Proportion (Including Word Problems)
ICSE Class 6 · Mathematics · Chapter 12
What this chapter covers
- Proportion as equality of two ratios
- Terms of a proportion
- Checking whether ratios are in proportion
- Finding a missing term
- Word problems on proportion
Key definitions
A proportion is a statement that two ratios are equal.
The extremes are the first and the fourth terms of a proportion.
The means are the second and the third terms of a proportion.
Key points
- A proportion is a statement that two ratios are equal.
- A proportion such as 2 : 4 :: 5 : 10 is read as "2 is to 4 as 5 is to 10".
- The terms of a proportion are its four numbers, taken in order.
- The extremes are the first and fourth terms; the means are the second and third terms.
- Four numbers are in proportion when their two ratios simplify to the same ratio.
- Four numbers are in proportion when the product of the extremes equals the product of the means.
- A missing term is found by making the two products equal and dividing.
- Each ratio must compare quantities of the same kind, in the same unit.
- In a word problem, write both ratios in the same order and give the answer with its unit.
- Use proportion only when both quantities grow together in the same ratio.
Questions answered
What is a proportion?
A proportion is a statement that two ratios are equal, such as 3 : 4 :: 6 : 8.
Read 5 : 8 :: 15 : 24 aloud in words.
"5 is to 8 as 15 is to 24."
Name the extremes and the means in 7 : 3 :: 21 : 9.
The extremes are 7 and 9. The means are 3 and 21.
Are 5, 6, 20 and 24 in proportion?
Yes. The product of the extremes is 5 × 24 = 120 and the product of the means is 6 × 20 = 120.
Are 2, 9, 4 and 20 in proportion?
No. The product of the extremes is 2 × 20 = 40, but the product of the means is 9 × 4 = 36.
Find the missing term in 4 : ? :: 12 : 27.
The product of the extremes is 4 × 27 = 108. So ? × 12 = 108, and the missing term is 9.
Six notebooks cost ₹150. What do 9 notebooks cost?
6 : 9 :: 150 : ?. The product of the means is 9 × 150 = 1350, and 1350 ÷ 6 = 225. Nine notebooks cost ₹225.
A tap fills 3 buckets in 12 minutes. How long does it take to fill 5 buckets at the same rate?
3 : 5 :: 12 : ?. The product of the means is 5 × 12 = 60, and 60 ÷ 3 = 20. It takes 20 minutes.