# 3 ways to calculate percentages

Calculating percentages is often an academic exercise, but it is a very practical skill throughout life, as there are discounts, rebates and other discounts every day in stores or on the Internet. We also find percentages in statistics (sports betting), in finance (taxes) or in the industrial environment (machining margins): they are everywhere! This is why it is so important to know how to manipulate and calculate them, as well not to make mistakes as to make good business.

## Steps

### Method 1 of 3: Calculate the percentage of a whole #### Step 1. Observe what a percentage is

A percentage is the part of a whole, expressed as a percent (%). Thus, 0% is no part of a whole and 100%, the whole of the whole. Of course, then there are all the possibilities between these two extremes!

• Consider a basket with 10 apples. Say you ate two, what percentage of apples are gone? You ate 2 out of 10, which is the same as 20 out of 100: you ate 20% of the apples in the basket, and there are 8 out of 10 left, or 80 out of 100, that is to say 80 %.
• The expression "per cent" is translated verbatim from the Latin per centum, which means "per 100", "referred to 100".

The percentage symbol (%) is just convenient, but it is not a unit. In statistical calculation, mathematicians use the raw number, between 0 and 1; 1 representing the whole of reference. In everyday life, we prefer to multiply this value by 100 to get a percentage. #### Step 2. Determine the workforce at all

In class, in an exercise, you will always end up having, given or calculated, the two essential elements of a percentage, the value of the whole and the part in question. Regardless of the size of one or the other, you will have to reduce everything to a fraction in 100. Consider a container with 1199 red marbles and 485 blue marbles. You therefore have a total of 1,684 balls (1,199 + 485): this value represents the whole, and by convention, 100%. #### Step 3. Begin calculating the percentage

Let us take the example of the container containing 1,684 balls, and among them, 485 are blue. 1 684 therefore represents here the whole, the set of balls, and 485 is only a part of this whole, the only blue balls. We will find the percentage of blue beads in this container. #### Step 4. Put these two values ​​as a fraction

The part (blue balls) will be put in the numerator (above the fraction line), while the whole will be in the denominator (below the fraction line). The fraction looks like this: partietout = 4851684 { displaystyle { frac {partie} {tout}} = { frac {485} {1684}}} ### Lorsque vous mettez en place deux proportions, il est plus facile de les mettre toutes les deux en haut comme numérateur au-dessus du dénominateur de n'importe quel côté de l'équation #### Step 5. Convert the fraction to a decimal value

This step makes it easier to calculate the percentage. To transform 4851684 { displaystyle { frac {485} {1684}}}

en une valeur décimale, il suffit de diviser, à la main ou avec une calculatrice, 485 par 1684: vous obtiendrez 0, 288. #### Step 6. Convert a decimal number to a percentage

Multiply the previous result by 100… to get percentages! We had 0.288 which, multiplied by 100, gives 28.8%.

Multiplying a decimal value by 100 amounts to moving its decimal point two rows to the right, and possibly adding zeros.

Be careful in such an operation not to forget the% symbol, otherwise it will mean nothing.

### Method 2 of 3: Start with a percentage to find a value #### Step 1. Locate the encrypted data that matters

Say you borrowed money from a friend who charges you interest every day. Consider a loan of € 15 at a daily rate of 3%. 15 and 3 are the two key elements of the calculation. #### Step 2. Convert the percentage to a decimal number between 0 and 1

To transform a percentage into a decimal number, just divide it by 100 (or, which is the same thing, multiply it by 0.01). So our example of 3% becomes 0.03 (3100 { displaystyle { frac {3} {100}}}

).

### En d'autres termes, vous pouvez transformer n'importe quel pourcentage en décimale en le divisant par 100. Par exemple: 26 % = 26/100 = 0, 26

C'est comme si l’on avait déplacé la virgule de deux rangs vers la gauche en ajoutant des zéros. #### Step 3. Rewrite the problem data with this new value

Theoretically, you can rewrite a percentage as follows: x of y worth z, where x is the percentage in decimal form, of to be translated as "multiplied by", y is the count of the whole and z, the numerical value of the part of the whole. If we take the example of the loan, you will therefore have the following operation: 0.03 x € 15 is worth € 0.45.

• In absolute terms, you should pay him this amount of € 0.45 every day, the sum is not very important, but you should give him back his sum and leave him quickly… forever!
• If you do not repay the interest as you go, it will be added to the starting capital (accumulated interest). On the second day, you will need: € 15 + (0.45 x 1 day) = € 15.45.

### Method 3 of 3: Calculate a discount #### Step 1. Enter the item's original price and discount percentage

On a label, the price written in wholesale and in black is the starting price. In red, are indicated the discount and the sale price. So, you can see firsthand the good deal you could get by buying it.

### During sales, three cases arise: either all the items are on sale at the same percentage, or some only, or finally, the items are on sale at different rates (-10%, -30%, -50%)

In the first case, do your shopping, go to the cashier where you will be given a general discount. In the second and third cases, discounts will be made item by item. #### Step 2. Calculate the complementary percentage

You then only have one operation to do. The additional percentage actually represents the share of the price of the item on sale. This percentage is obtained simply by subtracting the discount from 100%. For example, you have found a shirt on sale at 30%, so it is only worth 70% (100 - 70 = 30) of the starting price. #### Step 3. Convert the complementary percentage to a decimal number

To do this, you only have to divide it by 100. This is how 70% is strictly equivalent to 0.7 (70100 { displaystyle { frac {70} {100}}}

). Si vous aviez eu 25, 56 %, cela aurait donné 0, 2556, la virgule est déplacée de deux rangs vers la gauche, avec adjonction de zéros. #### Step 4. Multiply the starting price by this decimal value

With the example of the shirt on sale at 30%, you will pay, discount made: € 20 x 0.7, or € 14. #### Step 5. Calculate your earnings

If you have done the sales and bought several items in various stores, you can, when you get home, use the slips to add up the discounts you have made. Thus, on the simple shirt sold at 20 €, you will ultimately pay only 14 €, a saving of 6 € (20 - 14 = 6).