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UNDERSTANDING FRACTIONS

Simplifying Fractions

​What is a Simplified Fraction?

Some fractions can be simplified.

For example, the fraction 2/4  can be simplified to 1/2.

A simplified fraction is a fraction that is already in its simplest form. If you can’t find an equivalent fraction with a smaller numerator and denominator then you’ve got a simplified fraction.

General Information

BASIC CONCEPTS

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  • Any number multiplied or divided by 1 doesn’t change its value.

  • Similarly, dividing the numerator and the denominator by the same number won’t change the value of the fraction.

  • The simplest form of a fraction has no common factors in the numerator and denominator.

  • Factors are numbers that are multiplied to give a product. 

What Fraction of Fish can be Shaded Blue

  • 6 blue fish

  • 12 total fish

  •  6/12 of the fish are blue

  •  We can simplify this fraction further because 6 and 12 both have common factors.

       1/2  is the simplest form of  6/12

How to Simplify Fractions

A fraction can be simplified by dividing both the numerator and denominator by a common factor.

6/8 = 6/8 ÷ 2/2 = 3/4

Let’s look at the fraction  :

  • The numerator and denominator are both multiples of 2.

  • If we divide the numerator and denominator by 2, we’ll get an equivalent fraction.

  • 6/8 can be simplified to 3/4

How to Simplify Fractions

  • If you divide the numerator and denominator of a fraction by the same number, you get an equivalent fraction. In the previous example we divided both 6 and 8 by 2.

  • 6 and 8 are both divisible by 2. This means 6 and 8 can be divided by 2 without a remainder.

  • Since 6 and 8 are both divisible by 2, we can also say that 2 is a factor of 6 and 8.

  • 2 as a factor of 6 can be written as: 2 x 3 = 6

  • 2 as a factor of 8 can be written as: 4 x 2 = 8

   Therefore 2 is a factor of both 6 and 8. This is also why we coulddivide the numerator, 6, and the denominator, 8, by 2 to get 3/4.

Finding Factors

Let’s review factors!

  • Factors are numbers that multiply together to make a larger number. 

Example: What are the factors of 10?

Example Factors 

Find the Simplest Form of the Fraction

We can see above that 2 and 4 are both divisible by 2 because

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2÷2 = 1

4÷2 = 2

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Since 2 and 4 are both divisible by 2, it means that 2 is a factor of these numbers. 

Divide the numerator and denominator both by 2 to get the simplest fraction  1/2.

Find the Simplest Form of the Fraction

We can see above that 4 and 10 are both divisible by 2 because

4÷2 = 2

10÷2 = 5

Since 4 and 10 are both divisible by 2, it means that 2 is a factor of these numbers.

Divide the numerator and denominator both by 2 to get the simplest fraction 2/5  .

Quick Review!

5/10 ÷ 5/5 = 1/2

5/5 = 1

Notice: The value of the fraction doesn’t change.

Dividing the numerator and denominator by the same number is the same as dividing by 1.

Find the Simplest Form of the fraction

4/16

  • First, find the common factors of the numerator and denominator.

Factors of 4:   1 , 2 , 4

(1 × 4 = 4; 2 × 2 = 4; 4 × 1 = 4)

Factors of 16:  1 , 2 , 4 , 8 , 16

(1 × 16 = 16; 2 × 8 = 16; 4 × 4 = 16;

8 × 2 = 16; 16 × 1 = 16)

Find the Simplest Form of the fraction

  • Greatest Common Factor (GCF)

    •  GCF is the greatest number that is both a factor for the numerator and denominator.

    •  In the previous example, it is 4.

  • ​Divide the numerator and denominator by the GCF.

4 ÷ 4 = 1

16 ÷ 4 = 4

•   So, the simplest form of 4/16  is 1/4  .

Find the Simplest Form of the Fraction

 

Common factors:

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16 : 1 , 2 , 4 , 8 , 16

84 : 1 , 2 , 4 , 6 , 7, 12 , 14 , 21 , 42 , 84

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  • Once past the maximum value of the numerator, there won’t be a common factor.

  • Greatest Common Factor = 4

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16/84 ÷ 4/4 = 4/21

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Find the Simplest Form of the Fraction

 

Toy Cars

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Alex has six toy cars.  Three of the cars are blue. How can you write a fraction for the blue cars in simplest form?

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Fraction 3/6     Blue cars (numerator)

                             Total cars (denominator) 

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  • Common factors

3 : 1,  3

6 : 1,2, 3, 6

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3/6 ÷ 3/3 = 1/2

Video: Simplifying Fractions

How to Convert an Improper Fraction to its Simplified Form?

Divide the numerator by denominator to obtain quotient and remainder. Then, the mixed fraction or the simplified fraction can be written as Quotient=Remainder Divisor Quotient/Remainder Divisor.

​How are Fractions Reduced to their Simplified Form?

To reduce a fraction into its simplest form, divide the numerator and denominator by their highest common factor.

What is the Easiest way to Simplifying Fractions?

One of the quickest ways to reduce a fraction to its simplest form is to divide the numerator and denominator of the fraction by their highest common factor.

Frequently asked questions

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