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"Basic Properties of Ratio" Understanding Ratio PPT Courseware 2
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What is ratio?
The division of two numbers is also called the ratio of the two numbers.
How to find the ratio?
Antecedent ÷ Consequent term = ratio
Properties of quotient invariance: The dividend and divisor (simultaneously) are multiplied or divided by (the same number) (0), except that (the quotient) remains unchanged.
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 magnitude of the fraction remains unchanged.
The method of induction and simplification
(1) Ratio of integers - both the front and back terms of the ratio are divided by their greatest common factor → the simplest ratio.
(2) Fractional ratio - multiply both the front and back terms of the ratio by the least common multiple of their denominators → the ratio of integers → the simplest ratio.
(3) Decimal ratio - both the front and back terms of the ratio are expanded by the same multiple → integer ratio → the simplest ratio.
Expansion exercises
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 ( ) � ( )
Wisdom Island
1. The antecedent term of the ratio is 3, and the consequent term is 4. If the antecedent term of the ratio is added to 9, to keep the ratio unchanged, the consequent term of the ratio should be added ( )
2. The ratio of the area of the shaded area to the total area in the figure below is ( )
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