Ray's New Practical Arithmetic · Arts. 218–220 · Unit 22: Ratio and Proportion
102. Ratio principles; lowest terms; clearing fractions
Goal: Your child knows a ratio behaves like a fraction, reduces a ratio to lowest terms, and clears a ratio of fractions.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 280 shows how a ratio is like a fraction (Art. 218), with three principles. Page 281 reduces ratios to lowest terms (Art. 219) and clears them of fractions (Art. 220), with problems and printed answers.
The lesson, step by step
Warm-up
Ask: Is 2/4 the same as 1/2? What did we do to 2/4 to get 1/2?
The idea
The terms of a ratio correspond to the terms of a fraction, the antecedent to the numerator, the consequent to the denominator.
So the fraction rules carry over:
III. A ratio is not changed 1st. By multiplying both terms by the same number. 2d. By dividing both terms by the same number.
Lowest terms
Reduce 16 : 24 to its lowest terms.
The greatest common divisor of 16 and 24 is 8, so 16 : 24 becomes 2 : 3.
Divide both terms of the ratio by their greatest common divisor.
Clearing fractions
The book's example is 1½ : 2⅓. The least common multiple of the denominators 2 and 3 is 6. Multiply both terms by 6: 9 : 14.
Multiply both terms of the ratio by the least common multiple of the denominators of the fractions.
Guided practice
Together, reduce 20 : 25 and 75 : 225 to lowest terms, and clear 2½ : 3⅓ of fractions.
Independent practice and check
Your child works the problems under Arts. 219 and 220 on page 281. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Aloud: lowest terms of 10 : 15, 12 : 18, 14 : 21; double the ratio 3 : 4 by changing only the first term.