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Mixed fractions: Multiplying and adding

How do we multiply mixed fractions.

 

We could treat the parts separately.  I mean, its the multiplication of two mixed numbers and we’ve been asked to give the answer as a mixed number..  so we can use multiply each part of the first number with each part of the second.

1 x 3     +   1 x 1/3   + 3/4 x 3  +  3/4 x 1/3

= 3  + 1/3 + 9/4 + 1/4

Then we need to get the three fractions over the same number, 12

= 3 + (4 + 27 + 3)/12 = 3 + 34/12 = 3 + 17/6 = 3 + 2 5/6 = 5 5/6

But actually that’s actually quite a lot of work,  and changing these mixed numbers into ‘top-heavy’* fractions  and back again can save time….

In this pic you’ll see I’ve converted the two numbers into 7/4 and 10/3 – done just a little cancelling, and then multiplied

The answer is 35/6   which we can convert back into 6 5/6. This  the same answer as before,  which is always a relief!

We can also add these two mixed numbers. I think the first method is easier then.  Don’t convert into top heavy fractions. We don’t need to multiply all parts together.  Just add the whole numbers. Then add the fractions separately, which does mean looking for a common denominator

1 + 3 = 4
3/4 + 1/3 = 9/12 + 4/14 = 13/12 = 1 1/12

So the answer is 5 1/12

 

If you would like some more practice in working with mixed numbers, look at this document

 

*The proper word for top heavy fractions is ‘vulgar’ fractions and I’m sure you’ll here a teacher use this word..  Its just not a words I like for numbers..  all numbers are fun, none of them vulgar at all  IMHO!!

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