Adding and Subtracting Fractions with Regrouping

Adding and Subtracting Fractions

Like denominators and unlike denominators

Add Fractions with Like Denominators

• If denominators are the same...

• Add the numerators

• Denominator does not change

Multiple Choice

$$\frac{7}{9}+\frac{1}{9}=$$  

• $$\frac{8}{9}$$  

• $$\frac{6}{9}$$  

• $$\frac{8}{18}$$  

• $$\frac{7}{81}$$  

Multiple Choice

$$\frac{9}{15}+\frac{4}{15}$$  

• $$\frac{5}{15}$$  

• $$\frac{1}{5}$$  

• $$\frac{13}{15}$$  

• $$\frac{13}{30}$$  

Subtract Fractions with Like Denominators

• If denominators are the same...

• Subtract the numerators

• Denominator does not change

Multiple Choice

$$\frac{12}{17}-\frac{5}{17}$$  

• $$\frac{17}{17}$$  

• $$\frac{7}{17}$$  

• $$\frac{6}{17}$$  

• 1

• 0

Why you need like denominators

• 1/2 + 1/4 is NOT 2/6 (or 2/4, or 2/2)

• You need to obtain like denominators to add or subtract fractions

Least Common Multiple

LCM

First lets define what a multiple is..

Multiple is our key word!

Say we are just doing multples of 4: you can just keep adding 4.

Multiple Choice

What are multiples of 7

• 7, 14, 21, 28, ...

• 7, 14, 22, 24, ...

• 7, 14, 19, 21, ...

• 7, 14, 19, 26, ...

Multiple Choice

What are multiples of 6

• 6, 12, 19, 24, ...

• 6, 13, 18, 23, ...

• 6, 12, 18, 24, ...

• 1, 3, 6, ...

Least Common Multiple

When finding the least common multiple we COMPARE

For ex:

What is the least common multiple (LCM) of 2 and 3?

LCM: 6

6 is the least common multiple because its the lowest number they have in common

Lets do another example

• What is the Least Common Multiple (LCM) of 4 and 10?

• multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...

• multiples of 10: 10, 20, 30, 40, ......

• 
  

  LCM: 20

• its the lowest number they have in common

Multiple Choice

What is the least common multiple of 5 and 8?

• 24

• 16

• 59

• 40

Multiple Choice

What is the least common multiple (LCM) of 3 and 12?

• 12

• 24

• 6

• 15

Multiple Choice

Challenge question: What is the LCM of 2, 4, and 6?

• 6

• 4

• 12

• 2

Open Ended

$$\frac{2}{7}+\frac{3}{5}=\frac{5}{12}$$  

Describe why the problem is wrong?
Describir por qué el problema es un error?



Finding common denominators (multiples)

• Identify the denominators •

• Write or think of the multiples for each number

• Find the Least Common Denominator

Multiple Choice

$$\frac{1}{8}-\frac{1}{6}$$  

What is the Least Common Denominator?

• 8

• 6

• 48

• 14

• 24

Multiple Choice

$$\frac{3}{5}+\frac{10}{15}$$  

What is the Least Common Denominator?

• 5

• 15

• 75

• 20

• 30

Unlike Denominators

• Find LCM of denominators * Busque LCM

• Multiply numerator and denominator of each fraction by the multiple

• Write the equivalent fractions *

• Add or subtract the numerators

Multiple Choice

$$\frac{9}{10}-\frac{3}{4}$$  

• 5/7

• 3/20

• 3/8 

• 9/10

Multiple Choice

$$\frac{2}{6}+\frac{1}{2}$$  

• 5/6

• 3/6

• 4/6

• 3/8

Multiple Choice

Solve.

• ³/₄
• ³/₈
• ²/₄
• ³/₁₆

Multiple Choice

$$1\ \frac{5}{10}+\ \frac{3}{10}$$  

• $$1\ \frac{4}{5}$$  

•   $$4\ \frac{8}{10}$$  

•   $$2\ \frac{4}{5}$$  

• $$\frac{1}{3}$$  
  

Multiple Choice

$$8\ \frac{8}{11}+\ 1\ \frac{1}{11}$$  

•   $$7\ \frac{9}{11}$$  

•   $$9\ \frac{3}{4}$$  

•   $$9\ \frac{9}{11}$$  

• $$7\ \frac{9}{11}$$  

Multiple Choice

5 5/12 - 5 2/12

• 1/4

• 3/5

• 5 1/12

• 5 7/12

Multiple Choice

9 11/12 - 4 1/12

• 2 5/8

• 6 1/3

• 5 5/6

• 5 10/12

Multiple Choice

7 2/3 - 1 1/3

• 6 1/3

• 6 3/3

• 8

• 8 1/3