Fractions

Fractions

Equivalent, Simplifying, Adding and Subtracting

Multiple Choice

What is the definition of a numerator?

• Going up, from smallest to largest

• The number of parts being considered in a fraction

• The number of equal parts in the whole

• A whole number that divides into another number without a remainder

Multiple Choice

What is the definition of a denominator?

• Going down, from largest to smallest

• The number of equal parts in a whole

• The number of parts being considered in a fraction

• Part of a whole

Equivalent & Simplifying Fractions

Part 1

Equivalent Fractions

• Equivalent fractions can be bigger or smaller than the given fraction

• These can be found using the operations of multiplication and division

• When multiplying or dividing, you need to apply the operation to both the numerator and denominator

Multiple Select

Select all equivalent fractions below to  $\frac{4}{6}$ 

•  $\frac{3}{6}$  

•  $\frac{2}{3}$  

•  $\frac{10}{15}$  

•  $\frac{8}{9}$  

Equivalent Fractions (Multiplication)

• When multiplying your given fraction by another number, your equivalent fraction will be bigger

• Multiply both the numerator and denominator by the same number

Equivalent Fractions (Division)

• When dividing your given fraction by another number, your equivalent fraction will be smaller (can only be done using factors)

• Divide both the numerator and denominator by the same number

Multiple Choice

An equivalent fraction to  $\frac{2}{3}$  is  $\frac{10}{15}$ . What operation and number was used to find the second fraction?

• Multiplication, 3

• Multiplication, 5

• Division, 5

• Division, 4

Special Fractions

• There are some special fractions which we can easily find equivalent values

• All whole numbers are written over a denominator of 1 (e.g.  $\frac{3}{1}=3$ )

• Another type is where both the numerator and denominator are the same number. This will equal just 1 whole (e.g.  $\frac{5}{5}=1$  and  $\frac{7}{7}=1$ , so  $\frac{5}{5}=\frac{7}{7}$  )

Multiple Choice

What is an equivalent fraction to  $\frac{4}{4}$ ?

•  $\frac{4}{1}$  

•  $\frac{8}{4}$  

•  $\frac{10}{4}$  

•  $\frac{10}{10}$  

Poll

How confident do you feel about finding equivalent fractions?

• Very good

• Good

• Okay

• Not very

• Not at all

Simplifying Fractions

• Different from equivalent fractions, simplifying a fraction will always result in a fraction with smaller numbers

• It can be done by either dividing or cancelling out the HCF (highest common factor) between the numerator and denominator

Simplifying Fractions (HCF)

• HCF: the biggest number that fits into (divides into) both numbers perfectly (no remainders)

• E.g. 3 is a factor of both 9 and 12.  $9\div3=3$  and  $12\div3=4$  OR  $3\times3=9$  and  $3\times4=12$  
  

• E.g. 9 is NOT a factor of 9 and 12 although it fits into both, you cannot make 12 using 9 through multiplication or divide 12 by 9 perfectly.  $12\div9=1.33$ 

Multiple Select

What are the common factors of 16 and 32?

• 8

• 6

• 9

• 4

• 2

Multiple Choice

What is  $\frac{9}{21}$  simplified?

•  $\frac{6}{11}$  

•  $\frac{3}{16}$  

•  $\frac{3}{7}$  

•  $\frac{4}{9}$  

Poll

How confident do you feel about simplifying fractions?

• Very good

• Good

• Okay

• Not very

• Not at all

Adding & Subtracting Fractions

Part 2

Like Fractions

• Like fractions have the same denominator but can have different numerators (also can be the same)

• To add or subtract using fractions, they need to be like fractions

• To turn your fractions into like fractions, you need to find an equivalent fraction with the same denominator

Multiple Choice

Are the fractions  $\frac{2}{5}$  and  $\frac{5}{2}$  like or unlike fractions?

• Like

• Unlike

Multiple Choice

Are the fractions  $\frac{3}{7}$  and  $\frac{5}{7}$  like or unlike fractions?

• Like

• Unlike

LCM (lowest common multiple)

• Sometimes you will need to change more than one fraction so that they are like fractions

• To find a common denominator for both, use LCM (lowest common multiple)

• Multiple: a number made by multiplying your given number with any other number (1, 2, 3...)

Multiple Select

What are the common multiples between 2 and 5?

• 10

• 25

• 20

• 15

• 24

Multiple Choice

What is the LCM (lowest common multiple) of 2 and 5?

• 10

• 20

• 8

• 18

• 5

Adding & Subtracting Fractions

• Make both fractions like fractions through multiplication to get a common denominator

• You only add or subtract the numerator part of the fractions

• The denominator stays the same and doesn't change

• Simplify (if possible) when done

Multiple Choice

What is  $\frac{7}{11}-\frac{4}{11}$  ?

•  $\frac{3}{11}$  

•  $\frac{11}{11}$  

•  $\frac{3}{0}$  

•  $\frac{11}{0}$  

Multiple Choice

What is  $\frac{1}{2}+\frac{1}{5}$ ?

•  $\frac{7}{10}$  

•  $\frac{2}{10}$  

•  $\frac{2}{7}$  

•  $\frac{1}{10}$  

Poll

How confident do you feel about adding and subtracting fractions?

• Very good

• Good

• Okay

• Not very

• Not at all