Ratio
ICSE Class 6 · Mathematics · Chapter 11
What this chapter covers
- The concept of ratio
- Ratio and fraction
- Ratio in simplest form
- Equivalent ratios and comparing ratios
- Word problems on ratio
Key points
- Two quantities can be compared by subtraction (how much more) or by division (how many times).
- A ratio is a comparison of two quantities of the same kind by division.
- The ratio of a to b is written a : b and read "a is to b".
- The first term is the antecedent and the second term is the consequent.
- The order of the terms matters: 2 : 3 is not the same as 3 : 2.
- Both quantities must be in the same unit, and a ratio itself has no unit.
- A fraction shows a part of a whole, while a ratio compares two quantities.
- A ratio is in its simplest form when its terms have no common factor other than 1; divide both terms by their HCF.
- Equivalent ratios come from multiplying or dividing both terms by the same non-zero number.
- To compare two ratios, write them as fractions with the same denominator.
- To share an amount in a ratio, add the terms to find the total parts, then find the value of one part.
Questions answered
Aarav has ₹40 and Ishaan has ₹10. Compare their money in two ways.
By subtraction, Aarav has ₹30 more. By division, Aarav has 4 times as much, so the ratio is 4 : 1.
In the ratio 7 : 9, name the antecedent and the consequent.
The antecedent is 7 and the consequent is 9.
Why can you not write a ratio of 3 kg to 5 m?
A ratio compares quantities of the same kind. Mass and length are different kinds of quantity.
Give one difference between the fraction (2)/(5) and the ratio 2 : 5.
The fraction shows 2 parts out of a whole of 5 parts. The ratio compares two separate quantities, 2 and 5, and has no unit.
Express 45 : 60 in its simplest form.
The HCF is 15, so 45 : 60 = 3 : 4.
Find the ratio of 50 cm to 2 m in its simplest form.
2 m = 200 cm. The ratio is 50 : 200 = 1 : 4.
Are 6 : 9 and 10 : 15 equivalent ratios?
Yes. Both simplify to 2 : 3.
Which is greater, 3 : 4 or 5 : 8?
(3)/(4) = (6)/(8), which is more than (5)/(8). So 3 : 4 is greater.