Revision: Fractions and Decimals Maths Secondary School (English Medium) (5 to 8) Class 7 CBSE

A fraction is a numerical quantity that represents a part of a whole.

In a proper fraction, the numerator is less than the denominator.
i.e., numerator < denominator.

Example:

`3/4, 1/2, 9/10, 5/8` are examples of a proper fraction.

A fraction is called an improper fraction when the numerator is greater than or equal to the denominator.

i.e., numerator > denominator.

Example:

`3/2, 12/7, 18/5` are all examples of improper fractions

A fraction that contains a whole number and a proper fraction is called a mixed fraction.
`3 2/3, 4 2/3, 3 7/8` are all examples of mixed fractions.

 If two or more fractions have the same value, they are called equivalent or equal fractions.
E.g., `1/3`, `3/9`, `6/18` and `9/27` are equivalent fractions.

The product of the numerator of the first and the denominator of the second is equal to the product of the denominator of the first and the numerator of the second. These two products are called cross-products.

`a/b = c/d`

`a xx d = c xx b`.

A like fraction is a collection of two or more fractions with the same denominator.
Example:

`2/6`, `3/6` and `4/6` are examples of like fractions.

Unlike fractions are fractions with different denominators.
Example:

`1/2`, `1/3` and `2/5` are examples of unlike fractions.

• If the denominator is 10 → place the decimal after 1 digit from the right.

• If the denominator is 100 → place it after 2 digits from the right.

• If the denominator is 1000 → after 3 digits from the right. 

`a/c` × `c/d` = `"a × c" / "b × d"`

`a/b` ÷ `c/d` = `a/b` × `d/c`