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Pre-Algebra Online Tutoring: Proportions

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Learn about Proportions from Certified Online Pre-Algebra Tutor

A proportion is simply two ratios that are equivalent to each other. The missing element in a math problem is usually found by using Proportions.

It can be written in two ways:

Two equal fractions,

a/b = c/d
OR
in colon notation,    a: b = c: d

In a proportion,

Product of the means = Product of the extremes.

Proportions

Extremes

Means are the terms that are close together.

Extremes are the terms that are further apart.

Cross Product Property of Proportions:

When two ratios are equal, then the cross products of the ratios are equal.

That is, for the proportion,

a: b = c: d,
a x d = b x c   
Means = Extremes

 

Let’s understand with an example:

1. Fill in the missing number to complete the proportion.
6/13= 42/x

Proportions1

Write an equivalent fraction with 42 as the numerator

Proportions2

2. Harry read 30 medieval books over the course of 15 weeks .How many books would he have read in 20 weeks? Assume the relationship is directly proportional.

Use cross products to solve the problem

Set up a proportion and solve for n.

Proportions3

Proportions4

After 20 weeks, Harry would have read 40 medieval books.

Check Point

  1. Fill in the missing number to complete the proportion    3/5 = x/75
  2.  Fill in the missing number to complete the proportion    8/9= 120/y
  3. The Yankee candle making company can make 1600 candles in 4 minutes. How many candles can they make in 15 minutes?
  4. A writer can type 250 words in 100 seconds. At that rate, how many seconds would it take him to type 500 words?
  5.  At the school summer camp the ratio of number of boys and girls is 7: 3. If there are 27 girls in the summer camp, find the number of boys in the summer camp and the total number of students in the summer camp.
Answer Key
  1. x = 45
  2. y= 135
  3. 6000 candles
  4. 200 seconds
  5. 63 boys ,90 students
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