Kids who are looking for various types of ratio numbers to practice can take the help from this Worksheet on Types of Ratios. Here, we will discuss different types of ratios that make students calculate the ratios in any manner. Without knowing the types of ratios, it becomes difficult to solve their relative sizes so go for these types of ratios practice worksheets and make your calculations so perfect.
The ratio is the mathematical expression of two or more quantities of the same units by dividing the one ratio by the other part of the ratio and must have the same unit measurements. The following different types of ratios worksheet with answers helps the students & teachers to perceive the various expression easily. Practice and express the below ratios in the respected kind of ratio.
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Different Types of Ratios Worksheet with Answers
Example 1.
Find the compound ratio of the following ratios.
(i) 4: 5 and 3: 2
(ii) b: d and g: f
(iii) 12: 8 and 7: 15 and 5: 9
Solution:
(i) Given ratio is 4: 5 and 3: 2
To find the compound ratio, if we multiply two or more ratios termwise, then the ratio is obtained as a compound ratio.
Now, 4: 5 and 3: 2 = 4×3 : 5×2 = 12: 10.
So, the compound ratio is 12: 10.
(ii) Given ratio is b: d and g: f.
The compound ratio for b: d and g: f = b×g : d×f = bg : df.
Thus, the ratio is bg: df.
(iii) Given ratio is 12: 8 and 7: 15 and 5: 9.
To find the compound ratio for three ratios, we use the ratio formula
if m: n, p: q, and r: s, the compound ratio is (m× p× r) : (n× q× s).
Now, the ratio of 12: 8 and 7: 15 and 5: 9 = (12× 7× 5) : (8× 15× 9) = 420: 1080 = 7: 18.
Therefore, the compound ratio is 7: 18.
Example 2.
Get the duplicate ratio of the following expressions.
(i) √3: √4
(ii) a2: b2
(iii) 5√p: √20q
Solution:
(i) Given ratio is √3: √4
The duplicate ratio is the ratio of two equal ratios. For example, m: n = m2: n2.
Now, the ratio for √3: √4 = (√3)2: (√4)2 = 3: 4.
Thus, the duplicate ratio is 3: 4.
(ii) Given ratio is a2: b2
Now, duplicate ratio a2: b2 = (a²)² : (b²)² = a4: b4.
a4: b4 is the duplicate ratio of a2: b2.
(iii) Given ratio is 5√p: √20q.
The duplicate ratio of 5√p: √20q = (5√p)²: (√20q)² = 5²×√p² : √20q×√20q = 25p: 20q = 5p: 4q.
So, the duplicate ratio is 5p: 4q.
Example 3.
Find the triplicate ratio of the following expressions.
(i) ³√9m: 4
(ii) a/3: ³√a
(iii) p/2: q/4
Solution:
(i) Given ratio is ³√9m: 4.
The triplicate ratio is the compound ratio of three equal ratios. For example, m: n = m³: n³.
Now, ³√9m: 4 = (³√9m)³ : 4³ = 9m: 64.
The triplicate ratio is 9m: 64.
(ii) Given ratio is a/3: ³√a.
To find the triplicate ratio we apply the formula a: b = a³: b³.
a/3: ³√a = (a/3)³: (³√a)³ = a³/3³: (³√a)³ =a³/9: a = a²: 9.
So, the ratio is a²: 9.
(iii) Given ratio is p/2: q/4.
Now, the triplicate ratio of p/2: q/4 = (p/2)³: (q/4)³ = p³/8: q³/64 = 64p³: 8q³ = 8p³: q³.
Therefore, the triplicate ratio is 8p³: q³.
Example 4.
Find the subduplicate ratio of (a+b)²: (a-b)4.
Solution:
Given ratio (a+b)²: (a-b)4.
The subduplicate ratio of p: q is √p: √q.
Now, we find the subduplicate ratio of (a+b)²: (a-b)4.
(a+b)²: (a-b)4 = √(a+b)²: √(a-b)4 = (a+b): (a-b)².
Thus, the subduplicate ratio of (a+b)²: (a-b)4 is (a+b): (a-b)².
Example 5.
Find the subtriplicate ratio of 343x³: 8y³.
Solution:
The given ratio is 343x³: 8y³.
The subtriplicate ratio of a: b is ³√a: ³√b.
Now, the subtriplicate ratio of 343x³: 8y³
343x³: 8y³ = ³√(343x³): ³√(8y³) = 7x: 2y (since, 7³=343, 2³=8).
Hence, the subtriplicate ratio of 343x³: 8y³ is 7x: 2y.
Example 6.
Find the reciprocal ratio of a/9: b/6.
Solution:
The given ratio is a/9: b/6.
The reciprocal ratio of p: q (p≠0, q≠0) is the ratio 1/p: 1/q = q: p.
Now, to find the reciprocal ratio of a/9: b/6
a/9: b/6 = 1/(a/9): 1/(b/6) = 9/a: 6/b = 9b: 6a = 3b: 2a.
Simply, we can say the reciprocal ratio is the inverse ratio. For, example 4: 5 is the inverse ratio of 5: 4.
Thus, the reciprocal ratio of a/9: b/6 is 3b: 2a.
Example 7.
Find x if (2x + 1) : (3x + 6) is the duplicate ratio of 4 : 6.
Solution:
(2x + 1) : (3x + 6) is the duplicate ratio of 4: 6.
Also, the duplicate ratio of 4: 6 is 4²: 6² = 16: 36.
Now, (2x+1)/(3x+6) = 16/36
⇒ 36(2x+1) = 16(3x+6)
⇒ 72x+36 = 48x+96
⇒ 72x- 48x = 96-36
⇒ 24x = 60
⇒ x = 60/24
⇒ x = 2.5
Therefore, the value of x is 2.5.