Ratio: A ratio is a way to compare two quantities by using division as in miles per
hour where we compare miles and hours.
A ratio can be written in three different ways and all are read as "the ratio of x to
y" i.e x to y
x:y
x/y
Proportion: A proportion on the other hand is an equation that says that two ratios
are equivalent. For instance if one package of chocolate mix results in 30
chocolates than that would be the same as to say that two packages will result in 60
chocolates.
30/1 = 60/2
A proportion is read as "x is to y as z is to w"
x/y = z/w where y,w ≠ 0
If one number in a proportion is unknown you can find that number by solving the
proportion.
, Q.1 Arrange the following ratios in ascending order of magnitude:
2: 3, 17: 21, 11: 14 and 5: 7
Solution:
It is given that
2: 3, 17: 21, 11: 14 and 5: 7
We can write it in fractions as
2/3, 17/21, 11/14, 5/7
Here the LCM of 3, 21, 14 and 7 is 42
By converting the ratio as equivalent
2/3 = (2 × 14)/ (3 × 14) = 28/42
17/21 = (17 × 2)/ (21 × 2) = 34/ 42
11/14 = (11 × 3)/ (14 × 3) = 33/42
5/7 = (5 × 6)/ (7 × 6) = 30/42
Now writing it in ascending order
28/42, 30/42, 33/42, 34/42
By further simplification
2/3, 5/7, 11/14, 17/21
So we get, 2: 3, 5: 7, 11: 14 and 17: 21
Q.2 (i) If (x – 9): (3x + 6) is the duplicate ratio of 4: 9, find the value of x.
(ii) If (3x + 1): (5x + 3) is the triplicate ratio of 3: 4, find the value of x.
(iii) If (x + 2y): (2x – y) is equal to the duplicate ratio of 3: 2, find x: y.
Solution:
(i) (x – 9)/ (3x + 6) = (4/9)2
So we get, (x – 9)/ (3x + 6) = 16/81
By cross multiplication
81x – 729 = 48x + 96
81x – 48x = 96 + 729
hour where we compare miles and hours.
A ratio can be written in three different ways and all are read as "the ratio of x to
y" i.e x to y
x:y
x/y
Proportion: A proportion on the other hand is an equation that says that two ratios
are equivalent. For instance if one package of chocolate mix results in 30
chocolates than that would be the same as to say that two packages will result in 60
chocolates.
30/1 = 60/2
A proportion is read as "x is to y as z is to w"
x/y = z/w where y,w ≠ 0
If one number in a proportion is unknown you can find that number by solving the
proportion.
, Q.1 Arrange the following ratios in ascending order of magnitude:
2: 3, 17: 21, 11: 14 and 5: 7
Solution:
It is given that
2: 3, 17: 21, 11: 14 and 5: 7
We can write it in fractions as
2/3, 17/21, 11/14, 5/7
Here the LCM of 3, 21, 14 and 7 is 42
By converting the ratio as equivalent
2/3 = (2 × 14)/ (3 × 14) = 28/42
17/21 = (17 × 2)/ (21 × 2) = 34/ 42
11/14 = (11 × 3)/ (14 × 3) = 33/42
5/7 = (5 × 6)/ (7 × 6) = 30/42
Now writing it in ascending order
28/42, 30/42, 33/42, 34/42
By further simplification
2/3, 5/7, 11/14, 17/21
So we get, 2: 3, 5: 7, 11: 14 and 17: 21
Q.2 (i) If (x – 9): (3x + 6) is the duplicate ratio of 4: 9, find the value of x.
(ii) If (3x + 1): (5x + 3) is the triplicate ratio of 3: 4, find the value of x.
(iii) If (x + 2y): (2x – y) is equal to the duplicate ratio of 3: 2, find x: y.
Solution:
(i) (x – 9)/ (3x + 6) = (4/9)2
So we get, (x – 9)/ (3x + 6) = 16/81
By cross multiplication
81x – 729 = 48x + 96
81x – 48x = 96 + 729
