Introductions to ratio of a to b:
Ratio:
In the mathematical explanation a ratio expresses the magnitude of quantities relative to each other. Particularly, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient.I like to share this what is a ratio with you all through my article.
The ratio of quantities a and b can be expressed as,
The ratio of A to B
A is to B
A: B
(Source: Wikipedia)
Example Problems on Ratio of a to B:
Problem 1:
The ratio of a to b is 5/2. The sum of a and b is 35. What is the ratio of a +b to b-a?
Solution:
The ratio of a to b is 5/2.
so a / b = 5/2
The sum of a and b is 35.
a + b = 35
Divide –b on both sides,
a +b-b= 35 - b
a = 35 – b.
a/b = 5/2
Substituting a value in the ratio of a to b(a/b = 5/2),
(35 - b)/b = 5/2
(35/b - b/b) = 5/2
35/b - 1 = 5/2
Add 1 on both sides,
35/b - 1 +1 = 5/2+1
35/b = 5/2 + 1
35/b = (5+2)/2
35/b = 7/2
b = (35 * 2) / 7
b = 70/7
b = 10
Substituting values of b.
a = 35- b = 35 - 10 = 25
a = 25; b = 10
a + b = 35
b - a = 10 - 25 = -15
so The ratio of a +b to b-a is
(a + b) / (b - a) = 25/-15 = 5/-3
Answer: The ratio of a +b to b – a is -5/3.
Problem 2:
The ratio of a to b is 3/4. The sum of a and b is 12. What is the ratio of a * b to a-b?
Solution:
The ratio of a to b is 3/4.
So a / b = ¾.
The sum of a and b is 12.
a + b = 12
Divide –b on both sides,
a +b-b= 12 - b
a = 12 – b.
a/b = 3/4
Substituting a value in the ratio of a to b (a/b = 5/2),
(12 - b)/b = 3/4
(12/b - b/b) = 3/4
12/b - 1 = 3/4
Add 1 on both sides,
12/b - 1 +1 = 3/4+1
12/b = 3/4 + 1
12/b = (3+4)/4
12/b = 7/4
b = (12 * 4) / 7 b = 48/7
b = 6.8
Substituting values of b.
a = 35- b = 35 – 6.8 = 28.2
a = 28.2; b = 6.8
a * b = 28.2 * 6.8 = 191.76
a-b = 28.2 – 6.8 = 21.4
so The ratio of a *b to a-b is,
(a * b) / (a-b) = 191.76/21.4 = 8.96
Answer: The ratio of a * b to a - b is 8.96.
Understanding Is Pie a Rational Number is always challenging for me but thanks to all math help websites to help me out.
Practice Problems of Ratio of a to B.
The sum of a and b is 34. The difference of a and is 12. Find the ratio of a to b.
The product of a and b is 22. The sum of a and b is 66. find the ratio of a to b.
The difference of a and b is 7. The product of a and b is 32. Find the ratio of a to b.
Ratio:
In the mathematical explanation a ratio expresses the magnitude of quantities relative to each other. Particularly, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient.I like to share this what is a ratio with you all through my article.
The ratio of quantities a and b can be expressed as,
The ratio of A to B
A is to B
A: B
(Source: Wikipedia)
Example Problems on Ratio of a to B:
Problem 1:
The ratio of a to b is 5/2. The sum of a and b is 35. What is the ratio of a +b to b-a?
Solution:
The ratio of a to b is 5/2.
so a / b = 5/2
The sum of a and b is 35.
a + b = 35
Divide –b on both sides,
a +b-b= 35 - b
a = 35 – b.
a/b = 5/2
Substituting a value in the ratio of a to b(a/b = 5/2),
(35 - b)/b = 5/2
(35/b - b/b) = 5/2
35/b - 1 = 5/2
Add 1 on both sides,
35/b - 1 +1 = 5/2+1
35/b = 5/2 + 1
35/b = (5+2)/2
35/b = 7/2
b = (35 * 2) / 7
b = 70/7
b = 10
Substituting values of b.
a = 35- b = 35 - 10 = 25
a = 25; b = 10
a + b = 35
b - a = 10 - 25 = -15
so The ratio of a +b to b-a is
(a + b) / (b - a) = 25/-15 = 5/-3
Answer: The ratio of a +b to b – a is -5/3.
Problem 2:
The ratio of a to b is 3/4. The sum of a and b is 12. What is the ratio of a * b to a-b?
Solution:
The ratio of a to b is 3/4.
So a / b = ¾.
The sum of a and b is 12.
a + b = 12
Divide –b on both sides,
a +b-b= 12 - b
a = 12 – b.
a/b = 3/4
Substituting a value in the ratio of a to b (a/b = 5/2),
(12 - b)/b = 3/4
(12/b - b/b) = 3/4
12/b - 1 = 3/4
Add 1 on both sides,
12/b - 1 +1 = 3/4+1
12/b = 3/4 + 1
12/b = (3+4)/4
12/b = 7/4
b = (12 * 4) / 7 b = 48/7
b = 6.8
Substituting values of b.
a = 35- b = 35 – 6.8 = 28.2
a = 28.2; b = 6.8
a * b = 28.2 * 6.8 = 191.76
a-b = 28.2 – 6.8 = 21.4
so The ratio of a *b to a-b is,
(a * b) / (a-b) = 191.76/21.4 = 8.96
Answer: The ratio of a * b to a - b is 8.96.
Understanding Is Pie a Rational Number is always challenging for me but thanks to all math help websites to help me out.
Practice Problems of Ratio of a to B.
The sum of a and b is 34. The difference of a and is 12. Find the ratio of a to b.
The product of a and b is 22. The sum of a and b is 66. find the ratio of a to b.
The difference of a and b is 7. The product of a and b is 32. Find the ratio of a to b.
No comments:
Post a Comment