Adding and Subtracting Rational Functions

Adding and Subtracting Rational Expressions

​

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

Home

Open in new tab

Copy link

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

$$\frac{4}{3}+\frac{1}{8}=$$  

• $$\frac{35}{24}$$  

• $$\frac{5}{11}$$  

• $$\frac{5}{24}$$  

Home

Open in new tab

Copy link

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​

​

Demoninators must be the same in order to begin!

Adding and subtracting fractions

Home

Open in new tab

Copy link

Home

Open in new tab

Copy link

Home

Open in new tab

Copy link

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