Multiplication of Fraction
Multiplication is actually a repeated addition. Let’s understand this with following example.
Dia distributed chocolates equally among her 6 friends. Each of them got ½ a chocolate. How many chocolates did Dia distributed?
Repeated addition: ½ + ½ + ½ + ½ + ½ + ½ = 3
Multiplication: ½ x 6
= 3
So, Dia distributed 3 chocolates.
We found that multiplication is faster than adding numbers.
Note: ‘Of’ stands for multiplication.
Multiplication of a Fractional Number by a Whole Number
Step 1: If the given fraction is a mixed fraction, convert it into improper fraction.
Step 2: Rewrite given whole number as a fraction by simply placing 1 below the whole number.
Step 3: Multiply the numerator of the first fraction with the numerator of the second fraction to get the new numerator.
Step 4: Multiply the denominator of the first fraction with the denominator of the second fraction to get the new denominator.
Step 5: Now write the new numerator over the new denominator.
Step 6: Simplify the fraction formed in its lowest terms by dividing the numerator and denominator by the same factor.
Step 7: Always write the answer as a mixed fraction, if it is not a proper fraction/whole number.
Example 1:
Example 2:
Multiplication of a Fraction by a Fraction
Step 1: Convert mixed fraction into improper fraction.
Step 2: Simplify the fractions if not in lowest terms.
Step 3: Multiply the numerators of the fractions to get the new numerator.
Step 4: Multiply the denominators of the fractions to get the new denominator.
Step 5: Now write the new numerator over the new denominator.
Step 6: Simplify the new fraction if needed.
Step 7: The answer should always be a whole number, a mixed fraction or a proper fraction and never an improper fraction.
Example 1:
Example 2:
Example 3:
Properties of Multiplication Of Fractional Numbers
Property 1: Changing the order of fractional number does not change the product.
Example:
Property 2: When a fractional number is multiplied by 1, the product is the fractional number itself.
Example:
Property 3: The product of any fractional number and zero (0) is zero (0).
Example:
Multiplicative Inverse or Reciprocal
To find the multiplicative inverse of a proper or improper fraction, we interchange the numerator and denominator of the given fraction. If the given number is a mixed fraction or whole number, then first change it into an improper fraction, then interchange the numerator and denominator. Another name for Multiplicative Inverse is Reciprocal.
When we multiply any number by its multiplicative inverse, we get 1 as answer.
Important Facts
1. The reciprocal of a proper fraction is an improper fraction.
2. The reciprocal of an improper fraction is a proper fraction.
3. The reciprocal of a whole number excluding “0” will always have a numerator 1 i.e. it will be a unit fraction.
4. The multiplicative inverse of 1 is 1.
5. The multiplicative inverse of 0 cannot be found.