Properties of Ratios
To know about the properties of ratios it’s important to know that a ratio is a method to compare two quantities of the same kind with same unit; by dividing first quantity by the second. It is denoted by the colon ':'.
The ratio of P to Q = P/Q, and it is represented as P : Q. The quantities P and Q are called terms; P is the antecedent and Q is the consequent.
Suppose there are two mobile towers of heights 25 m and 15 m. Now to compare their heights we divide the height of the first mobile tower by the height of the second mobile tower and get (25 m)/(15 m) = (25 ÷ 5)/(15 ÷ 5) [dividing both numerator and denominator by 5] = 3/2.
Thus, it is evident from the above discussion that the height of the first mobile tower is 3/2 times the height of the second mobile tower and the fraction 3/2 is called the ratio of the heights of the two mobile towers. Therefore, we can also say that the ratio of heights of the mobile towers is 3 : 2.
Properties of Ratios:
1. The ratio of a number ‘P’ to the another number ‘Q’ (Q ≠ 0) is a fraction P/Q, and it is written as P : Q.
2. In the ratio P : Q, the first term is P and second term is Q.
3. In the ratio P : Q, the first term P is called antecedent and the second term Q is called consequent.
4. The two quantities compared in a ratio must have the same units of measurement.
In order to find the ratio between two quantities, both the quantities must be in the same unit e.g., ratio between 30 cm and 2 metre
= 30 cm : 200 cm [Since, 2 metre = 200 cm]
= 30/200
= 3/20
= 3 : 20
5. The ratio of two numbers is always expressed in its lowest terms in simplest form.
6. When two ratio P : Q is in its lowest term, P and Q are co-prime, or their HCF is 1.
7. The ratio of two quantities is an abstract quantity, i.e., it has no units in itself.
8. A ratio is a pure number.
9. The order of a ratio is important. By reversing the antecedent and the consequent of a ratio, a different ratio is obtained.
10. The ratio can be expressed as a fraction and a decimal.
11. The antecedent and the consequent of a ratio are always expressed as whole numbers. When they are not, they are converted into whole numbers.
6th Grade Page
From Properties of Ratios to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Addition of Decimals | How to Add Decimals? | Adding Decimals|Addition
Apr 24, 25 01:45 AM
We will discuss here about the addition of decimals. Decimals are added in the same way as we add ordinary numbers. We arrange the digits in columns and then add as required. Let us consider some -
Addition of Like Fractions | Examples | Videos | Worksheet | Fractions
Apr 23, 25 09:23 AM
To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com… -
Subtraction | How to Subtract 2-digit, 3-digit, 4-digit Numbers?|Steps
Apr 23, 25 12:41 AM
The answer of a subtraction sum is called DIFFERENCE. How to subtract 2-digit numbers? Steps are shown to subtract 2-digit numbers. -
Subtraction of 4-Digit Numbers | Subtract Numbers with Four Digit
Apr 23, 25 12:38 AM
We will learn about the subtraction of 4-digit numbers (without borrowing and with borrowing). We know when one number is subtracted from another number the result obtained is called the difference. -
Subtraction with Regrouping | 4-Digit, 5-Digit and 6-Digit Subtraction
Apr 23, 25 12:34 AM
We will learn subtraction 4-digit, 5-digit and 6-digit numbers with regrouping. Subtraction of 4-digit numbers can be done in the same way as we do subtraction of smaller numbers. We first arrange the…
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.