Equivalent Fractions

Pizza fractions


In the pizza on the left, what fraction is one slice of pizza? The answer is 1 part out of the 8 parts, one-eighth or 18.

In the pizza on the right, what fraction is two slices of pizza? The answer is 2 parts out of the 16 parts, two-sixteenths or 216.

These pizza servings are the same so 18 and 216 are equivalent fractions.



Examples

Multiplying both numerator and denominator by the same number:

One-half diagram
12 = 24 = 48
To change 12 to 24, multiply both the numerator and the denominator by 2.
To change 24 to 48, multiply both the numerator and the denominator by 2.

Two-thirds diagram
23 = 46 = 812
To change 23 to 46, multiply both the numerator and the denominator by 2.
To change 46 to 812, multiply both the numerator and the denominator by 2.

Dividing both numerator and denominator by the same number:

One-half dividing diagram
48 = 24 = 12
To change 48 to 24, divide both the numerator and the denominator by 2.
To change 24 to 12, divide both the numerator and the denominator by 2.

Two-thirds dividing diagram
812 = 46 = 23
To change 812 to 46, divide both the numerator and the denominator by 2.
To change 46 to 23, divide both the numerator and the denominator by 2.

More examples of equivalent fractions:

34 = 912 (Multiplied by 3)

56 = 2024 (Multiplied by 4)

3036 = 56 (Divided by 6)

2030 = 23 (Divided by 10)

Questions

What is the missing number, X?

Q1. 12 = X10
Q2. 13 = X12
Q3. 12 = 10X
Q4. 23 = X18
Q5. 25100 = X4

Answers
A1. 5
A2. 4
A3. 20
A4. 12
A5. 1

Changing a Mixed Number to an Improper Fraction

A mixed number is a mixture of a whole number and a fraction. An example of a mixed number is 212 When a mixed number is converted to a fraction only, it is called an improper fraction. An example of an improper fraction is 52

1 3/4 diagram
134 = 74
To change the mixed number of 134 to the improper fraction of 74,
multiply the whole number 1 by the denominator 4,
and then add on the numerator 3.

Changing an Improper Fraction Back to a Mixed Number

1 2/3 diagram
123 = 53
To change the mixed number of 123 to the improper fraction of 53,
multiply the whole number 1 by the denominator 3,
and then add on the numerator 2.