Answer:
1. a part, share, or number considered in
comparative relation to a whole.
2.A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."
3.If the ratios are equivalent, they form a proportion. Since the ratios are not equivalent, the ratios do not form a proportion.
4.Direct Proportion.
Inverse Proportion
5. Example 1
Find out if the following ratios are in proportion: 8:10 and 12:15.
Explanation
Multiply the first and fourth terms of the ratios.
8 × 15 = 120
Now multiply the second and third term.
10 × 12 = 120
Since the product of the extremes is equal to the product of the means,
Since, the product of means (120) = product of extremes (120),
Therefore, 8: 10 and 12:15 are proportional.
Example 2
Verify if the ratio 6:12::12:24 is proportion.
Explanation
This is a case of continued proportion, therefore apply the formula a x c =b x b,
In this case, a: b:c =6:12:24, therefore a=6, b=12 and c=24
Multiply the first and third terms:
6 × 24 = 144
Square of the middle terms:
(12) ² = 12 × 12 = 144
Therefore, the ratio 6:12:24 is in proportion.
Example 3
If 12:18::20: p. Find the value of x to make the ratios proportional?
Explanation
Given: 12: 18::20: p
Equate the product of extremes to the product of means;
⇒ 12 × p = 20 × 18
⇒ p = (20 × 18)/12
Solve for p;
⇒ p = 30
Hence, the value of p= 30
Example 4
Find the third proportional to 3 and 6.
Explanation
Let the third proportional be c.
Then, b² = ac
6 x 6 = 3 x c
C= 36/3
= 12
Thus, the third proportional to 3 and 6 is 12
Example 5
Calculate mean proportional between 3 and 27
Explanation
Let the mean proportional between 3 and 27 be m.
By applying the formula b² = ac; ‘
Therefore, m x m = 27 x 3 = 81
m2 =81
⇒ m = √81
⇒ m = 9
Hence, the mean proportional between 3 and 27 is 9
