}\)

3. \(\displaystyle\frac{9}{x}-\displaystyle\frac{3}{x}\)

4. \(\displaystyle\frac{3}{7}+\displaystyle\frac{2}{7}-\displaystyle\frac{9}{7}\)

Add: \(\displaystyle\frac{5}{12}+\displaystyle\frac{7}{18}\)

Add: \(\displaystyle\frac{3}{4}+\displaystyle\frac{1}{6}\)

Subtract: \(\displaystyle\frac{7}{15}-\displaystyle\frac{3}{10}\)

Add: \(\displaystyle\frac{1}{6}+\displaystyle\frac{1}{8}+\displaystyle\frac{1}{4}\)

Subtract: \(3-\displaystyle\frac{5}{6}\)

Simplify.

1. \(10\left(\displaystyle\frac{x}{2}\right)\)

2. \(a\left(\displaystyle\frac{3}{a}-4\right)\)

State the property that justifies each statement

1. \(x+5=5+x\)

2. \((2+x)+y=2+(x+y)\)

3. \(6(x+3)=6x+18\)

4. \(2+(-2)=0\)

5. \(3\left(\displaystyle\frac{1}{3}\right)=1\)

6. \((2+0)+3=2+3\)

7. \((2+3)+4=3+(2+4)\)

8. \((x+2)+y=(x+y)+2\)