Percentage Flashcards
Example: Transform 3% to decimal form.
0.03
the result when you multiply a number by a percent.
Percentage
Follow these steps if you want to find the percentage:
Step 1: Convert the given percent (the one with the % sign) into decimal.
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Again, to convert percent into its decimal form, we just drop the percent sign and then move the decimal point two places to the left. Thus, 20% = 0.20
Step 2: Multiply the decimal you have obtained from Step 1 to the given number. The result is the percentage.
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To multiply 0.20 by 10, we just ignored the decimal point for a while and multiplied the given decimals just like whole numbers. We have obtained 0200. Since 0.20 has two decimal places while 10 has no decimal place, then the final answer should have two decimal places. We count two digits from the right of 0200 and put the decimal point there. Hence, the answer is 02.00 which is equivalent to 2.
Hence, 20% of 10 is 2. This means that out of 10 cookies that your mother prepared, 2 of those were eaten by your brother.
Example: What is 50% of 120?
Step 1: Convert the given percent (the one with the % sign) into decimal.
We just drop the % sign of 50% and move the decimal point two places to the left.
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Thus, 50% = 0.50
Step 2: Multiply the decimal you have obtained from Step 1 to the given number. The result is the percentage.
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ADVERTISING
To multiply 0.50 by 120, we just ignored the decimal point for a while and multiplied the given decimals just like whole numbers. Through this process, we have obtained 06000. Since 0.50 has two decimal places while 120 has no decimal place, then the final answer should have two decimal places. We count two digits from the right of 06000 and put the decimal point there. Hence, the answer is 060.00 which is equivalent to 60.
Hence, 50% of 120 is 60.
What are the Simple Tricks in Computing Percentage
We always want to make our computations in mathematics faster and more accurate. For this reason, I will share with you two tricks that you can use when computing percentages
Trick #1: You can actually compute some percentages using only mental computation.
If you want to determine the 25%, 50%, 75%, or 100% of a number, you can do so without the help of pen and paper.
25% is equivalent to 25⁄100 or 1⁄4. Hence, to find the 25% of a number, just divide the given number by 4.
Example: 25% of 40 is just 40 ÷ 4 = 10
50% is equivalent to 50⁄100 or 1⁄2. Thus, to find the 50% of a number, just divide the given number by 2. This means that 50% of a number is just half of the given number
Example: 50% of 40 is just 40 ÷ 2 = 20
75% is equivalent to 75⁄100 or 3⁄4. Thus, to find the 75% of a number, multiply the given number by 3 and then divide the result by 4.
Example: 75% of 40 is just 40 x 3 = 120 ÷ 4 = 30
100% is equivalent to 100⁄100 or 1. Thus, 100% of a number is the number itself.
Example: 100% of 40 is just 40 itself.
Trick #2: X% of a number Y is equal to Y% of number X
This trick means that we can transfer the % sign to the other number and the result will be the same.
Example: What is 40% of 25?
Using trick #2, we can transfer the % sign from 40% to 25. Thus, we have 25%. This means that 40% of 25 is the same as 25% of 40.
Thus, applying our first trick on finding the 25% of a number, 40 ÷ 4 = 10, Hence, 40% of 25 is 10.
Example: What is 92% of 50?
92% of 50 is the same as 50% of 92. Hence, we can just simply divide 92 by 2 to obtain the answer, 92 ÷ 2 = 46
Therefore, 92% of 50 is 46.
The product of the base and the rate is the percentage.
Percentage = Base × Rate
The formula to find the percentage, as we have stated, is:
Percentage = Base × Rate
We can manipulate the mathematical equation above to obtain the formulas for computing the base and the rate:
Formula to Find the Base
Base = Percentage ÷ Rate
Formula to Find the Rate
Rate = Percentage ÷ Base
Example 1: If 10% of a number is 90, what is the number?
Solution:
We can interpret this question as 10% of ______ = 90. Since “of” is a signal word for multiplication, it also implies 10% x ______ = 90
This means that 10% is the rate while 90 is the percentage. The unknown number is the base. Thus, we need to compute the base.
Using the formula to find the base:
Base = Percentage ÷ Rate
Base = 90 ÷ 10%
Convert the given percent into decimal:
Base = 90 ÷ 0.10
Now that you have already transformed the rate into decimal form, you may now divide 90 by 0.10 to obtain the answer.
To perform division with decimal numbers, we need to transform the divisor (0.10) into a whole number by moving two decimal places to the right. Thus, the new divisor is 10. We also move two decimal places for the dividend (90). Thus, the new dividend is 9000.
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We now perform long division with our new dividend and divisor:
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To find the base, we compute 90 ÷ 0.10 = 900
Hence, the base is 900.
Example 2: What percent of 720 is 90?
Solution:
We can translate the question above in this form: _____% of 720 is 90 or _____% x 720 = 90. Therefore, 720 is the base while 90 is the percentage. The missing number is the rate.
We will now use the formula for finding the rate.
Rate = Percentage Base
Again, based on the given problem, the percentage is 90 while the base is 720
Rate = 90 ÷ 720
Notice that the dividend (the first number) is smaller than the divisor (the second number). In this case, you may apply the same steps in transforming fractions into decimal form because 90 ÷ 720 is actually a proper fraction which is 90⁄720.
Let us divide 90 by 720 using the steps in transforming fractions into decimal form.
We start by adding some zeros and decimal points so we can proceed with the division process.
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We can now divide 900 by 720.
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Take note that every time the remainder becomes smaller than the divisor, we just add zeros to 900 and to the remainder so we can continue the division process.
The quotient we obtained is 0.125. Thus, 0.125 is our rate.
However, the rate must always be expressed with a percent sign. To do this, we just multiply 0.125 by 100 or move two decimal places to the right of it and put a percent sign. Thus, 0.125 is equal to 12.5%.
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Therefore, the rate is 12.5%
How To Use the Percentage, Base, and Rate Triangle
Suppose you are looking for the base. What you have to do is to cover the B in the triangle and look at the remaining letters and the operation between them. Notice that if you cover B, the remaining letters are P and R with a division sign between them. This means that to find the base, you need to divide P by R.
1) Which of the following fraction represents 92%
a)
92
100
b)
23
25
c)
24
25
d) Both A and B
D
2) Which of the following has the least value?
a) 50% of 320
b) 75% of 100
c) 100% of 70
d) 25% of 420
C
3) What is 40% of 30?
a) 12
b) 13
c) 14
d) 15
A
