Fractions and Decimals

A fraction is a part of the whole (object, thing, region). For example, 5/12 is a fraction. Here 12 is the number of equal part into which the whole has been divided, is called denominator and 5 is the number of equal parts which have been taken out, is called numerator.

Lowest Term of a Fraction

Dividing the numerator and denominator by the highest common element (or number) in them, you get the fraction in its lowest form.

For example, to find the fraction 6/14 in lowest form: since 2 is highest common element in numerator 6 and denominator 14, so dividing them by 2, you get 3/7.

Equivalent Fractions

If numerator and denominator of any fraction are multiplied by the same number then all resulting fractions are called equivalent fractions.

Addition and Subtraction of Fractions

Here, two cases arise as denominators of the fraction are same or not.

Case I: When denominators of the two fractions are same then you write denominator once and add (or subtract) the numerators.

Case II: If denominators are different, you need to find a common denominator that both denominators will divide into.

Multiplication and Division of Fractions

To multiply fractions, the numerators are multiplied together and denominators are multiplied together.

In division of fraction, the numerator of first fraction is multiplied by the denominator of second fraction and gives the numerators. Also denominator of first fraction is multiplied by the nemerator of second fraction and gives the denominator.

Proper and Improper Fractions

The fractions in which the number in numerator is less than that of denominator, are called proper fractions. If the number in numerator is greater than that of denominator, then the fractions are called improper fractions. For example, 4/3 is an improper fraction while 3/4 is a proper fraction.

Mixed Numbers

A mixed number is that, which contains both a whole number and a fraction. Improper fractions can be generally converted to mixed numbers.

Decimal Fractions

The fractions in which denominators has the power of 10 are called decimal fractions. For example, 0.25 = 25/100 = 1/4

HCF and LCM of Decimal Fractions

First, you make the decimal digits of the given decimal numbers, same by putting some number of zero if necessary. Then, find HCF or LCM ignoring decimals. Finally, put the decimal according as the given numbers.

Terminating and Non-Terminating Recurring Decimals

If decimal expression of any fraction be terminated then fraction is called terminating. For example, 5/16 = 0.3125

When the process of division is non terminating, such decimal expressions are called non terminating repeating (recurring) decimals. For example, 33/26 = 1.2692307

Non-Terminating, Non-Recurring Decimals

Every fraction can be put in the form of terminating or non-terminating recurring decimals. These decimal numbers can be put in the form of p/q. These are called rational numbers.

But some decimals numbers are there that can’t be put in the form of p/q. These are non-terminating, non-recurring decimals. Also these are called irrational numbers.

To convert Non-terminating Recurring Decimals Into Simple Fraction

First, write the non-terminating recurring decimal in bar notation. Then write the digit 9 in the denominator as many times as number of digits recurring in the numerator. Also, don’t put decimal in the numerator.

For example, 0.18181818... = 18/99 = 2/11

Mixed Recurring Decimals

A decimal fraction in which some digits are not repeated and some are repeated is called mixed recurring decimal.

To Convert Mixed Recurring Decimal Into Simple Fraction

First, you subtract non repeated part from the number (without decimal) and put number 9 as many times as number of recurring digits and also put the number 0 as many times odd number of non-recurring digits.

For example, 0.18888... = (18-1)/90 = 17/90