How to Subtract Fractions in 5 Simple Steps

The method for sub­tract­ing frac­tions is very sim­i­lar to the method for adding frac­tions. The key point is that you have to make the denom­i­na­tors (the bot­tom num­bers) equal before you carry out the subtraction.

There are 5 sim­ple steps to fol­low to sub­tract any frac­tion from another. It’s only as many as 5 because in some cases you have to deal with mixed num­bers (a com­bi­na­tion of a whole num­ber and a frac­tion) and improper frac­tions (a frac­tion where the top num­ber or numer­a­tor is greater then the denom­i­na­tor or bot­tom number).

I’ve already sneaked in a few def­i­n­i­tions, but here’s a reminder of terms that you’ll need:-

Subtraction of Fractions, Key Definitions- Numerator, Denominator, Mixed Number, Improper Fraction

 Video Worked Exam­ple: How to Sub­tract Frac­tions in 5 Sim­ple Steps

This video steps through the 5 steps. For best results, watch the video and then read through the text below:-

Sub­tract­ing Frac­tions Worked Example

This worked exam­ple shows the five steps:

2¼ — 3/7

Step 1 If you have a mixed num­ber con­vert it to an Improper Fraction

2¼ — 3/7 = 9/4 — 3/7

Step 2 Find a com­mon denominator

9/4 — 3/7

Some­times a com­mon denom­i­na­tor will be obvi­ous. How­ever we need a fool­proof method. Sim­ply mul­ti­ply the denominators.

So, using our exam­ple, our denom­i­na­tors are 4 and 7 so we know that a com­mon denom­i­na­tor will be: 4 x 7 = 28

Step 3 Con­vert the Numerators

For each frac­tion we need to mul­ti­ply the numer­a­tor by the same amount as we mul­ti­plied the denom­i­na­tor. In this exam­ple we have

9/4 — we have to mul­ti­ply the denom­i­na­tor by 7 to get to the com­mon denom­i­na­tor of 28. There­fore we also have to mul­ti­ply the numer­a­tor by 7 to give 9 x 7 = 63

3/7 - we have to mul­ti­ply the denom­i­na­tor by 4 to get to the com­mon denom­i­na­tor of 28. There­fore we also have to mul­ti­ply the numer­a­tor by 4 to give 3 x 4 = 12.

So we have con­verted 9/4 — 3/7  to  63/28 — 12/28

Here’s a graphic rep­re­sen­ta­tion of Steps 2 & 3 together:-

Subtracting Fractions- Convert to a Common Denominator

 Step 4 Sub­tract one Numer­a­tor from another.

This is straight­for­ward as you might imagine:-

63/28 — 12/28 = 51/28

Step 5:-  Sim­plify (if pos­si­ble) and Con­vert Any Improper Frac­tion to a Mixed Number:-

Convert Improper farction to mixed number

 

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