How to cross multiply

Use of cross multiplication

• You may already know relative proportions of a scenario but need to know the specific numbers that apply. 
• Example as below; if I know that a colleague received 1/2 of something but need to know what 100% is (... perhaps because I want to use a percentage other than my colleague). 
• Another example; if retailers wish to calculate a sale price (x) based on a specific margin (like 40%) where a manufacturer's cost price equals the percentage difference (like 60%, ie 100% - 40%) between 100% (ie the sale price) and the the margin (of 40%).
• Another example; if a manufacturer knows the market's reservation price (aka walk-away price) which equals 100% and knows his margin, example 35%, he must calculate the highest tolerable cost price for the product to be worthwhile. 

Problem:

Colleague got $1,500 which equals 10%, what is 100%?

1,500 = 0.1

x = 1.00


Answer:

1,500 * 1.00 = 0.1 * x

1,500 = 0.1x

Create a common denominator with the value that is on the same side as the x.

1,500/0.1 = 0.1x/0.1



Cancel out the value that divides into itself

1,500/0.1 = 0.1x/0.1

1,500 / 0.1 = x

15,000 = x

CONTENT RELATED TO HOW TO PERFORM A CROSS MULTIPLICATION

• How to calculate the lowest cost price you should pay based on the market's reservation price (aka walk-away price)