Name the numerator and denominator for each.

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

2. \(\displaystyle\frac{a}{5}\)

3. \(\displaystyle\frac{7}{1}\)

Write \(\displaystyle\frac{3}{4}\) as an equivalent fraction with denominator \(20\).

Write \(\displaystyle\frac{3}{4}\) as an equivalent fraction with denominator \(12x\).

Write \(\displaystyle\frac{10}{12}\) as an equivalent fraction with denominator \(6\).

Simplify each expression.

1. \(\dfrac{24}{1}\)

2. \(\dfrac{24}{24}\)

3. \(\dfrac{48}{24}\)

4. \(\dfrac{72}{24}\)

Write each fraction as an equivalent fraction with denominator \(24\). Then write them in order from smallest to largest. \(\qquad \displaystyle\frac{5}{8} \qquad \displaystyle\frac{5}{6} \qquad \displaystyle\frac{3}{4} \qquad \displaystyle\frac{2}{3}\)

Change \(6\displaystyle\frac{5}{9}\) to an improper fraction.

Ntoe: The example in the book is slightly different than the one we are doing here.

Change \(5\dfrac{3}{4}\) to an improper fraction, use the shortcut.

Change \(-3\dfrac{7}{8}\) to an improper fraction.

Change \(\displaystyle\frac{11}{4}\) to a mixed number.

Write as a mixed number.

1. \(\displaystyle\frac{10}{3}\)

2. \(\displaystyle\frac{208}{24}\)

Identify each as either a prime number or a composite number. For those that are composite, give two divisors other than itself or \(1\).

1. \(43\)

2. \(12\)

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

Reduce the fraction \(\displaystyle\frac{12}{15}\) to lowest terms.

Laura is having a party. She puts 4 six-packs of soda in a cooler. At the end of the party she finds that only \(4\) sodas have been consumed. What fraction of the sodas are left? Write your answer in lowest terms.

Reduce \(\displaystyle\frac{6}{42}\) to lowest terms.

Reduce \(\displaystyle\frac{4}{40}\) to lowest terms.

Reduce \(\displaystyle\frac{105}{30}\) to lowest terms.

Multiply: \(\displaystyle\frac{3}{5}\cdot \displaystyle\frac{2}{7}\)

Multiply: \(\displaystyle\frac{3}{8}\cdot 5\)

Multiply: \(\displaystyle\frac{1}{2}\left(\displaystyle\frac{3}{4}\cdot \displaystyle\frac{1}{5}\right)\)

Multiply: \(\displaystyle\frac{15}{8}\cdot \displaystyle\frac{4}{9}\)

Multiply: \(-\displaystyle\frac{9}{2}\cdot \displaystyle\frac{8}{18}\)

Multiply: \(\displaystyle\frac{2}{3}\cdot \displaystyle\frac{6}{5}\cdot \displaystyle\frac{5}{8}\)

Simplify: \(\left(-\displaystyle\frac{3}{4}\right)^2\)

Simplify: \(\left(\displaystyle\frac{5}{6}\right)^2 \cdot \displaystyle\frac{1}{2}\)

Find \(\displaystyle\frac{1}{2}\) of \(\displaystyle\frac{2}{3}\)

Apply the distributive property, then simplify.

1. \(6\left(2+\dfrac{1}{3}\right)\)

2. \(12\left(\dfrac{3}{4}-\dfrac{1}{2}\right)\)

Apply the distributive property, then simplify.

3. \(-5\left(4-\dfrac{2}{3}\right)\)

Find the area of the triangle in Figure \(3\).

Divide \(\displaystyle\frac{1}{2}\div \displaystyle\frac{1}{4}\)

Divide \(\dfrac{3}{8}\div\dfrac{9}{4}\)

Divide \(\displaystyle\frac{2}{3}\div 2\)

Divide \(2\div \left(-\displaystyle\frac{1}{3}\right)\)

Divide \(-\displaystyle\frac{4}{27}\div \displaystyle\frac{16}{9}\)

Divide

1. \(\displaystyle\frac{16}{35}\div 8\)

2. \(27\div\displaystyle\frac{3}{2}\)

Simplify \(32\div \left(\displaystyle\frac{4}{3}\right)^2 +75\div \left(\displaystyle\frac{5}{2}\right)^2\)

What is the quotient of \(\displaystyle\frac{8}{3}\) and \(\displaystyle\frac{1}{6}\), increased by \(5\).

A \(4\)-H Club is making blankets to keep their lambs clean at the county fair. If each blanket requires \(\dfrac{3}{4}\) yard of material, how many blankets can they make from \(9\) yards of material?

Add or subtract.

1. \(\dfrac{3}{8}+\dfrac{1}{8}\)

2. \(\dfrac{9}{5}-\dfrac{3}{5}\)

3. \(\dfrac{3}{7}+\dfrac{2}{7}\)

Find the LCD for the fractions \(\displaystyle\frac{5}{12}\) and \(\displaystyle\frac{7}{18}\).

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

Find the LCD for \(\displaystyle\frac{3}{4}\) and \(\displaystyle\frac{1}{6}\).

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

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

Subtract: \(\displaystyle\frac{3}{5}-\displaystyle\frac{1}{6}\)

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

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

Add: \(\;\displaystyle\frac{3}{8}+\left(-\displaystyle\frac{1}{8}\right)\)

Add: \(\;\displaystyle\frac{1}{10}+\left(-\displaystyle\frac{4}{5}\right)+\left(-\displaystyle\frac{3}{20}\right)\)

Find the difference of \(-\displaystyle\frac{3}{5}\) and \(\displaystyle\frac{2}{5}\).

Multiply: \(2\displaystyle\frac{3}{4}\cdot 3\displaystyle\frac{1}{5}\)

Multiply: \(3\cdot 4\displaystyle\frac{5}{8}\)

Divide: \(1\displaystyle\frac{3}{5}\div 2\displaystyle\frac{4}{5}\)

Divide: \(5\displaystyle\frac{9}{10}\div 2\)

Add: \(3\displaystyle\frac{2}{3}+4\displaystyle\frac{1}{5}\)

Add: \(5\displaystyle\frac{3}{4}+9\displaystyle\frac{5}{6}\)

Add: \(3\dfrac{1}{4}+2\dfrac{3}{5}+1\dfrac{9}{10}\)

Subtract: \(3\dfrac{9}{10}-1\dfrac{3}{10}\)

Subtract: \(12\displaystyle\frac{7}{10}-8\displaystyle\frac{3}{5}\)

Subtract: \(10-5\displaystyle\frac{2}{7}\)

Subtract: \(8\dfrac{1}{4}-3\dfrac{3}{4}\)

Subtract: \(4\dfrac{3}{4}-1\dfrac{5}{6}\)

Simplify: \(5+\left(2\displaystyle\frac{1}{2}\right)\cdot\left(3\displaystyle\frac{2}{3}\right)\)

Simplifty: \[\left(\frac{3}{4}+\frac{5}{8}\right)\left(2\frac{3}{8}+1\frac{1}{4}\right)\]

Simplify: \(\displaystyle\frac{3}{5}+\displaystyle\frac{1}{2}\left(3\displaystyle\frac{2}{3}+4\displaystyle\frac{1}{3}\right)^2\)

Simplify: \(\displaystyle\frac{\displaystyle\frac{3}{4}}{\displaystyle\frac{5}{6}}\)

Simplify: \(\displaystyle\frac{\displaystyle\frac{1}{2}+\displaystyle\frac{2}{3}}{\displaystyle\frac{3}{4}-\displaystyle\frac{1}{6}}\)

Simplify: \(\displaystyle\frac{3+\displaystyle\frac{1}{2}}{2-\displaystyle\frac{3}{4}}\)

Simplify: \(\displaystyle\frac{10\displaystyle\frac{1}{3}}{8\displaystyle\frac{2}{3}}\)

Solve: \(-24x=36\)

Solve: \(\dfrac{1}{7}x-4=-8\)

Solve: \(x-\dfrac{3}{4}=\dfrac{5}{8}\)

Solve: \(-\dfrac{4}{5}x=\dfrac{8}{15}\)

Mini Lecture
Solve.

1. \(6(x-3)=-6\)

2. \(7y-3=4y-15\)

3. \(2(3x-6)+1=7\)

4. \(9x-6=-3(x+2)-24\)

5. \(\dfrac{x}{5}-x=4\)

6. \(\dfrac{1}{x}-\dfrac{1}{2}=-\dfrac{1}{4}\)

Which ordered pairs, \((2, 3), (1, 5), (-2, -4)\), are solutions to \(y=3x+2\)?

Given \(2x+3y=6\), complete the ordered pairs \((0, \quad), (\quad ,1), (3, \quad )\).

Given \(2x-5y=20\), complete the ordered pairs \((0, \quad), (\quad, 2), (\quad, 0), (-5, \quad)\).

Given \(y=2x-1\), complete the ordered pairs \((0, \quad), (5, \quad), (\quad, 7), (\quad, 3)\).

Graph the ordered pairs \((3, 4)\), \((3, -4)\), \((-3, 4)\), and \((-3, -4)\).

Graph the ordered pairs \((-1, 3)\), \((2, 5)\), \((0, 0)\), \((0, -3)\) and \((4, 0)\).

Graph \(x+y=5\)

Graph \(y=3x-1\)

Graph \(y=-\displaystyle\frac{1}{3}x+2\)

Graph \(3x-2y=6\)

Graph each of the following lines.

1. \(y=\displaystyle\frac{1}{2}x\)

2. \(x=3\)

3. \(y=-2\)