# Fractions

## Free Fraction Calculator (by Radu Turcan)

Operator: + - * /

=

Solution:

#### Fraction Definition

Let a and b are whole numbers and b is not 0.
A number a/b is called fraction.
The number a is called numerator, and b is denominator. A fraction is a number that expresses part of a group.
Denominator shows on how many equal parts we divide and numerator shows how many parts we take.

#### Fraction examples

Example 1: Becky, Merry and John want to divide a chocolate. What part of the chocolate will they take?
What part of the chocolate will the girls take?

The children divide the chocolate on three parts. So everyone takes 1/3 from the whole chocolate.
The girls are two so they will take two parts of the devided chololate in math language they will take 2/3 from the chocolate.

Example 2: How many are the yellow solders from all soldiers?

Example 3: What part of the apples are missing?

#### Fraction Properties

Propery I: All hatched parts from the circles are half(1/2) of the circles and they are equal to 1/2, 2/4 and 3/6. But they all represents half of the circles so 1/2 = 2/4 = 3/6

The fraction 2/4 is result of 1/2 when we multiply the numerator and the denomerator of the fraction by 2. From 3/6 => 1/2 when we devide the numerator and the denomerator by 3. Let's a, b and c are whole numbers, and b and c are not 0.

 a b
=
 a.c b.c
and
 a b
=
 a:c b:c

Property II: Every two fractions with equal denomerators the bigger fracrion is with the bigger nomerator. If a, b and c are whole numbers and c is not 0:

 a c
>
 b c
, if a > b

Property III : Every two fractions with equal nomerator the bigger fraction is with the smaller denomerator.
If a, b and c are whole numbers, b and c are not 0.

 a b
>
 a c
, if b < c

#### Fraction Test

1. A tennis player won 6 from 12 sets. Then he won all the other 6 sets until the end of the game. What part of the sets he won?
1/3      2/3      1/2

2. A boy had \$36. He went to a shop and after buying something he had \$8. How much money did he spend?
2/9      2/7      7/9

3. In my class there are 30 pupils - 12 from them are girls. A year later there were 6 new boys. What is the part of the girls?
1/2      3/5      1/3

4. If the fraction n/40 is between 1/5 and 1/4 then n can be:
8      9      10

5. 6/24 is equal to:
1/4      3/4      6/12

6. Which fraction is twice bigger than 3/8?
6/16      3/16      3/4

7.* Which fraction is the biggest 12/13, 13/14, 14/15 or 15/16?
15/16      12/13      14/15

8. In which group the fractions are in decreasing order? 7/11, 5/8, 3/5, 2/3; 4/3, 7/11, 5/8, 3/5; 21/11, 2/3, 3/5, 5/8
2      3      1

9.* In which group the fractions are in increasing order? 1. 13/19, 13/23, 17/23; 2. 13/23, 17/23, 13/19; 3. 13/23, 13/19, 17/23;
1      2      3

10. The result from (20+4.3)/120 is a fraction equal to:
2/5      3/5      4/15

11. The result from (1+2+3+4+5)/(1.2.3.4.5) is a fraction equal to:
5      1      1/8

#### More about fractions in the maths forum

Send us math lessons, lectures, tests to: