21
The ratio. Proportions
Textbook, pp. 88–92
GoalUnderstand ratio and proportion; name the terms of a proportion.
New words
ratio · nisbatproportion · proporsiyaextremes (outer terms) · chekka hadlarmeans (middle terms) · o‘rta hadlar
Explanation
The quotient of two numbers is called their ratio: a : b = a/b. A ratio shows how many times the first number is greater than the second, or what part the first is of the second. For example 12 : 4 = 3, so 12 is 3 times 4. The equality of two ratios is called a proportion: a : b = c : d. Here a and d are the extremes (outer terms) and b and c are the means (middle terms). In a ratio both quantities must be in the same unit.
Worked examples
15 : 20 = 15/20 = 3/4, so the ratio is 3 : 4.
6 : 3 = 10 : 5 is a proportion, because both ratios equal 2. The extremes are 6 and 5, the means are 3 and 10.
Class activity
“Ratio cards”: find the ratio of girls to boys in the class. Groups write their ratio, reduce it, then check whether it forms a proportion with other groups' ratios.
Practice
1
Write the ratio 15 : 20 in lowest terms.
3:4
2
A class has 12 girls and 18 boys. Find the ratio of girls to boys.
2:3
3
Is 4 : 6 = 6 : 9 a proportion?
Yes: 4/6 = 2/3 and 6/9 = 2/3, so the ratios are equal.
4
Why do we change 2 m and 50 cm to the same unit before finding their ratio?
Writing 2 : 50 would be wrong. 200 cm : 50 cm = 4 gives the true ratio, a number without units.