Introduction to math proportion:
Algebra is that separation of mathematics in which calculation are made by using any arbitrary characters to stand for the quantities or things considered. Which are used to correspond to numbers is often given the name literal numbers or simply literals. Since the literal numbers are used to represent numbers,
In our daily life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’. If two ratios are equal, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.
Math proportion – Definition and types:
Definition of proportion:
If two ratios are not equal, then we state that they are not in proportion. In a statement of learning proportion, the four quantities involved when taken in order are known as respective terms. First and fourth terms are known as extreme terms. Second and third terms are known as middle terms.
a: b = c : d
There are two types of propositions,
1. Simple proposition:
A propositions consisting of just one subject and one predicate is called a simple proposition.
Example: The following are simple proposition
1. Ram is blind.
2. The flower is not red.
2. Compound proposition
A proposition consisting of two or more simple propositions in the form of a single sentence is called a compound proposition.
Example: The following are compound propositions,
Quadrilateral ABCD is a square and each side of this quadrilateral is 4cm long.
Math proportion – Example problems:
Problem 1:
Are the ratios 60g: 30g and 32 kg: 48 kg in proportion?
Solution:
60 g: 30 g =60/30 = 2:1
= 2:1
32 kg: 56 kg = 4 / 7 = 4:7
= 4: 7 So, 60: 30 = 32: 56.
Therefore, the ratios 60 g: 30 g and 32 kg: 56 kg are in proportion,
i.e. 60 : 30 :: 32 : 56.
The middle terms in this are 30, 32 and the extreme terms are 60, 56.
Problem 2:
If 4: 5 = 8: X is a proportion, find the missing term.
Solution:
Product of extremes = 4 × x
Product of means = 5 × 8 = 40.
Since it is a proportion, 4 × x = 40
Divide both sides by 4
(4 × x) / 4 = 40 / 4
x =40 / 4 = 10.
X = 10
Problem 3:
The income and Savings of a family are in the ratio 5: 2. If the income of the family is Rs.5, 800. Find how much is being saved.
Solution:
Let the savings be Rs. x.
The proportion is 5: 2 = 5800: x
(Income: Saving) = (Income: Saving)
5x = 2 × 5800
5x / 5 = (2 × 5800) / 5
x = 11600 / 5
x = 2320
The Savings = Rs.2320.
Algebra is that separation of mathematics in which calculation are made by using any arbitrary characters to stand for the quantities or things considered. Which are used to correspond to numbers is often given the name literal numbers or simply literals. Since the literal numbers are used to represent numbers,
In our daily life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’. If two ratios are equal, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.
Math proportion – Definition and types:
Definition of proportion:
If two ratios are not equal, then we state that they are not in proportion. In a statement of learning proportion, the four quantities involved when taken in order are known as respective terms. First and fourth terms are known as extreme terms. Second and third terms are known as middle terms.
a: b = c : d
There are two types of propositions,
1. Simple proposition:
A propositions consisting of just one subject and one predicate is called a simple proposition.
Example: The following are simple proposition
1. Ram is blind.
2. The flower is not red.
2. Compound proposition
A proposition consisting of two or more simple propositions in the form of a single sentence is called a compound proposition.
Example: The following are compound propositions,
Quadrilateral ABCD is a square and each side of this quadrilateral is 4cm long.
Math proportion – Example problems:
Problem 1:
Are the ratios 60g: 30g and 32 kg: 48 kg in proportion?
Solution:
60 g: 30 g =60/30 = 2:1
= 2:1
32 kg: 56 kg = 4 / 7 = 4:7
= 4: 7 So, 60: 30 = 32: 56.
Therefore, the ratios 60 g: 30 g and 32 kg: 56 kg are in proportion,
i.e. 60 : 30 :: 32 : 56.
The middle terms in this are 30, 32 and the extreme terms are 60, 56.
Problem 2:
If 4: 5 = 8: X is a proportion, find the missing term.
Solution:
Product of extremes = 4 × x
Product of means = 5 × 8 = 40.
Since it is a proportion, 4 × x = 40
Divide both sides by 4
(4 × x) / 4 = 40 / 4
x =40 / 4 = 10.
X = 10
Problem 3:
The income and Savings of a family are in the ratio 5: 2. If the income of the family is Rs.5, 800. Find how much is being saved.
Solution:
Let the savings be Rs. x.
The proportion is 5: 2 = 5800: x
(Income: Saving) = (Income: Saving)
5x = 2 × 5800
5x / 5 = (2 × 5800) / 5
x = 11600 / 5
x = 2320
The Savings = Rs.2320.
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