### Multiplying Fraction / Properties Of Multiplication Of Fractions

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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?*__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.**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.**Properties Of Multiplication Of Fractional Numbers****Property 1:**Changing the order of fractional number does not change the product.**Property 2:**When a fractional number is multiplied by 1, the product is the fractional number itself.**Property 3:**The product of any fractional number and zero (0) is zero (0).**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.

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