Adding and Subtracting Fractions

Fractions

Mr. Rodriguez​

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

$$\frac{9}{15}+\frac{4}{15}$$  

• $$\frac{5}{15}$$  

• $$\frac{1}{5}$$  

• $$\frac{13}{15}$$  

• $$\frac{13}{30}$$  

Multiple Choice

How do I add this fraction? 

• 7/8
• 10/8
• 10/64
• 5/8

Multiple Choice

How do I add this fraction? 

• 3/10
• 2/5
• 3/5
• 3/25

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

Multiple Choice

What is ¹⁵/₁₆ - ¹²/₁₆?

• ¹/₃
• ⁴/₁₆ or ¹/₄
• ³/₁₆
• ²/₁₆ or ¹/₈

Multiple Choice

Subtract: $$\frac{8}{9}\ -\ \frac{4}{9}$$  

• 4/9

• 4/0

• 12/9

• 12/18

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 ^ Es necesario obtener como denominadores para sumar o restar fracciones

Finding common denominators (multiples)

• Identify the denominators • Identificar los denominadores

• Write or think of the multiples for each number • Escribe los multiplicars

• Find the Least Common Denominator • Busque el denomindor en común

Unlike Denominators

• Find LCM of denominators * Busque LCM

• Multiply numerator and denominator of each fraction by the multiple

• Write the equivalent fractions * Escribe fracciones equivalentes (1/2=5/10)

• Add or subtract the numerators * Agregar o restar las numeradores

Multiple Choice

• 1/12
• 1
• 2/35
• 23/25

Multiple Choice

What is the sum of these fractions?

• 4/5
• 3/20
• 17/20
• 4/20

Multiple Choice

• 1/12
• 1
• 2/35
• 23/25

Multiple Choice

What is the sum of these fractions?

• 4/5
• 3/20
• 17/20
• 4/20

Multiplying Fractions by Fractions

Multiplying Fractions

• The first step in multiplying fractions is to multiply the two numerators

• For example, you would multiply 2x2 to get 4 as your new numerator

• Next, you multiply both denominators, 3x5, to get 15 as your new denominator

• Your new fraction should now be 4/15

Simplifying your answer

Multiple Choice

What is the fraction 2/4 in simplest form?

• 1/2

• 1/4

• 2/2

• It is in simplest form

Multiple Choice

Find the product:

• 9/24
• 9/28
• 6/32
• 1/28

Multiple Choice

Multiply these fractions:

• 1/5
• 1 / 1
• 1 / 6
• 0

Multiple Choice

What is the fraction 2/4 in simplest form?

• 1/2

• 1/4

• 2/2

• It is in simplest form

Reciprocals Fractions

Reciprocal Notes

• Reciprocal is what you multiply by to get a value of 1

• Reciprocal can also be called a multiplicative inverse

• Reciprocals are important when dividing fractions, solving equations, and using proportions.

• Every number has a reciprocal except 0 because you can’t divide a number by zero

Multiple Choice

What is the reciprocal of 1/4

• 1

• 4/1

• 2

Multiple Choice

What is the reciprocal of 8/14

• 14/8

• 1/4

• 8/14

Multiple Choice

What is the reciprocal of 2/5

• 2/5

• 4

• 5/2

Fill in the Blanks

What is the reciprocal of 3/4

Multiple Choice

What is the reciprocal of 2/15

• 2

• 15/2

• 9/1

Multiple Choice

What is the reciprocal of 6/35

• 35/6

• 2/4

• 1

Fill in the Blanks

What is the reciprocal of 7

Dividing Fractions

What do you know?

Remember: The rules to divide fractions are Keep Change Flip

Recuerde: las reglas para dividir fracciones son Keep Change Flip

Multiple Choice

Solve:

$$\frac{1}{2}\div\frac{3}{4}$$  

• $$\frac{3}{8}$$  

• $$\frac{4}{6}=\frac{2}{3}$$  

• $$\frac{6}{4}=\frac{3}{2}=1\ \frac{1}{2}$$  

Multiple Choice

3/8 DIVIDED BY 1/6 =

• 1 1/4

• 1 1/2

• 2 1/4

• 2 1/2

Multiple Choice

9/10 DIVIDED BY 1/3 =

• 9/30

• 2 7/10

• 2 4/5

• 3 9/30

Multiple Choice

5/9 DIVIDED BY 1/2 =

• 5/18

• 1 1/9

• 1 5/18

• 1 1/2

Multiple Choice

6/7 DIVIDED BY 1/2 =

• 3/7

• 1 2/7

• 1 3/7

• 1 5/7

Multiple Choice

2/3 DIVIDED BY 1/5 =

• 2/15

• 3 1/3

• 3 3/5

• 4 2/15