Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions

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Multiple Choice

Can a rational number have 0 as a denominator?

• No

• Yes

Adding/Subtracting Rational Numbers

• Must have a common denominator!

• Once you have a common denominator, you add/subtract the numerator.

Reviewing parts of a fraction

• Numerator = the top number

• Denominator = the bottom number

Multiple Select

What is the top number of a fraction called?

• Denominator

• Numerator

Multiple Select

What is the bottom number of a fraction called?

• Denominator

• Numerator

Adding fractions with a common denominator

• Add the numerators

• Keep the denominators the same

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Multiple Choice

$$\frac{1}{6}+\frac{3}{6}=$$  

• $$\frac{2}{6}$$  

• $$\frac{4}{6}$$  

• $$\frac{4}{12}$$  

Multiple Choice

$$\frac{4}{9}+\frac{4}{9}=$$  

• $$\frac{8}{9}$$  

• $$\frac{4}{9}$$  

• $$\frac{8}{18}$$  

Adding fractions with different denominators

• Multiply the denominators (to get a common denominator - QCD)

• Multiply the numerator of the first fraction by the opposite denominator

• Multiply the numerator of the second fraction by the opposite denominator

Multiple Choice

$$\frac{2}{3}+\frac{1}{6}=$$  

• $$\frac{3}{6}$$  

• $$\frac{3}{9}$$  

• $$\frac{15}{18}$$  

Multiple Choice

$$\frac{1}{9}+\frac{5}{2}=$$  

• $$\frac{47}{18}$$  

• $$\frac{6}{18}$$  

• $$\frac{6}{11}$$  

Multiple Choice

$$\frac{4}{3}+\frac{1}{8}=$$  

• $$\frac{35}{24}$$  

• $$\frac{5}{11}$$  

• $$\frac{5}{24}$$  

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Find the LCM of 21 and 7
21: 21, 42, 63
7: 7, 14, 21, 28
The LCM is 21. Therefore both fractions with have the same denominator which is 21.

• denominators must be equal

• if not, convert using LCM

• when done, simplify using GCF​

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Demoninators must be the same in order to begin!

Adding and subtracting fractions

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Adding and Subtracting Rational Numbers

• 1. In order to add or subtract fractions, they must have a common denominator

• 2. The lowest common denominator is the smallest number that is a multiple of all of the denominators

Adding and Subtracting Rational Numbers

• 3. Once the lowest common denominator is found, rewrite all of the fractions as equivalent fractions with that denominator

• 4. Then add (or subtract) numerators, and keep the common denominator

Multiple Choice

What is the lowest common denominator of 1/2, 1/3, 1/5?

• 12

• 6

• 30

• 5

Multiple Choice

What is the lowest common denominator of 9, 8, 12?

• 56

• 64

• 108

• 72

Multiple Choice

What is the equivalent fraction for 3/8 if the common denominator is 24?

• 6/24

• 4/24

• 9/24

• 12/32

Adding Rational Expressions with the Same Denominator

• 1. if the denominators of the expressions you are trying to add are the same, simply add the numerators and keep the common denominator

• Simplify the numerator by combining like terms

• Factor the numerator and denominator to see if the expression can be reduced

Multiple Choice

Simplify the expression

• (2a + 4b) / 12b²

• (2a - 4b) / 12b²

• (a - b) / 6b²

• (a + 2b) / 6b²

Multiple Choice

Simplify the expression

• n / 2m

• n / 3m

• (m² + 4n²) / 12m

• n / 4m

Multiple Choice

Simplify the expression

• 6x / 20xy

• 3 / 10y

• (6x+1) / (20xy)

• 3 / 20xy

Adding or Subtracting Rational Expressions with Different Denominators

• 1. Before you can combine rational expressions, they must have a common denominator

• 2. Check to see if the smaller denominator is a factor of the larger denominator

• 
  

Adding and Subtracting Rational Expressions with Different Denominators

• 3. If one denominator appears as a factor in another denominator, you don't have to repeat that expression in the common denominator

• 4. The lowest common denominator must contain factors that appear in all the denominators

Adding or Subtracting Rational Expressions with Different Denominators

• 5. Once you have decided upon the common denominator, rewrite each expression as an equivalent fraction with the new denominator

• 6. Simplify by combining like terms in the numerator

• 7. Factor the numerator and denominator

• 8. Reduce by canceling like terms.

Multiple Choice

What is the common denominator when simplifying $$\frac{4}{x+8}+\frac{3}{x-5}$$  

• $$x^2-40$$  

• $$2x+3$$  

• $$\left(x+8\right)+\left(x-5\right)$$  

• $$\left(x+8\right)\left(x-5\right)$$  

Multiple Choice

Which is the next correct setup for simplifying $$\frac{7x}{x+1}+\frac{2}{x-3}$$  

• $$\frac{7x}{x+1}\cdot\frac{2}{x-3}+\frac{2}{x-3}\cdot\frac{7x}{x+1}$$  

• $$\frac{7x}{x+1}\cdot\frac{7x}{x+1}+\frac{2}{x-3}\cdot\frac{2}{x-3}$$  

• $$\frac{7x}{x+1}\cdot\frac{x-3}{x-3}+\frac{2}{x-3}\cdot\frac{x+1}{x+1}$$  

• $$\frac{7x}{x+1}\cdot\frac{x+1}{x+1}+\frac{2}{x-3}\cdot\frac{x-3}{x-3}$$  

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Simplify

• (x-9)/(x+9)

• 1/(x-9)

• (x+9)

• 1/(x+9)

Multiple Choice

Simplify

• (x-9)/(x+9)

• 1/(x-9)

• (x+9)

• 1/(x+9)

Multiple Choice

Simplify the expression

• (-17x - 12y) / 15x

• (23x - 4y) / 15x

• (-17x - 4y) / 15x

• (-3x - 4y) / 8x