"Basic Properties of Ratio" Understanding Ratio PPT Courseware

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"Basic Properties of Ratio" Understanding Ratio PPT Courseware

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What is ratio?

The division of two numbers is also called the ratio of the two numbers.

16÷25=（16×4）÷(25 × 4)=64 ÷ 100=0.64

30÷10＝(30÷10)÷(10÷10)＝3÷1＝3

The property of constant quotient: In division, if the dividend and divisor are multiplied (or divided) by the same number (except 0) at the same time, the quotient remains unchanged.

The basic properties of fractions: If the numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, the size of the fraction remains unchanged.

Using the invariant property of quotients, we can perform simple calculations of division.

According to the basic properties of fractions, we can reduce fractions into simplest fractions.

Applying the basic properties of ratio, we can convert the ratio into the simplest integer ratio.

Method of inductive simplification:

(1) Integer ratio - the first and last terms of the ratio are divided by their greatest common divisor → the simplest ratio.

(2) Decimal ratio - the first and last terms of the ratio are expanded by the same multiple → integer ratio → the simplest ratio.

(3) Fractional ratio - the first and last terms of the ratio are multiplied by the least common multiple of their denominators → the ratio of integers → the simplest ratio.

1. Whose eyes can see accurately? (Judge the following questions based on the basic properties of ratio)

(1) 4: 15＝ (4×3): (15÷3)＝12: 5 ( )

(2) 10 : 15＝(10÷5):(15÷3)=2 : 3 ( )

(3) 1/3 : 1/2＝ (1/3×6): (1/2×6) ＝ 2 : 3 ( )

(4) 0.6 : 0.13 = (0.6×100) : (0.13×100) = 60 : 13 ( )

2. Choose the correct answer.

(1) The ratio of 9�6 is ( )

(A) 3 � 2 (B) 1— (C) 2 � 3

(2) The simplest ratio of 9/0.03 is ( )

(A) 300� 1 (B) 300 (C) 1� 300

(3) The simplest ratio of 0.25 �1.25 is ( )

(A) 25� 125 (B) 1� 5 (C) 5� 1

3. To produce a batch of parts, A alone takes 6 hours to complete, and B alone takes 8 hours to complete.

(1). The simplest ratio of the time it takes A to complete the task to the time it takes B to complete the task is ( ) � ( )

(2). The simplest ratio of A’s work efficiency to B’s work efficiency is ( ) � ( )

(3). The simplest ratio of B’s work efficiency to A’s work efficiency is ( ) � ( )

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Update Time: 2024-10-04

This template belongs to Mathematics courseware Jiangsu Education Edition Sixth Grade Mathematics Volume 1 industry PPT template

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