What fraction is largest?

Answer 1

If you mean from a given list of fractions, without giving those fractions we cannot say.

To do it yourself:

In any fraction:

• the denominator (bottom number) tells you how many parts make up a whole;
• the numerator (top number) tells you how many parts (of the given denominator) there are.

In general:

• the smaller the denominator the larger the fraction

The denominator tells you how many parts make up one whole, so the less parts there are, the larger each part must be and thus the larger the fraction will be (for a given numerator).

• the larger the numerator (top number) the larger the fraction

The numerator tells you how many of the parts there are, so the more parts there are, the larger the fraction will be (for a given denominator)

This can be used to find out whether fractions are larger or smaller than other ones.

Examples:

• 1/4, 1/2, 1/5

when divided into 4 parts each part is smaller than when divided into 2 parts, but larger than when divided into 5 parts, thus:

1/2 > 1/4 > 1/5

• 5/7, 3/7, 4/7

when the parts are the same size and there are 5 parts there is more than when there are 3 or 4 parts; when there are 3 parts, there is less than when there are 4 parts, thus:

5/7 > 4/7 > 3/7

• 1/2, 3/4, 5/7

When the denominators are different sizes, it's not so obvious which is larger. However, by splitting the parts into smaller parts so that the total number of parts in each fraction is the same (ie making them into equivalent fractions with the same denominator), then a comparison of how many of the new parts there are (their numerators) can be made:

1/2 each part split into 14 smaller parts gives 14/28

3/4 each part split into 7 smaller parts gives 21/28

5/7 each part split into 4 smaller parts gives 20/28

14 parts are less than 21 and 20 parts; 21 parts are more than 20 parts, thus:

21/28 > 20/28 > 14/28

or using the original fractions:

3/4 > 5/7 > 1/2