English for Mathematics

1. FRACTION
Addition of Fractions
Adding fraction is very easy. You have to remember just one thing. The denominator
always must be the same. Let’s take a hexagon as our example. Each piece is one sixth of
the hexagon. So four pieces will be four sixths of the hexagon. Let’s try and add one sixth
and four over six. Hmm.. It would be five, five over six. So, one sixth plus four sixths
equals five sixths. Wasn’t that easy? I’m sure that you noticed that we are just adding the
numerators. But we have to make sure that the denominators must be the same. Let’s look
at one more example quickly. Take a pizza with eight slices. One piece is one eighth and
five pieces is five eighths. Let’s add the two. We get six eighths. So, we see that one
eighth plus five eighths is equal to one plus five over eight which equals six over eight. If
we reduce six over eight, we get three over four. Did you notice what happening? We are
just adding the numerators and we can only do this when the denominators are the same.
Now let’s do one without pictures. Two over nine plus three over nine. Since the
denominators are the same, we can simply add the numerator. Therefore, we have the
numerator as two plus three and the denominator remains nine. Hence, the answer is five
over nine. Now, let’s try and add two fractions which have different denominators. It is
easy once you do a couple of examples. Let’s add a half and one third. We can add the
numerator only if the denominators are the same. So how do we make the denominators
same? The LCM of two and three is six. So six ,which is the LCM, is our new denominator.
Change the first number, a half, so that it has six as the denominator. And change the
second number, one third, so that it has six as denominator. Note that we have the same
the denominators. We can simply add the numerators, three plus two equals five. So the
answer is five over six.
Subtraction of Fractions
What’s a lot like addition. Like an addition, just remember that the denominators always
must be the same. Let’s try seven over eight minus three over eight. Let’s look at a pizza,
cut into eight pieces. Seven over eight equals seven pieces. Take away three eighths that is
three pieces. We are left with four pieces. So seven eights minus three eights equals four
eights. But look what we really did. We just subtracted the numerators. We can reduce
four eights to an half. Now, let’s do one without pictures. Ten over fifteen minus eight
over fifteen equals how much? Numerator will be ten minus eight, the denominator will be
fifteen, which is equal to two. Therefore the answer will be two over fifteen. Now let’s try
and subtract two fractions which have different denominators. Take two thirds minus three
fifths. Here we have to find the common the denominator which is the LCM. The LCM of
three and five is fifteen. Therefore the denominator for both of fractions will be fifteen.
Change the first number, two thirds, so that it has fifteen as the denominator. And change
the second number, three fifths, so that it has fifteen as the denominator. And the
numbers will be ten over fifteen minus nine over fifteen equals to one over fifteen.
Therefore one over fifteen will be our answer. Let’s try one more. Seven over ten minus
thirteen over twenty. The LCM will be.. Hemm.. Twenty. Seven over ten will become seven
multiplied by two over ten multipled by two which equals fourteen over twenty. Thus,
fourteen over twenty minus thirteen over twenty will be fourteen minus thirteen over
twenty equals to one over twenty.