Simplifying fractions Describe the basic property of fractions

Simplifying fractions

Describe the basic property of fractions A fraction remains the same value, when both its numerator and denominator are multiplied or divided by the same non-zero number.

Review Complete these fractions （3） ＝ （8） ＝（4） （2） ＝ ＝（8）＝ ＝（2） （4） ＝

Adam has to swim 100 meters and he’s already swum 75 meters. He swam Is of the distance. equivalent fraction with ?

If the numerator and the denominator are multiplied or divided by the same number (except for 0), the value of the fraction remains the same. 75 100 15 20 = = 75÷ 5 100÷ 5 15÷ 5 20÷ 5 = = 15 20 3 4

3 75 100 = 4 When we reduce a fraction to an equivalent fraction with a smaller numerator and smaller denominator, it is called simplifying fractions. Could continue to be simplified? If the numerator and the denominator have only one common factor 1, the fraction is in its simplest form.

Exercise 1、Write down 3 fractions with a denominator of 6, that are already in their simplest form 。。。 2、Write down all the proper fractions with a denominator of 6 that are already in their simplest form

Simplify to its simplest form We can divide both the numerator and the denominator by a common factor (except for 1). 24 24÷ 2 12 = = 30 30÷ 2 15 12 12÷ 3 4 = = 15 15÷ 3 5 The simplest form

We can divide both the numerator and the denominator by the highest common factor (except for 1). 24 24÷ 6 = 4 = 30 5 30÷ 6 The simplest form

Simplifying fractions can be written as: Step by step 4 12 4 24 = or 5 30 15 5 Only one step 4 24 4 = 30 5 5

Exercise Are the following fractions in their simplest form or not? If not, simplify them. √ √

Tips: If you can find the highest common factor of the numerator and the denominator immediately, it’s easier to find the simplest form by dividing the numerator and the denominator by it. Usually, we should leave fractions in the simplest form.

Exercise Find the highest common factor of the numerator and the denominator for the following fractions, and simplify them. 30 2 = 45 3 15 5 = 21 7 （30，45）=15 （15，21）=3 8 2 = 12 3 （8，12）=4

Try your best 1、Judge the following equations. Which one is in its simplest form? Why? 6 2 12 10 (√ ) = = (× ) 15 12 3 24 4 5 = 2 3 (× ) 20 24 = 5 6 (√ )

2、Check the mistakes in the following equation 7 （1） 42 7 = 56 8 ＝ 8 6 （2） 18 12 4 = 6 4 =1 2 4 ＝ 1

3、Put each apple into the corresponding basket 12 12 36 36 4 16 6 24 1 3 3 18 8 24 5 20 6 18 4 24 5 30 1 4 1 6

4、Write the following result in its simplest form （a） Jay sleeps 9 hours everyday. Express 9 hours of 1 day as a fraction. 1 day=24 hours 3 9÷ 24= = 8 9 hours can be expressed as of 1 day.

（b）Express 24 cm out of 1 m as a fraction. 1 m = 100 cm 6 24÷ 100= = 25 24 cm can be expressed as of 1 m.

Summary What’s the simplest form of a fraction? How do we simplify fractions?