## Key Concepts

**Summary of Fraction Operations****Fraction multiplication:**Multiply the numerators and multiply the denominators.

[latex]\Large\frac{a}{b}\cdot\Large\frac{c}{d}=\Large\frac{ac}{bd}[/latex]**Fraction division:**Multiply the first fraction by the reciprocal of the second.

[latex]\Large\frac{a}{b}+\Large\frac{c}{d}=\Large\frac{a}{b}\cdot\Large\frac{d}{c}[/latex]**Fraction addition:**Add the numerators and place the sum over the common denominator. If the fractions have different denominators, first convert them to equivalent forms with the LCD.

[latex]\Large\frac{a}{c}+\Large\frac{b}{c}=\Large\frac{a+b}{c}[/latex]**Fraction subtraction:**Subtract the numerators and place the difference over the common denominator. If the fractions have different denominators, first convert them to equivalent forms with the LCD.

[latex]\Large\frac{a}{c}-\Large\frac{b}{c}=\Large\frac{a-b}{c}[/latex]

**Simplify complex fractions.**- Simplify the numerator.
- Simplify the denominator.
- Divide the numerator by the denominator.
- Simplify if possible.

**Determine whether a number is a solution to an equation.**- Substitute the number for the variable in the equation.
- Simplify the expressions on both sides of the equation.
- Determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.

**Addition, Subtraction, and Division Properties of Equality**- For any numbers [latex]a[/latex], [latex]b[/latex]
*,*and [latex]c[/latex], if [latex]a=b[/latex] , then [latex]a+c=b+c[/latex] . Addition Property of Equality - if [latex]a=b[/latex] , then [latex]a-c=b-c[/latex] . Subtraction Property of Equality
- if [latex]a=b[/latex] , then [latex]\Large\frac{a}{c}=\Large\frac{b}{c}[/latex] , [latex]c\ne 0[/latex] . Division Property of Equality

- For any numbers [latex]a[/latex], [latex]b[/latex]
**The Multiplication Property of Equality**- For any numbers [latex]a[/latex], [latex]b[/latex]
*,*and [latex]c[/latex], [latex]a=b[/latex] , then [latex]ac=bc[/latex] . - If you multiply both sides of an equation by the same quantity, you still have equality.

- For any numbers [latex]a[/latex], [latex]b[/latex]

**Translate a word sentence to an algebraic equation.**- Locate the “equals” word(s). Translate to an equal sign.
- Translate the words to the left of the “equals” word(s) into an algebraic expression.
- Translate the words to the right of the “equals” word(s) into an algebraic expression.

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