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A fraction is a number that is not a whole number. It is written as one number divided another number, e.g. ¾. The top number, 3, is called the numerator and the bottom number, 4, is called the denominator: the denominator can NEVER be zero.

Fractions are read as follows: ⅜ is read as 'three eighths'. The numerator is read as an ordinary counting number, BUT the denominator is read as an ordinal number: third(s), fourth(s), fifth(s) and so on.

1.

What does ^{7}⁄_{9} − ^{4}⁄_{9} equal?

2.

Which one of the following fractions is the same as six-eighths (^{6}⁄_{8})?

If you divide the denominator and the numerator by the SAME number, you can reduce the fraction to its simplest form. In this case, you divide the denominator AND the numerator by 2

3.

Which fraction lies between ^{2}⁄_{6} and ^{4}⁄_{6}?

4.

What does ^{3}⁄_{8} + ^{2}⁄_{8} equal?

If the denominators are the same, you can add the fractions by simply adding their numerators - it really is as easy as that!

5.

How many fifths (^{1}⁄_{5}) are there in 2?

10

5

20

There are five fifths in 1, so there are 5 × 2 = 10 fifths in 2. In general, the number in the denominator tells you how many fractions of that type are needed to make 1. For example, you need three thirds, ^{1}⁄_{3}, to make 1, but you need ten tenths, ^{1}⁄_{10}, to make 1 and so on. REMEMBER this stuff, and you won't get confused with fractions

6.

In a battle, ^{1}⁄_{10} of the general's army was destroyed. If he had 10,000 soldiers, how many soldiers were lost in the battle?

10,000

100

1,000

10

He lost ^{1}⁄_{10} × 10,000 = 1,000 soldiers

7.

How is ^{22}⁄_{30} read?

twenty-second thirty

twenty-two thirties

twenty-second thirtieth

twenty-two thirtieths

If you don't know your ordinal numbers, learn them now! For example, 20th = twentieth, 30th = thirtieth, 40th = fortieth and so on

8.

If you eat ^{5}⁄_{7} of a cake, how much cake will be left?

There are seven sevenths in 1. If you have eaten ^{5}⁄_{7}, there can only be ^{2}⁄_{7} left because 5 + 2 = 7: if the denominators are the same, you can add/subtract the fractions by simply adding/subtracting their numerators

9.

Which one of the fractions below is the biggest?

All the other fractions can be reduced to ^{1}⁄_{4} which is smaller than ^{1}⁄_{3} because you are dividing the same numerator, 1 in this case, by a smaller number: 3 in this case

10.

Peter's granny wanted to see if he understood his fractions. She asked him if he wanted ^{3}⁄_{5} or ^{6}⁄_{10} of the candies. What did Peter say?

He said that he wanted ^{3}⁄_{5} of the candies

He said that it didn't matter what fraction of the candies he took because the fractions were the same

He said that he wanted ^{6}⁄_{10} of the candies

He said that he wanted ^{3}⁄_{5} of the candies because ^{3}⁄_{5} was closer to a half than ^{6}⁄_{10}

The fractions are the same. If you divide the denominator and the numerator in ^{6}⁄_{10} by 2, you will get ^{3}⁄_{5}. The same is true if you multiply the denominator and the numerator in ^{3}⁄_{5} by 2, you will get ^{6}⁄_{10}

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^{3}⁄_{9}BUT this can be reduced to^{1}⁄_{3}if you divide the denominator and the numerator by the SAME number, in this case 3