The cross product is a calculation method for solving many proportionality problems. Indeed, it can be particularly effective when it comes to calculating percentages. Also called the rule of 3, it allows you to find an unknown value from three known values. Here’s how to make it.
Do you want to quickly calculate the new promotion carried out on the new fashionable video game console? The cross product will be your best ally during the sales or in progress!
What is the cross product?
The cross product, also known as the rule of 3 or proportionality, is a mathematical method used to calculate an unknown fourth proportional. This technique relies on the equality of cross products, which means that the two fractions or cross products are equal in case of proportionality. The cross product is often used in everyday situations, such as calculating the ingredients of a cooking recipe, determining the fuel consumption of a vehicle per 100 km or even estimating the distances traveled at constant speed as a function of time.
There are two common methods for performing calculations using the cross product: the proportionality table and the proportionality coefficient. The proportionality table consists of organizing known and unknown values in a table, while the proportionality coefficient is used to simplify the calculation by multiplying or dividing the values by the same coefficient.
When do we learn the cross product?
The cross product is a mathematical method that is taught in 4th gradee. It is important to understand that the cross product only works in a proportionality situation. This method is not a magic formula, but rather a mental representation to facilitate the calculation necessary to apply the rule of three. It is therefore essential to read the instructions carefully before using it. Mastery of the cross product is one of the concepts necessary for college certificate. In addition, this method provides a basis for calculating percentages and rates of change.
In what situation can I use a cross product?
The cross product is a versatile mathematical method that is useful in many everyday situations. In particular, in cooking, when you want to adjust the quantities of ingredients in a recipe, the cross product allows you to find the right proportion to obtain the desired result. But also in the field of transport, it can be used to determine the fuel consumption of a vehicle for a given distance, such as 100 km. This allows you to better manage your budget and estimate travel costs. When you want to calculate the distance traveled as a function of time or, conversely, predict the arrival time by knowing the distance and constant speed, the cross product is an effective tool.
In the field of chemistry or pharmacy, the cross product can also be used to carry out a precise dilution of a chemical product or a drug, respecting the required ratios. Finally, for the biggest spenders, it also allows you to express a value as a percentage, whether for financial calculations, reductions, increases, or variations.
What formula should I use to calculate a cross product?
The cross product formula
The cross product is a mathematical method for solving proportionality situations using the rule of three. To apply the product crosswise, simply fill in a proportionality table with four values: a, b, c and d.
Let’s imagine that you want to find an unknown value, represented by d, in a proportionality situation. You can use the cross product by placing the known values in the columns of the table. So, you will fill the first column with the values a and b, and the second column with the values c and d.
The rule of proportionality states that the products of diagonal numbers must be equal. This means that A multiplied by D must be equal to B multiplied by C, i.e. a × d = b × c. Using this equality you can solve the equation and find the value of d.
Steps to follow
Calculating a cross product follows a few key steps. First of all, it is essential to verify that this is indeed a situation of proportionality. Next, you will need to locate the three known values in the problem. These values will then be reported in a proportionality table. Once the values are entered in the table, you draw a diagonal connecting the two known values. Then, you multiply the two values located diagonally from each other. The result of this multiplication is then divided by the third known value present in the table.
These steps allow you to obtain the value of the fourth proportional in the cross table. By following these steps, you are now able to quickly and accurately calculate the cross product.
How to make a proportionality table?
Let’s say that I want to estimate how much this pair of shoes for 250 euros which is on sale at 25% will cost me. So I have 3 values in my possession:
- The price of the pair of shoes, i.e. 250 euros
- The reduction, i.e. 25%
- Its proportional, i.e. 100
The technique to follow is therefore the following, here we have 25/100 = X/250. If I want to calculate the unknown (X), I create the following table:
| 25 | X |
| 100 | 250 |
So I multiply the two known values diagonally. Here, 25 and 250, then I divide them by the third value we have, which is 100. So, 25*250/100 = 62.5.
250 – 62.5 = 187.5. After reduction, the pair of shoes will cost me 187.50 euros.
