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"Basic Properties of Ratio" Ratio and Proportion PPT Courseware
teaching objectives
1. Combined with specific examples, go through the process of understanding and comparing.
2. Understand the meaning of ratio and ratio, and know the relationship between each part of ratio and the parts of division and fraction; be able to write the ratio of two numbers, and be able to calculate the ratio.
3. Feel the close connection between mathematics and life, and be full of curiosity about comparative knowledge.
review review
Find the ratio.
(1) 9�45＝9÷45＝0.2
(2) 15：5＝15÷5＝3
Do the math: Is the ratio of crude protein to total mass of the two bags of feed the same?
If the first and last terms of a ratio are multiplied or divided by the same number (except 0) at the same time, the ratio remains unchanged. This is called the fundamental property of ratio.
Applying this property can draw the simplest integer ratio.
Summary: If the preterm and consequent of a ratio are both integers, you can directly divide the preterm and consequent of the ratio by their greatest common factors when simplifying.
practice
1. Convert the following ratios into their simplest integer ratios.
0.12:2.5=12:250=6:125
2. There are 21 boys and 24 girls in a certain class. The ratio of the number of boys to the number of girls is ( ): ( ), and the ratio of the number of girls to the class is ( ): ( ).
3. Fill in the blanks according to the basic properties of ratio.
①6 �8=（ ）
(A) 3 � 4 (B) 2 � 3 (C) 12 �18
②10 �20= ( )
(A) 2 � 5 (B) 2 � 3 (C) 40 � 80
3. Prepare a salt water by adding 5 grams of salt to 120 grams of water.
(1) Find the mass ratio of salt and water.
(2) Find the mass ratio of salt and brine.
(3) Find the mass ratio of water and salt water.
method of simplification
(1) Ratio of integers - both the front and back terms of the ratio are divided by their greatest common divisor → the simplest ratio.
(2) Decimal ratio - both the front and back terms of the ratio are expanded by the same multiple → integer ratio → the simplest ratio.
(3) Fractional ratio - multiply both the front and rear terms of the ratio by the least common multiple of their denominators → the ratio of integers → the simplest ratio.
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