Equivalent Fractions

What Is a Fraction

A fraction is when an object is divided into a number of equal parts then each part is called a fraction.

Equivalent Fractions are fractions that have the same value, they represent the same number even though they may look different. These fractions all have the same value:

1 = 2 = 4

2 4 8

These fractions are the same because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value.

The rule to remember is:

"Change the bottom using multiply or divide,

And the same to the top must be applied"

How To Do Equivalent Fractions

WHEN FRACTIONS ARE EQUIVALENT.

Equivalent fractions are obtained by multiplying or dividing both the numerator and the denominator by the same number.

It must follow that 1 2 4

2 = 4 = 8

In the example above, we see that 1 1x2 2

2 = 4x2 = 4

Both numerator and denominator are multiplied by 2

Going in the opposite direction, we see that 4 2x2 2

8= 4x2 4

Example:

2 ?

5 = 10

SOLUTION: =

2 2x2 4

5 = 2x5 = 10

Simplifying Fractions

Simplifying fractions means to make the fraction as simple as possible.To simplify a fraction, both the numerator and denominator must be divided by the same number. This method is also called cancelling down or reducing the fraction.

The fraction is in the SIMPLEST FORM when it cannot be any more simplified.

When you are asked to simplify or reduce down a fraction, you should always try to simplify as much as you can to achieve the simplest form. You will do it by dividing both numerator and denominator by their Highest Common Factor

Example:

Simplify 32

48

SOLUTION:

32 4x8 4

48 = 6x8 = 6

(Both sides are divided by 8, so the fraction is canceled by 8)

The result is not in the Simplest form it may be simplified to:

4 = 2x2 = 2

6 3x2 3

(Both sides are divided by 2, so the fraction is reduced by 2)

The result is now in the Simplest Form

Converting Improper Fractions To Mixed Numbers and vice versa

IMPROPER FRACTION

An Improper fraction is a fraction that has a numerator larger than or equal to its denominator.

MIXED NUMBER

A mixed fraction is a whole number and a fraction combined into one e.g. 1 1

2

Example:

the improper fraction Example: The improper fraction 8

5

can be changed to the mixed number 1 3

5

by dividing the numerator 8 by the denominator 5. This gives a quotient of 1 and a remainder of 3. The remainder is placed over the divisor 5.

8 1 3

5 = 5

Improper Fraction To a Mixed Number

Converting Mixed Number To a Improper Fraction

example: 3 2

5

to covert this mixed fraction to an improper fraction multiply the whole number part by the fractions denominator (3x5=15) add that to the numerator (15+2=17) then write that down above the denominator 17

5

3 2 17

5 = 5

**Teach Me How To Fraction**

Adding and Subtracting Fractions And Mixed Numbers

fractions with the same denominator. You can add and subtract like fractions easily - simply add or subtract the numerators and write the sum over the common denominator.

Before you can add or subtract fractions with different denominators, you must first find equivalent fractions with the same denominator, like this:

Find the smallest multiple (LCM) of both numbers.

Rewrite the fractions as equivalent fractions with the LCM as the denominator.

(ADDING)

Example:

Find 1 + 2

5 5

Both fractions have the same denominator of 5, so we can simply add the numerators:

1 + 2 = 3

5 5 5

(SUBTRACTING)

Example:

Find 7 - 3

8 8

Both fractions have the same denominator of 8, so we can simply subtract the numerators:

7 - 3 = 4 = 1

8 8 8 2

the result was simplified the numerator and the denominator divided by 4.

(adding mixed numbers)

To add mixed fractions add the whole parts of the mixed fractions first

and then the fraction parts..

Example:

Find 3 8 + 5 5

9 6

Solution

3 8 + 5 5 = (3 + 5) + ( 8 + 5 ) = Must first make the denominators equal

9 6 9 6

8 + ( 16 + 15 ) = 8 31 = (8 + 1) 13 = 9 13 18 18 18 18 18

the resulting fraction part was improper , therefore it was changed to a mixed fraction.

(subtracting mixed numbers)

To subtract mixed fractions subtract the whole parts of the mixed fractions first and then the fraction parts.

But what to do if the left side fraction part is smaller than the right side fraction part?

Example:

Find 7 2 - 2 4

5 5

Solution:

7 2 - 2 4 = (7 - 2) + ( 2 - 4 ) = 5 + ( 2 - 4 ) =

5 5 5 5 5 5

Our problem is 2 < 4

5 5

4 + ( 5 + 2 - 4 ) = Take 1 from 5 and add it to 2

5 5 Remember? 1 = 5 )

5

4 + ( 7 - 4 ) = 4 3

5 5 5

Multiplying fractions is easy: you multiply the top numbers and multiply the bottom numbers. For instance:

2 4 2.4 8

3 15 = 3.15 = 45

When possible, you reduce. In the example above, however, nothing reduces, because 8 and 45 have no factors in common. If you're not sure whether anything can be cancelled off, you can always factor the numerator and denominator, and check for any shared factor

**Multiplying And Dividing Fractions**

(dividing)

there are 3 simple steps to divide fractions

step 1:Turn the second fraction (the one you want to divide by) upside-down

(this is now a reciprocal).

Step 2. Multiply the first fraction by that reciprocal

Step 3. Simplify the fraction (if needed)

Example:

1 ÷ 1

2 6

Step 1. Turn the second fraction upside-down (it becomes a reciprocal):

1 becomes 6

6 1

Step 2. Multiply the first fraction by that reciprocal:

1 × 6 = 1 × 6 = 6

2 1 2 × 1 2

how to simplify fractions