Ratio and Proportion
Overview
Ratio and Proportion is an important chapter in Class 6 Maths that teaches us how to compare two quantities of the same kind. A ratio tells us how many times one quantity is compared to another. When two ratios are equal, they form a proportion. This chapter helps us solve real-life problems like sharing things fairly, finding unit price, and checking if quantities are in proportion using simple multiplication methods.
Typed Notes
What is a Ratio?
A ratio is a way to compare two quantities of the same kind using division. For example, if there are 4 apples and 6 oranges, the ratio of apples to oranges is 4:6, which simplifies to 2:3 by dividing both numbers by their HCF, which is 2. The first number in a ratio is called the antecedent and the second is called the consequent. Always make sure both quantities are in the same unit before writing a ratio. Ratios have no units attached to them.
Simplifying Ratios and Equivalent Ratios
A ratio is in its simplest form when the HCF of both terms is 1. To simplify 15:20, find HCF of 15 and 20, which is 5. Divide both by 5 to get 3:4. Equivalent ratios are formed by multiplying or dividing both terms by the same number, just like equivalent fractions. For example, 2:3, 4:6, and 6:9 are all equivalent ratios. We can check if two ratios are equal by cross-multiplying. If 2×9 equals 3×6, that is 18=18, so the ratios are equal.
Proportion
When two ratios are equal, the four quantities involved are said to be in proportion. We write it as a:b::c:d and read it as 'a is to b as c is to d.' Here a and d are called extremes and b and c are called means. The rule is: product of extremes equals product of means, that is a×d = b×c. For example, 2:4::3:6 is a proportion because 2×6=12 and 4×3=12. If the products are not equal, the quantities are not in proportion.
Unitary Method
The unitary method is used to find the value of many units when the value of one unit is known, or to find the value of one unit when the value of many units is known. First, find the value of one unit by dividing. Then multiply to find the required value. For example, if 5 pens cost ₹30, then 1 pen costs ₹30÷5=₹6. So 8 pens will cost 8×₹6=₹48. This method is very useful in daily life for shopping, cooking, and many other situations.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01A ratio compares two quantities of the same unit and is written as a:b or a/b.
- 02A ratio must always be expressed in its simplest form by dividing both terms by their HCF.
- 03Four quantities a, b, c, d are in proportion if a:b = c:d, meaning a×d = b×c (cross-product rule).
- 04Unitary method finds the value of one unit first, then uses it to find the value of many units.
- 05Ratio has no units; both quantities compared must be in the same unit before writing a ratio.
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Simplify the ratio 24:36.
Are 3:4 and 9:12 in proportion?
If 6 notebooks cost ₹48, find the cost of 10 notebooks using the unitary method.
In a class, there are 18 girls and 12 boys. Find the ratio of girls to boys in simplest form.
Find the missing value x if 4:6 = x:18.
Ratio compares two same-unit quantities written as a:b in simplest form. Equivalent ratios are formed by multiplying or dividing both terms by the same number. When two ratios are equal, the four quantities are in proportion, and the product of extremes equals the product of means. The unitary method helps find unknown values by first calculating the value of one unit and then scaling up or down as needed.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.What is the simplest form of the ratio 20:30?
Q2.If a:b = 3:5 and b:c = 5:7, are 3, 5, 5, 7 in proportion?
Q3.Which of the following pairs of ratios are in proportion?
Q4.If 3 kg of sugar costs ₹90, what is the cost of 7 kg?
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