Page 233 - Start Up Mathematics_6

Example 14: Determine if the following ratios form a proportion. Also, write the middle terms
and extreme terms where the ratios form a proportion.

(a) 500 g : 2 kg and 250 mL : 1 L (b) 3 kg : 12 kg and 10 g : 50 g
Solution: (a) 500 g : 2 kg = 500 g : 2,000 g = 1 : 4
250 mL : 1 L = 250 mL : 1,000 mL = 1 : 4

Since, 500 g : 2 kg = 250 mL : 1 L = 1 : 4
Therefore, the two ratios are in proportion.

The middle terms are 2 kg and 250 mL. The extreme terms are 500 g and 1 L.
(b) 3 kg : 12 kg = 3 : 12 = 1 : 4 A dog who could think proportion!

10 g : 50 g = 10 : 50 = 1 : 5 1
7 • One year to my master is like seven
Since 3 kg : 12 kg ≠ 10 g : 50 g years to me
Therefore, the two ratios are not • One day to my master is like one
in proportion. 1 week to me
7 • My master enjoys 3 meals in a day.
Example 15: Find x if 15 : 60 : : x : 20.
1 day for my master
Solution: 15 : 60 : : x : 20 7 days for me
15 x
⇒ = 3 meals for my master
Let me
60 20 eat more! = x meals for me
1
⇒ 1 = x ⇒ = 3
4 20 7 x
⇒ x = 21 meals for me.
⇒ x = 5
Example 16: Write True or False against each of the following statements:

(a) 4, 6 and 9 are in continued proportion.
(b) 12 is the mean proportion of 6 and 24.

(c) If a, b and c are in continued proportion then a, b, c and c are proportional.
Solution: (a) True (b) True (c) False

EXERCISE 12.2

1. Determine which of the following are in proportion:
(a) 18, 36, 9, 18 (b) 14, 35, 16, 40 (c) 80, 32, 60, 24 (d) 72, 18, 64, 12
2. Find x in each of the following:

(a) x : 5 = 10 : 50 (b) 12 : 30 = 8 : x (c) 16 : x = x : 121 (d) 21 : 12 : : x : 8
3. Find the mean proportion between:
(a) 12 and 3 (b) 50 and 8 (c) 27 and 48 (d) 50 and 98
4. Determine whether the following ratios form a proportion or not.

(a) 1 L : 250 mL and ` 1,000 : ` 250 (b) ` 2,000 : ` 200 and 100 bottles : 50 bottles
5. In a proportion, the first, second and fourth terms are 32, 112 and 217 respectively. Find
the third term.

225