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Solving Proportions

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A proportion is obtained by equating two ratios, which means that two fractions are equal to each other. The quantities which are compared should be of the same type and unit of measurement.

It can be written as a : b = c : d or a : b :: c : d

The first and the fourth quantities are called the ‘extremes’ while the second and the third quantities are called the “means”.

In a proportion, the product of the extremes is equal to the product of the means.


11 × 9 = 12v

99 = 12v \Rightarrow v = 8.25

Example: Mary bought one bulb of elephant garlic for $2. How many bulbs can Mofor buy if he has $10?

Let us assume that Mofor can buy x bulbs for $10.

Ratio of bulbs = Ratio of costs

1 : x = 2 : 10 implies 2x = 10

So, x = 5


Check Point:

  1. Solve the proportion, 2 : 8 = 8 : n
  2. Jaidee reduced the size of a frame to a height of 5 inches. What is the new width if it was originally 49 in wide and 35 in tall?One package of basil costs $
  3. One package of basil costs $How may packages of basil can be bought for $6?
  4. \frac{4}{7}=\frac{11}{x}
  5. 15 bunches of seedless black grapes cost $36.How many bunches can you buy for $12?
Answer key
  1. 32
  2. 7 in
  3. 2
  4. 25
  5. 5

Download/Solve a Worksheet for Solving Proportions

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