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How to subtract mixed numbers that have unlike denominators | Fractions | Pre-Algebra | Khan Academy

2m read
·Nov 10, 2024

Let's try to evaluate 7 and 6 9ths - 3 and 25ths.

So, like always, I like to separate out the whole number parts from the fractional parts. This is the same thing as 7 + 6/9 - 3 - 25/100. The reason why I'm saying -3 and -25/100 is this is the same thing as -3 + 25/100.

So, you distribute the negative sign: you're subtracting a 3 and then you're subtracting the 25/100. Now we can worry about the whole number parts: 7 - 3. Well, 7 minus 3 is going to give us 4. So that's going to give us 4.

Then we're going to have 6/9 - 25/100. Let me think about what 6/9 - 25/100 is. We're going to have to find a common denominator. The least common multiple of 9 and 100 is going to be 900.

Now, they have no common factors, so it's going to be over 900. To go from 9 to 900, I have to multiply by 100. So, I'm going to have to multiply the numerator by 100: 6 * 100 is 600.

To go from 100 to 900, I had to multiply by 9, so I have to multiply the numerator by 9 if I don't want to change the value: 25 * 9 is 225.

So, 600/900 - 225/900 is going to be something over 900. 600 minus 225 is 375. So this is, if I subtract these two fractions right over here, I get 375/900.

So it's 4 + 375/900. If we wanted to write it as a mixed number, this is equal to 4 and 375/900, but we're not done yet.

We can simplify this further: 375 and 900 have common factors. They are both divisible by 75. So, we can say that this is actually...

If we divide the numerator by 75 and the denominator by 75, we end up with 4 and 375/75 is 5, and 900/75 is 12.

So we have 4 and 5/12. Actually, we're done. These two can't be simplified anymore: 4 and 5/12.

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