Lesson 7: Lesson Seven--Multiplying, Dividing fractions; Decimals and Fractions
Lesson Seven: Multiplication and Division of fractions, Changing fractions to decimals and decimals to fractions.
Section One: Multiplication and division of fractions
Since multiplication and division of fractions is easy and very much alike, I will cover them both in the same section.
To multiply any fraction, first make sure the fraction is either proper (numerator smaller than denominator) or improper (numerator same of larger than denominator) before multiplying or dividing it--in other words, don't use mixed numbers! I have already explained to you that multiplying and especially dividing mixed numbers is very difficult and you don't need that kind of stress.
If you have a mixed number, turn it into an improper fraction. Multiply whole number by denominator, then add the numerator, keeping the same denominator.
To multiply fractions, multiply the numerators together, then multiply denominators together, and reduce. Such as:
4/5 x 3/7 = 12/35 (can't reduce)
3/4 x 4/9 = 12/36 = 1/3
In the above problem, you can cancel out the 4's, then cancel the 3 into the 9 to get 1/3. However, since it is almost impossible to show cancellation the usual way by crossing out the numbers being cancelled using a computer keyboard, I'll have to ignore it or say, "cancel out the 4's, then cancel the 3 into the 9."
If you have mixed numbers:
2 3/5 x 1 7/9 = 13/5 x 16/9 = 208/45 = 4 28/45 which cannot be reduced.
2 1/4 x 1 2/3 = 9/4 x 5/3 = 45/12 = 15/4 = 3 3/4
If you have whole numbers:
2 1/2 x 3 = 5/2 x 3/1 = 15/2 = 7 1/2
In any multiplication/division fraction situation with whole numbers, put the whole numbers over 1.
Now let's go on to division...
To divide fractions, keep the first fraction the way it is, but INVERT, or "flip over", or use the reciprocal, of the divisor (the second) fraction, then MULTIPLY the two fractions.
What's a reciprocal, you say? It is simply a "flipped over" fraction. The reciprocal of 2/3 is 3/2; the reciprocal of 6 (or 6/1) is 1/6, for example.
Thus:
3/4 divided by 2/3 = 3/4 x 3/2 = 9/8 = 1 1/8.
4/7 divided by 1 3/5 = 4/7 divided by 8/5 = 4/7 x 5/8 = 20/56 = 5/14
6/7 divided by 3 = 6/7 divided by 3/1 = 6/7 x 1/3 = 6/21 = 2/7
