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

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

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. \(-2.3\)

Factor \(525\) into the product of primes.

Reduce \(\dfrac{210}{231}\) to lowest terms.

Multiply: \(\dfrac{3}{5}\cdot\dfrac{7}{8}\)

Multiply: \(8\cdot\dfrac{1}{5}\)

Multiply: \(\left(\dfrac{2}{3}\right)^4\)

Give the reciprocal of each number.

1. \(5\)

2. \(2\)

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

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

Find the perimeter and area of the three figures.

1. The statement \(3+7=7+3\) is an example of the commutative property of addition.

2. The statement \(3\cdot x=x\cdot 3\) is an example of the commutative property of multiplication.

Simplify \(2+(3+y)\) by using the associative property.

Simplify \(5(4x)\) by using the associative property.

Simplify \(\dfrac{1}{4}(4a)\) by using the associative property.

Simplify \(2\left(\dfrac{1}{2}x\right)\) by using the associative property.

Simplify \(6\left(\dfrac{1}{3}x\right)\) by using the associative property.

Apply the distributive property to \(5(4x+3)\) and then simplify the result.

Apply the distributive property to \(6(3x+2y)\) and then simplify the result.

Apply the distributive property to \(\dfrac{1}{2}(3x+6)\) and then simplify the result.

Simplify: \(\,2(3y+4)+2\)

Apply the distributive property to \(a\left(1+\dfrac{1}{a}\right)\) and then simplify the result.

Apply the distributive property to \(3\left(\dfrac{1}{3}x+5\right)\) and then simplify the result.

Apply the distributive property to \(6\left(\dfrac{1}{3}x+\dfrac{1}{2}y\right)\) and then simplify the result.

Use the distributive property to combine similar terms for the expression \(3x+5x\).

Use the distributive property to combine similar terms for the expression \(3y+y\)

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

Simplify: \(7x+4+6x+3\)

Simplify: \(4+3(2y+5)+8y\)

Add all combinations of positive and negative \(5\) and \(7\).

Subtract \(-3\) from \(-9\).

Add \(-4\) to the difference of \(-2\) and \(5\).

Multiply all combinations of positive and negative \(7\) and \(3\).

Divide each of the following:

1. \(6\div 3\)

2. \(6\div -3\)

3. \(-6\div 3\)

4. \(-6\div -3\)

Simplify \((-2-3)(5-9)\)

Simplify \(2-5(7-4)-6\)

Simplify \(\; 2(4-7)^3+(-2-3)^2\)

Simplify: \(6\left(\dfrac{t}{3}\right)\)

Simplify: \(3\left(\dfrac{t}{3}-2\right)\)

Simplify: \(\dfrac{-8-8}{-5-3}\)

Simplify: \(\dfrac{-5(-4)+2(-3)}{2(-1)-5}\)

Simplify: \(\dfrac{2^3+3^3}{2^2-3^2}\)

Simplify: \(3(2y-1)+y\)

Simplify: \(8-3(4x-2)+5x\)

Simplify: \(5(2a+3)-(6a-4)\)

Divide \(\dfrac{3}{4}\div\dfrac{6}{11}\) and reduce to lowest terms.

Divide \(10\div\dfrac{5}{6}\) and reduce to lowest terms.

Evaluate the expressions \((a+4)^2\), \(a^2+16\), and \(a^2+8a+16\) when \(a\) is \(-2\), \(0\), and \(3\).

Write the product \(x^3\cdot x^4\) with a single exponent.

Write \(\left(5^3\right)^2\) with a single exponent.

Expand \((3x)^4\) and then multiply.

Simplify \(\left(-3x^2\right)\left(5x^4\right)\) using the properties of exponents.

Simplify \(\left(-2x^2\right)^3\left(4x^5\right)\) using the properties of exponents.

Simplify \(\left(x^2\right)^4\left(x^2y^3\right)^2\left(y^4\right)^3\) using the properties of exponents.

Write \(5^{-2}\) with positive exponents, then simplify.

Write \((-2)^{-3}\) with positive exponents, then simplify.

Write \(\left(\displaystyle\frac{3}{4}\right)^{-2}\) with positive exponents, then simplify.

Simplify:

1. \(\left(2x^2y^4\right)^0\)

2. \(\left(2x^2y^4\right)^1\)

Simplify \(\displaystyle\frac{\left(x^3\right)^{-2}\left(x^4\right)^5}{\left(x^{-2}\right)^7}\)

Simplify \(\displaystyle\frac{6a^5b^{-6}}{12a^3b^{-9}}\)

Simplify \(\displaystyle\frac{\left(4x^{-5}y^3\right)^2}{\left(x^4y^{-6}\right)^{-3}}\)

Write \(376,000\) in scientific notation.

Write \(4.52 \times 10^3\) in expanded form.

Simplify each expression, and write all answers in scientific notation.

1. \(\left(2 \times 10^8\right)\left(3 \times 10^{-3}\right)\)

2. \(\displaystyle\frac{4.8 \times 10^9}{2.4 \times 10^{-3}}\)

3. \(\displaystyle\frac{\left(6.8\times 10^5\right)\left(3.9 \times 10^{-7}\right)}{7.8 \times 10^{-4}}\)

Simplify: \(\; 5+3(2+4)\)

Simplify: \(\; 5\cdot 2^3-4\cdot 3^2\)

Simplify: \(\; 20-(2\cdot 5^2-30)\)