Content

• Initial Actions
• Steps
• Method 1 of 3: How to Calculate the Unknown Percentage
• Method 2 of 3: How to Compute an Unknown Integer
• Method 3 of 3: How to Calculate the Unknown Part of a Whole
• Tips
• Warnings
• What do you need

There are two main types of interest finding problems - direct comparison (for example, "Find a number with 5% of which equals 35") and increase / decrease (for example, "Calculate the new price of a blouse if its initial cost is 3000 rubles, and the discount is 20%"). A separate article is required to describe enlargement / reduction tasks, so here we will only consider problems for direct comparison.

Moreover, such problems can be solved in two main ways, namely using decimal fractions or proportions. Here we will consider the use of decimal fractions, that is, we will use the equality % x (whole) = (part of whole)... This equality can be written as follows: % = (part of a whole) / (whole) or like this: (whole) = (part of whole) /%... Which equality you choose depends on the task.

Initial Actions

First, understand the problem. There is three type of tasks for direct comparison. IN first you need to find the percentage, for example, what percentage of 25 is 16 or what percentage of 32 is 8. In second you need to calculate an integer, for example, 6% of which number is 15 or 78% of which number is 20. V third you need to find a part of the whole, for example, what is equal to 52% of 49 or what is equal to 14% of 225.

Steps

Method 1 of 3: How to Calculate the Unknown Percentage

If a problem does not contain a number with a "%" or the word "percent", most likely, in such a problem, you need to calculate percentages.

1. 1 Find out which number is "whole" and which is "part of a whole". For example, given a problem: what percentage of 32 is 8? In this problem, 32 is an integer and 8 is a part of a whole (note that there is a preposition "from" in front of 32, which indicates an integer).
2. 2 Use the equality% = (part of a whole) / (whole). On the calculator, first enter the part of the whole and press “divide”, and then enter the whole and press “equal”.
3. 3 The result is a decimal. It needs to be converted to percentages by moving the decimal point two places to the right.
   • In our example: enter 8, click divide, enter 32 and click equal. The screen will display 0.25, that is, 25%.
   • For example: what percentage of 25 is 16? Enter 16, click divide, enter 25 and click equal. The screen will display 0.64, that is, 64%.
   • For example: what percentage of 12 is 45? Enter 45, click divide, enter 12 and click equal. The screen will display 3.75, which is 375% (results greater than 100% are rare but correct).
   • For example: what percentage of 250 is 3? Enter 9, click divide, enter 250 and click equal. The screen will display 0.036, which is 3.6%.

Method 2 of 3: How to Compute an Unknown Integer

If percentages are given in the problem, then it is necessary to calculate either the whole or part of the whole. This can be clarified by the question in the problem.

1. 1 If the question in the problem contains the phrase "what number", you need to calculate the whole, and if the number is preceded by the preposition "from", you need to find a part of the whole.
   • For example: what is 10% of 16? Here the whole is given (this is evidenced by the preposition "from" in front of the number), therefore in the problem you need to find a part of the whole.
   • For example: What number is 25% equal to 15? Here, the unknown is the whole (there is the phrase "what number"), but a part of the whole is given (15).
2. 2 Solve the problem with an unknown integer. In our example (25% of which number is 15), convert the percentages to decimal: 25% = 0.25 (or, for example, 138% = 1.38; 7% = 0.07, and so on).
3. 3 Use equality: (whole) = (part of whole) /%.
4. 4 On the calculator, first enter a part of a whole and press divide, then enter a decimal (converted percentages) and press equal.
   • For example: What number is 25% equal to 15? Enter 15, click divide, enter 0.25 and click equal. The screen will display 60 (remember that this is just the number 60, not 60%).
   • For example: 32% of which number is 16? Enter 16, click divide, enter 0.32 and click equal. The screen will display 50.
   • For example: What number is 125% equal to 80? Enter 80, click divide, enter 1.25 and click equal. The screen will display 64.
   • For example: What number is 7.5% equal to 6? Enter 6, click divide, enter 0.075 and click equal. The screen will display 80.

Method 3 of 3: How to Calculate the Unknown Part of a Whole

1. 1 Look for the phrase "what is equal to" and the preposition "from". If they are present in the question of the problem, you need to find part of the whole in it (for example, what is equal to 10% of 16).
2. 2 To solve this problem, first convert the percentage to a decimal: 32% = 0.32; 75% = 0.75; 150% = 1.5; 6% = 0.06 and so on.
3. 3 Use equality: (part of a whole) = (whole) x% (that is, multiply the percent and the whole).
   • For example: what is 10% of 16? On the calculator, enter 0.1, press multiply, enter 16, and press equals. The screen will display 1.6 (this is not 1.6%).
   • For example: what is 230% of 40? On the calculator, enter 2.3, press multiply, enter 40, and press equals. The screen will display 92.
   • For example: what is 37% of 200? On the calculator, enter 0.37, press multiply, enter 200, and press equals. The screen will display 74.

Tips

• To solve the problem by percentage, you need to A) divide part of the whole into the whole; C) divide a part of a whole by a percentage; C) multiply whole and percent. The choice of a solution depends on the condition of the problem.
• Make sure that the answer “appears to be correct,” that is, it is reasonable.
• When calculating a part of an integer, the order of the multiplication does not matter. For example, to calculate what is 230% of 45, multiply 2.3 x 45 or 45 x 2.3.
• Multiply only when percent and whole are given. Otherwise, always divide.

Warnings

• The order of division is very important. On a calculator, always enter a part of a whole first, followed by a percentage or a whole.
• Most calculators have a percentage key. It automatically converts percentages to decimal, for example 35% to 0.35; 325% at 3.25; 6% at 0.06 and so on. We do not recommend using this key because many students convert percentages to decimals, enter them into the calculator, and then hit the percent key, which is very confusing.

What do you need

• Calculator or sheet of paper.