Operations with Fractions

Operations with Fractions

​Multiplying Fractions

​Multiply the numerators (tops)

Multiply the denominators (bottoms)

Simplify if possible

​

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

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Multiply these factions

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Perform the indicated operation.

(5/6) × (3/8)

Write answer in lowest terms.

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Find the product of

(1/6) and (2/3).

Reduce, or simplify answer.

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What is the product of these fractions in lowest terms?

​Dividing Fractions

​Fraction Division does not exist

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

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Perform the indicated operation.

(4/5) ÷ (5/6)

Write answer in lowest terms.

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Find the quotient of

(2/3) and (5/6) .

Reduce, or simplify.

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Divide these fractions
2/3 ÷ 3/4

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Divide these fractions. Simplify!!!
9/4 ÷ 1/6

​Adding and Subtracting Fractions

​SAME CHANGE CHANGE - addition is easier

Must have common denominators

Make equivalent ​fractions with common denominators

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What is the sum of these fractions in lowest terms?

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What is the difference of these fractions in lowest terms?

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Find the sum of

3/8 and 1/3.

Reduce, or simplify answer.

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Find the difference of

47 / 56 and 15 / 56.

Write answer in simplest form.

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Find the difference.

7/8 - 4/5

Reduce, or simplify answer.

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Add the fractions:
1/3 + 1/5 =

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8/15 + 2/3=

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Solve.

​Operations with fractions follows P(G)EMDAS

• Grouping symbols

• Exponents

• Multiplication and Division - tied left to right

• Addition and Subtraction - tied left to right​

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Evaluate the expression. Write the answer in simplest form. 
3/8 ÷ 3/4 - 1/6

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Evaluate the expression. Write the answer in simplest form. 
4/5 + 2/5 ÷ 4

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Perform the indicated operations.

(2/5) + (1/2) - (7/8)

Reduce, or simplify answer.

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( 2/5 + 1/3) ÷ (3/4 - 1/2)

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: $$\frac{x}{x+1}+\frac{2x}{x+2}$$  

• $$\frac{3x}{2x+3}$$  

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

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

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