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RULES OF FRACTIONS

Fractions are hard for many students. Here we explain the rules of fractions. You'll also learn some new words like numerator, denominator, like and unlike fractions, proper, improper and mixed fractions.

A fraction has two numbers. The top number is the numerator, it is the number of parts you have. The bottom number is the denominator, it is the number of parts the whole is divided into.

A proper fraction is a fraction where the numerator is less than the denominator. Example: 2/3 and 3/5 are proper fractions.

With improper fractions the numerator is greater than or equal to the denominator (bv. 6/5 of 4/4). A whole number and proper fraction together is called a mixed fraction (bv. 4 3/7).

When the numerator of a fraction is 1, than we have a unit fraction.

When fractions look different, but have the same value we call them equivalent fractions.

Simplifying fractions

Somtimes fractions have numerators and denominators that are numbers that have more factors than 1 and itself. Now you have to simplify the fraction.

Find the Greatest Common Factor (GCF) of the numerator and denominator. Divide the numerator and the denominator by the GCF. To reduce a fraction, divide the top and bottom by the highest number that can divide into both numbers exactly. Now the fractions is written in its simplest form. Dividing numerator and denominator of a fraction doesn"t change the value. You get an equivalent fraction in its simplest form.

EXAMPLE:

• 9/21 (you can divide the numerator 9 by 3 and 9; you can divide the denominator 21 by 3, 7 and 21)
• 3 is the GCF (now we divide numerator and demoninator by 3)
• 9/21 simplified gives us 3/7

To make addition, subtraction, multiplication and dividing of fractions easier, we recommend to look if you can simplify the fractions. After fraction operations you'll often have to simplify fractions and change improper fractions into mixed fractions.

Make unlike fractions like fractions

Only like fractions can be added or subtracted. So we first have to convert unlike fractions to equivalent like fractions. We need to find the smallest, or Least Common Denominator (LCD). The LCD is the smallest number that can be divided by both denominators.

You need to find the least common multiple of both denominators. Make a list the multiples of the highest denominator. Stop when you find a multiple that is also a multiple of the other denominator. Now you have found the least common multiple of both denominators.

Now that we have our least common denominator, we can make equivalent like fractions by multiplying the numerator and denominator of each fraction by the factor(s) needed.

EXAMPLE:

• 1/6 + 3/4 = (we have unlike fractions)
• 12 (least common multiple of 6 and 4)
• 1/6 is renamed as 2/12 (mulitply numerator and denominator by 2 to become 12)
• 3/4 is renamed as 9/12 (mulitply numerator and denominator by 3 to become 12)
• 2/12 + 9/12 = 11/12 (no we have like fractions that can be added)

Change improper fractions into mixed fractions

Knowledge of division tables is necassary to make mixed fractions out of improper fractions. How many times the denominator fits in the numerator. This gives you the whole number. The remainder is the numerator

EXAMPLE:

• 197 = (the denominator 7 fits 2 times in the numerator 19)
• 197 = 2 57 (19 - 14 = 5; 5 is the remainder and the new numerator)

Add or subtract the numerators. Put the answer over the denominator. Simplify the fraction if needed.

EXAMPLE:

27 + 37 = 57          49 - 39 = 19

Unlike fractions have a different denominator. If you have unlike fractions, you'll need to change them into like fractions before you can add or subtract.

Read rules on make unlike fractions like fractions.

EXAMPLE:

23 + 14 = 812 + 312 = 1112

23 - 15 = 1015 - 315 = 715

Multiply fractions

There are 3 simple steps to multiply fractions Multiply the numerators and multiply the denominators. Simplify the fraction if needed.

EXAMPLE:

37 * 25 = 3*27*5 = 635

Dividing fractions

Turn the second fraction upside down, then just multiply. Simplify the fraction if needed.

When dividing fractions by a number. A number is a fraction with 1 as denominator. Inverting the fraction gives you 1 as numerator.

EXAMPLE:

12 : 18 = 12 * 81 = 82 = 4

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