How to Multiply Fractions, Mixed Numbers and Improper Fractions

Mul­ti­ply­ing frac­tions is con­sid­er­ably eas­ier than adding or sub­tract­ing frac­tions. When you add or sub­tract frac­tions you have to first find a com­mon denom­i­na­tor and then con­vert the frac­tions so that they have that com­mon denom­i­na­tor. When you mul­ti­ply frac­tions, you can just go ahead and mul­ti­ply the numer­a­tors (the top num­ber of a frac­tion) and the denom­i­na­tors (the bot­tom num­ber of a frac­tion). It’s true that it’s advis­able to sim­plify the frac­tions before you mul­ti­ply them but mul­ti­ply­ing frac­tions is straightforward.

Because the mul­ti­pli­ca­tion of frac­tions is sim­ple, test ques­tions are likely to intro­duce a lit­tle bit of com­plex­ity by throw­ing in mixed num­bers and improper frac­tions. Here are some key definitions:-

Mul­ti­ply­ing Frac­tions in Four Sim­ple Steps

How­ever com­pli­cated you try to make it, any two frac­tions can be mul­ti­plied in four, sim­ple steps. This video walks you through these four steps:-

The video uses the multiplication:-

Multiplying Fractions question


Here are the four steps:-

Step 1:-  If you have a mixed num­ber con­vert it to an improper fraction.

3¾ is a mixed num­ber. To con­vert to an improper frac­tion, mul­ti­ply the whole num­ber by the denom­i­na­tor (the bot­tom num­ber) and add to the numer­a­tor (the top num­ber) and this gives the new numer­a­tor. In this case the numer­a­tor becomes:

(3×4) + 3 = 15.

This revised numer­a­tor is then placed over the denom­i­na­tor to give us an improper frac­tion (a frac­tion where the top num­ber is greater than the bot­tom num­ber) to give us:

3¾ = 15/4


Convert Mixed Number to Improper Fraction





Step 2:- Simplify

The more you can sim­plify the eas­ier it is to mul­ti­ply the frac­tions. In this exam­ple we have:-

Simplify fractions





Step 3:- Sim­ply Mul­ti­ply The Fractions

We just have to mul­ti­ply the numer­a­tors and denom­i­na­tors to give our ini­tial answer:-

Multiply Numerators and Denominators




Step 4:-  If you have an improper frac­tion con­vert it to a mixed number

Obvi­ously the answer will not always be an improper frac­tion but if it is, you need to tidy it up by con­vert­ing it to a mixed num­ber. Some teach­ers and exam boards will award you fewer marks if you do not com­plete this final step:

Convert Improper Fraction to Mixed Number





Here are the four steps in summary:-

Multiplying Fractions Summary

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