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May 2013

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(easy hangman)
(difficult)

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

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

10% is

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

1% is

. 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]

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