Operations with Fractions

Operations with Fractions

​Multiplying Fractions

​Multiply the numerators (tops)

Multiply the denominators (bottoms)

Simplify if possible

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If you can simplify BEFORE multiplying - common fractions in numerator (any) and denominator (any)

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​Dividing Fractions

​Fraction Division does not exist

Multiply by the reciprocal of the divisor (second fraction)​

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​Adding and Subtracting Fractions

​SAME CHANGE CHANGE - addition is easier

Must have common denominators

Make equivalent ​fractions with common denominators

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​Operations with fractions follows P(G)EMDAS

• Grouping symbols

• Exponents

• Multiplication and Division - tied left to right

• Addition and Subtraction - tied left to right​

Multiple Select

Select all operations with fractions that require a common denominator.

• addition

• division

• multiplication

• subtraction

Multiple Choice

When multiplying fractions, a common denominator is required.

• TRUE

• FALSE

Multiple Choice

"Multiply by the reciprocal" is the rule for which operation with fractions?

• addition

• division

• multiplication

• subtraction

​Taking Fractions to the Algebra II Level

​We will be doing the same operations but with fractions that are made up of polynomial expressions

​Math Concepts Needed

• ​Factoring

• Adding, subtracting, multiplying​ polynomials

Multiple Choice

Find the product: $$\frac{x-4}{x+7}\times\frac{x-3}{x-8}$$  

• $$\frac{x^2-7x+12}{x^2-x-56}$$  

• $$\frac{x^2-12x+32}{x^2+4x-21}$$  

• $$\frac{x^2+7x+12}{x^2-56}$$  

• $$\frac{x^2-12x+32}{x^2-21}$$  

Multiple Choice

Find the quotient: $$\frac{a^2-4}{3a}\div\frac{5a^2}{a-2}$$  

• $$\frac{5a\left(a+4\right)}{3}$$  

• $$\frac{a^3-2a^2-4a+8}{15a^3}$$  

• $$\frac{5a^2+20a}{3}$$  

• $$\frac{a^3-6a+8}{15a}$$  

Multiple Choice

Subtract: $$\frac{9x+1}{x-2}-\frac{3x-4}{x-2}$$  

• $$\frac{6x-3}{x-2}$$  

• $$\frac{12x+5}{x-2}$$  

• $$\frac{6x+5}{x-2}$$  

• $$\frac{12x-3}{x-2}$$  

Multiple Choice

Find the sum: $$\frac{x}{x+1}+\frac{2x}{x+2}$$  

• $$\frac{3x}{2x+3}$$  

• $$\frac{3x^2+4x}{\left(x+1\right)\left(x+23\right)}$$  

• $$\frac{3x}{\left(x+1\right)\left(x+23\right)}$$  

• $$\frac{3x^2+4x}{\left(x+1\right)\left(x+2\right)}$$