Ray's New Higher Arithmetic · Arts. 227–229 · Unit 12: Ratio
59. Ratio
Goal: Your student finds the ratio of two like numbers, names antecedent and consequent, and knows how changing a term changes the ratio.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Ratio defined, how to find it, the sign, terms, simple and compound ratios, reciprocal and inverse ratios, the value of a ratio, then general principles, a rule, and examples on ratios of compound numbers (answers printed, though faint in the scan).
The lesson, step by step
Warm-up
Ask: How many times larger is 12 than 4? Than 3? What part of 12 is 4?
The idea
Read:
A Ratio is found by dividing the first number by the second.
The Sign of Ratio is the colon (:).
The first term of a ratio is the antecedent.
The second is the consequent. The book's example: the ratio of 8 to 4 is 2.
Kinds
Read:
A Simple Ratio is a single ratio consisting of two terms.
The Reciprocal of a Ratio is 1 divided by the ratio.
Inverse Ratio is the quotient of the consequent divided by the antecedent.
A compound ratio is the product of two or more simple ratios.
Principles
Read:
Antecedent = Consequent X Ratio.
The Ratio is not changed by multiplying or dividing both terms by the same number.
Work the book's example: 15 : 36 = 15/36 = 5/12.
Compound numbers
Ratios only work between like numbers. To find the ratio of 2 ft. 6 in. to 1 yd., reduce both to inches: 30 : 36 = 5/6.
Independent practice
Your student works the book's four examples on ratios of compound numbers, reducing both terms to the same denomination first.
Wrap-up
Ask: What is the ratio of 1 mile to 1 rod? (320.) Of 1 rod to 1 mile? (1/320.)