This is What We Have Learned 2

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This is What We Have Learned 2

Table of Contents

Topic 9: Dividing Fractions and Mixed Numbers

Do you know how to simplify?!

There are two ways to simplify. The first one is the most common one. After you finished your operation and end up with a fraction that isn’t in its simplest form (simplest form is when you can’t divide the numerator and denominator of a fraction by any more number other than 1) you divide the numerator and denominator by their greatest common factor. For example the greatest common factor of 16/32 is 16 so we divide the numerator and denominator by 16 and end up with 1/2. The other way is to simplify is while we are multiplying fractions. If you have 3/5 x 10/11 you can divide the numerator and denominator of the different fraction, and vice versa, by their greatest common factor (if possible). So 5 becomes 1 and 10 becomes 2, then just multiply normally. This makes it so that you don’t have to simplify at the end and just do it while you are multiplying to end up with a fraction that's already in it simplest form.

Reciprocals of Fractions

To know how to divide fractions you first have to learn what's a reciprocal

A reciprocal is basically turning the fraction upside down, the numerator becomes the denominator and the denominator becomes the numerator. For example 3/4 becomes 4/3 and 2/5 becomes 5/2. Whole numbers have reciprocals as well. 3 equals 3/1 so its reciprocal is 1/3.

Now it's Time to Finally to Divide Fractions and Mixed Numbers

Now that we know what's a reciprocal we can start dividing fractions! (Took you long enough...). When we are dividing fractions we change the operation from division to multiplication. After that we transform the fraction of the divisor to its reciprocal. Finally you just got to multiply fractions normally. Remember to simplify if possible!!! Now I know it seems like a lot, but it’s actually pretty simple, so if you just practice a little, you’ll get really good at it.

But wait! How do we divide mixed numbers!? Oh yes... Well dividing mixed numbers will require an extra step, which is turning the mixed number into an improper fraction. If you don’t know how to turn a mixed number into an improper fraction, you just gotta multiply the whole number times the denominator and add the numerator. The denominator will stay the same even if it’s an improper fraction. For example 3 1/2 is 3x2+1 so this equals 7/2. After you did that you can now divide those fractions normally.

Don’t forget to simplify if possible!