Fractions

FRACTIONS

Fractions are numbers of the sort a/b (a divided by b) where a and b are whole numbers and a is less than b.

You need to be careful how you manipulate fractions. Adding and subtracting in particular!

A) Fractions can be multiplied together very easily - multiply the numerators together and divide by the denominators multiplied together:

1/2 x 3/4 = (1x3)/(2x4) = 3/8

B) Fractions can be divided quite easily. Invert one of the fractions and treat it as a multiplication problem:

1/2 3/4 = 1/2 x 4/3 (ie 3/4 inverted) = (1x4)/(2x3) = 4/6 = 2/3

C) Fractions can sometimes be simplified, as in the last example where 4/6 = 2/3. You should always try to express a fraction in its simplest form.

D) Fractions can be added but you need to make sure that the denominators are the same:

1/2 + 1/5 = 5/10 + 2/10 = 7/10

Note the method. You cannot add 1/2 to 1/5. Find the lowest common multiple, in this case 10, and convert both fractions to fractions with 10 as the denominator, then you can just add the numerators together.

The same method is used for subtracting fractions.

E) Finding a fraction of something:

3/5 of 460 = (1/5 of 460) x 3 = 92 x 3 = 276

F) Ordering fractions eg 1/2, 2/7, 3/5. Find the lowest common denominator, in this case 70, and convert each fraction to fractions with 70 as the denominator. Then add. So

1/2 = 35/70

2/7 = 20/70

3/5 = 42/70

so in ascending order we have 2/7, 1/2, 3/5. (Make sure you can calculate the lowest common denominator of 2 or 3 numbers. And make sure you can convert a fraction to one using a different denominator.)

Questions

Q1 Work out, then simplify:

a) 2/5 x 2/3, 3/8 x 5/6, 5/7 x 6/25

b) 2/5 + 2/3, 3/8 + 5/6, 5/7 + 6/25

c) 2/5 2/3, 3/8 5/6, 5/7 6/25

d) 2/3 - 2/5, 3/8 - 2/11, 5/7 - 6/25

Q2. What is two-fifths of 320?

Q3. What is 4/7ths of 287?

Q4. Put the following in ascending order:

a) 4/15, 1/5, 1/3, 7/30

b) 3/14, 1/7, 5/28, 2/7