A fraction is a number stated as a quotient with a numerator divided by a denominator into mathematical terms. A simple fraction is made up of two parts: an integer numerator and a non-zero integer denominator. Equivalent fractions are those with different numerators and denominators but their fractional values are the same. 5/10 and 7/14, for example, are similar fractions because they are both equal to 1 / 2 when simplified. Each fraction represents a part of a whole. If two or more fractions are equal to the same fraction when simplified, they are said to be equivalent.
There are three types of fractions,
- Proper fraction,
- Improper fraction, and
- Mixed fraction.
- Proper Fraction
- When the value in the numerator is smaller than the value in the denominator it is a proper fraction. For example ⅗, ⅚, ⅞, are all proper fractions.
- Improper Fraction
If the numerator is equal to greater than the denominator it is called the improper fraction. For example 8/5, 7/7, 9/4 are all improper fractions.
- Mixed Fraction
When a whole number and a fraction are together then it is a mixed fraction. For example, 2 ¾,5 ⅓,4 ⅖ are mixed fractions.
There are two ways in which you can find the Equivalent Fractions
- Multiplication Method
- Division Method
1. Multiplication Method
Step 1: Multiply both the numerator and denominator of a fraction by the same whole number.
Step 2: If you multiply the top and bottom of the fraction by the same number, you will not change the value of the fraction.
Find fractions equivalent to ⅖ by multiplying the numerator and denominator by the same whole number
Multiplying the numerator and denominator by 3
Multiplying the numerator and denominator by 4
Multiplying the numerator and denominator by 5
Multiplying the numerator and denominator by 6
Therefore these are all equivalent fractions:
2/5, 6/15, 8/20, 10/25 ,12/30
In the lowest terms, all of these fractions equal 2/5.
2. Division Method
Step 1: Divide the numerator and denominator of any fraction by the same number to find the equivalent fraction.
Example: Find an equivalent fraction of 60/90.
2 is a common factor of 60 and 90.
Again, 3 is a common factor of 30 and 45.
Here, 5 is a common factor of 10 and 15.
Therefore, a few equivalent fractions of 60/190 are 30/45, 10/15, 2/3,
To convert a mixed fraction to an improper fraction, follow these steps:
- The whole number part is multiplied by the denominator.
- Add that to the numerator
- Add the result to the denominator.
Example: Convert 4 to an improper fraction.
Solution: In multiplying the whole number by the denominator, you get:
4 × 5 = 20
Add that to the numerator:
20 + 3 = 23
Then write that result above the denominator:
∴ Fraction 4 = 23/5
In order to convert an improper fraction to a mixed fraction, follow these steps:
- Divide the numerator by the denominator.
- Write down the whole number answer
- Then write down any remainder above the denominator.
Example: Convert to a mixed fraction.
Divide 13 by 5 the remainder will be 3 and the quotient will be 2
First, write down the quotient 2 and then write down the remainder (3) above the denominator (5).
∴ Fraction = 2
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