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Create And Solve Proportions

Proportion:

Proportion is a statement in which two ratios are equal. Proportion can be written in two forms,

`a/b` = `c/d`

Or

a:b = c:d

or

a:b :: c:d

If the proportion is equal, then the cross product of the two ratios is also equal.  That is,

`a/b` = `c/d`   ,   a x d = b x c

Proportionis also defined as equivalent of two fractions. When we are going to write equivalent fractions, we need to create a proportion. For example,

`1/2` = `2/4`

This is called as proportion.

Ifany one of the four number is unknown, cross product can be used to find the unknown number. This process is known as solving the proportion. Here we use letter x in place of unknown number.

For example,

1 x 4 = 4

2 x 2 = 4

So two cross products are equal.

Let us learn about how to create and solve proportion problems.


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Example Problems:


Problem 1:

Solve this proportion:  `5/13` = `20/x`

Solution:

The given proportion:

`5/13` = `20/x`

To solve the proportion, we have three steps.

Step 1: Applying Cross multiply.

5 • x = 13 • 20

Step 2: Create an equation.

5x = 260

Step 3: Solve for x.

Divide by 5 each side.

`(5x)/5` = `260/5`

Simplify it,

X = 52.

Problem 2:

Solve this proportion:  `10/x` = `50/120`

Solution:

The given proportion:

`10/x` = `50/120`

To solve the proportion, we have three steps.

Step 1: Applying Cross multiply.

10 • 120 = x • 50

Step 2: Create an equation.

50x = 1200

Step 3: Solve for x.

Divide by 50 each side.

`(50x)/50` = `1200/50`

Simplify it,

X = 24.


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Example Word Problems in Proportions:


Proportionsare widely used to solve different type of word problems for real life application such as calculating populations, measuring distance on a map.

Problem 3:

If a place has rained 550 cm in the last 4 days, how many cm of rain will fall in the 7 days?

Solution:

To solve the real life problem, we have three steps.

Step 1: Identify the problem, write fraction,

Rained 550 cm in 4 days,

`550/4`

Step 2: Let x be unknown variable. Now make a fraction for second statement.

X cm in 7 days = `x/7`

Step 3: Create the proportion.

`550/4` = `x/7`

Solve the proportion,

Cross multiply the ratios,

550 • 7 = 4 • x

Create an equation,

4x = 3850

Solve for x,

Divide by 4 each side,

`(4x)/4` = `3850/4`

Simplify it,

X = 962.5

Therefore, 962.5 cm rained in the 7 days.

Problem 4:

If the cost of 6 kg of sugar is $ 150.6, what will be the cost of 9 kg of sugar?

Solution:

To solve the real life problem, we have three steps.

Step 1: Identify the problem, write fraction,

6kg of sugar is $ 150.6,

`6/150.6`

Step 2: Let x be unknown variable. Now make a fraction for second statement.

9 kg of sugar is X = `9/x`

Step 3: Create the proportion.

`6/150.6` = `9/x`

Solve the proportion,

Cross multiply the ratios,

6 • x = 150.6 • 9

Create an equation,

6x = 1355.4

Solve for x,

Divide by 6 each side,

`(6x)/6` = `1355.4/6`

Simplify it,

X = 225.9

Therefore, 9 kg of sugar is $ 225.9 .