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Percentage of a number using mental math

Learn how to solve percent problems in your head! Since 10% is 1/10, and it's so easy to find 1/10 of any number, we can use that to quickly calculate certain percentages of quantities in our heads. to find 20% of a number, first find 10% of it, and double that. And so on.



The basic concepts and ideas of this lesson are also explained in this video:


100% of something means all of it.     1% of something means 1/100 of it.

To calculate a percentage of a quantity, we use the same method as when we calculate a fractional part of that quantity because percent simply means a hundredth part. Therefore, percentages are just fractions.

How much is 1% of 200 kg?  This means how much is 1/100 of 200 kg?
It is simply 2 kg. You just divide by 100 to find a hundredth part!

To find 1% of something (1/100 of something), divide by 100.

Remember how to divide by 100 mentally: Just move the decimal point two places to the left. For example, 1% of 540 is 5.4. And 1% of 8.30 is 0.083.

To find 10% of some quantity, divide by 10.

Why does that work? 10% is 10/100. And 10/100 is equal to 1/10. So we just find 1/10 of the For example, 10% of 340 people is 34 people. Similarly, 10% of $2.30 is $0.23.
(To divide by 10 mentally, just move the decimal point one place to the left.)

1. Find 10% of these numbers.

a. 900   _______ b. 160   _______ c. 50   _______

2. Find 1% of these numbers.

a. 900   _______ b. 6,800   _______ c. 550   _______

3. If 1% of Cindy’s salary is $23, how much is her salary?

4. Ten percent of the cost of a pool is $430. How much does the pool cost?



To find 2% of a quantity, first find 1% of it, then double that.

For example, let’s find 2% of $6. Since 1% of 6 is $0.06, then 2% of 6 is $0.12.

Can you think of a way to find 20% of a number?
(Hint: Start with finding 10% of the number.)

________________________________________________________________

7. Fill in the table. Use mental math.

percentage / number 400 60 78 8 4.1
1% of the number          
2% of the number          
10% of the number          
20% of the number          

8. Fill in this guide for using mental math with percent:

Mental Math and Percent of a Number

50% is  

1

2

.  To find 50% of a number, divide by ______.

10% is  

1

     

.  To find 10% of a number, divide by ______.

1% is  

1

     

.  To find 1% of a number, divide by ______.
50% of 244 is _______.
10% of 47 is ________.
1% of 530 is ________ .
To find 20%, 30%, 40%, 60%, 70%, 80%, or 90% of a number, 
  • First find _________% of number and 
  • then multiply by 2, 3, 4, 6, 7, 8, or 9.
10% of 120 is _______.

30 % of 120 is _______.

60 % of 120 is _______.

9. Find percentages. Use mental math.

a. 10% of 60 kg   ________

    20% of 60 kg   ________

b. 10% of $14  ________

    30% of $14  ________

10. David pays a 20% income tax on his $2,100 salary.
      How many dollars is the tax?

      How much money does he have left after paying the tax?


 

12. Identify the errors that these children made. Then find the correct answers.

a. Find 90% of $55.

    Peter’s solution:
    10% of $55 is $5.50
    So subtract 100% − $5.50 = $94.50


 


90% of a quantity

First find 10% of the quantity and then
subtract that 10% from 100% of it.

25% of a quantity

25% is the same as 1/4. So to find
25% of a quantity, divide it by 4.

12% of a quantity

First find 10% of it. Then find 1% of it, and use that 1%
to find 2% of it. Then, add the 10% and the 2%.

75% of a quantity

75% is 3/4. First find 1/4 of the
quantity and multiply that by 3.

13. Find percentages. Use mental math.

a. 25% of 48 mi   _______

    75% of 48 mi   ________

14. Find percentages of the quantities.

a. 50% of 26 in.  _______ b. 25% of 40 ft  _______


15. Fill in the mental math method for finding 12% of $65.

    10% of $65 is $________.    1% of $65 is $_________.    2% of $65 is $_________.

    Now, add to get 12% of $54:   $_________  +  $_________  =  $_________
 

 

18. On her cell phone bill, Hannah noticed that of the 340 text messages
      that she sent last month, 15% were sent at the cheaper night rate.
      How many messages did Hannah send at night? During the day?
 

20. A carton contains 2 liters of tropical juice. The juice consists of
      25% mango juice, 30% pineapple juice, and the rest is guava
      juice. Find how many milliliters of each juice went into the
      2-liter carton of tropical juice.




This lesson is taken from Maria Miller's book Math Mammoth Percent, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.




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