The ideas in this lesson are taken from Math Mammoth Percent book.

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

# Percentage of a Number

 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   _______ d.-f. [available in the book]

2. Find 1% of these numbers.

 a. 900   _______ b. 6,800   _______ c. 550   _______ d.-f. [available in the book]

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?

5. [available in the book]

6. [available in the book]

 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  ________ c. -f.[available in the book]

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?

11. [available in the book]

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 b. [available in the book]

 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   ________ b. [available in the book] c. [available in the book]

14. Find percentages of the quantities.

 a. 50% of 26 in.  _______ b. 25% of 40 ft  _______ c.-f. [available in the book]

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:   \$_________  +  \$_________  =  \$_________

16. [available in the book]

17. [available in the book]

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?

19. [available in the book]

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.

21. [available in the book]

This lesson is taken from my book Math Mammoth Percent.

#### Math Mammoth Percent

A self-teaching worktext for 5th-7th grade that covers percent, percentage of a number, discounts, sales tax, percent of change, and comparisons with percent.