Solving Proportions Using Cross Products

Introduction to solving proportions using cross products:
A part considered in relation to its whole. Statement of equality between 2 or more ratios like a/b=c/d. When we multiply we get ad=bc. The two ratios are equivalent. And we can say, two set of numbers are proportional, if one set is a constant times the other. Here we are going to see solving proportions using cross products.

Example Problems of Solving Proportions Using Cross Products:

Example 1:

Solving the following proportion using cross products.

Given:   `(3)/(1)` = `(39)/(y)`

Solution:

Step 1: We need to find y value.

Step 2: Here we are using cross products to solve y.

Step 3: So, when we cross multiply we get 39 = 3y.

Step 4: Now we divide using 3 on both the sides.

Step 5: The value of y= 13.


Example 2:

Solving the following proportion using cross products.

Given: `(4)/(b)` = `(48)/(36)`

Solution:

Step 1:  From this question we need to find b value

Step 2: Using cross product we get, 144= 48b

Step 3: Now we divide using 48 on both the sides.

Step 4: b= `(144)/(48)` .

Step 5: b=3.


Example 3:

Solving the following proportion using cross products.

Given:  `(18)/(20)` = `(g)/(30)`

Solution:

Step 1:  From this question we need to find g value

Step 2: Using cross product we get, 540 = 20g

Step 3: Now we divide using 20 on both the sides

Step 4: g= `(540)/(20)`

Step 5: g = 27.

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Some more Examples for Solving Proportions Using Cross Products:

Example 4:

Solving the following proportion using cross products.

Given:  `(16)/(24)` = `(18)/(c)`

Solution:

Step 1:  From this question we need to find c value

Step 2: Using cross product we get, 432= 16c.

Step 3: Now we divide using 16 on both the sides

Step 4: c= `(432)/(16)`

Step 5: c = 27.


Example 5:

Solving the following proportion using cross products.

Given: `(p)/(36)` = `(8)/(9)`

Solution:

Step 1:  From this question we need to find p value.

Step 2: Using cross multiplication we get, 288= 9p.

Step 3: Now we divide using 9 on both the sides

Step 4: p= `(288)/(9)`

Step 5: p = 32.

These are the simple examples of solving proportions using cross products.