Find Half Of A Number

Lesson xvi Section 2

HOW TO TAKE Half
OF ANY NUMBER

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seven.	Which natural numbers are called the fifty-fifty numbers?

	Numbers that can be divided into 2 equal parts.

8 is an even number because we can dissever information technology "evenly" into 2 iv'southward.

4 is half of 8.

9 is not an fifty-fifty number. At that place is an "odd" 1:

Therefore we call 9 an odd number. Nosotros cannot have one-half of a natural number that is odd. We cannot accept half of 9 people.

The even numbers, then, are the numbers divisible by 2: ii, four, 6, 8, and so on. The odd numbers are ane, three, five, vii, and so on.

If you lot do not know half of some even number, you can observe it by decomposing it mentally into 2 fifty-fifty numbers whose half yous exercise know. We saw how to do that in Section ane, Example 8.

Example ane. How much is half of 54?

Answer. Half of 54	=	Half of 50 + One-half of 4

	=	25 + 2

	=	27.

As for odd numbers, annotation that every odd number is equal to an even number plus ane.

iii = 2 + i.

five = 4 + i.

vii = six + 1.

9 = 8 + 1.

And so on.

Again, if a natural number is odd, then nosotros cannot take half of it. Therefore, we will now assume that nosotros are not necessarily dealing with natural numbers, and that 1 is now a continuous unit -- a unit we use to measure -- and that has a half: i minute, one centimeter, 1 pound, and then on. (Lesson xx.)

8.	What number is one-half of one?

	½ ("One-half")

½ must be ane one-half of something. It is one half of i.

Half of $one, of course, is $.50.

9.	How can we take half of an odd number?

One-half of 7

	Take half of its even part, and add one-half of 1.

Case 2. How much is half of 7?

Answer. seven = vi + 1. Half of 6 is iii; one-half of ane is ½; therefore one-half of vii
is 3½.

One-half of $7.00 is $3.50.

Example iii. A scarf that normally sells for $17 is existence sold at one-half toll. What practise you pay?

Reply. 17 = 16 + i. One-half of xvi is 8. Therefore, half of $17 is $8 .50.

Example 4. How much is one-half of 25%?

Reply. 12½%.

25 = 24 + 1. Half of 24 is 12. Half of 1 is ½.

And so if you knew that 25% ways a quarter, then you now know that 12½% means an eighth.

(See Lesson 27, Case 7.)

Example five How much is half of $27.twoscore?

Answer. Nosotros will have half of $27 and add information technology to half of $.40.

Since 27 = 26 + ane, and so

One-half of $27 is $thirteen .50.

Half of $.twoscore is $ .xx.

Therefore, half of $27.40 is $13 .70.

Example half dozen. How much is one-half of 90?

Reply. 90 = 80 + ten. One-half of 80 is 40; half of x is 5; therefore half of 90 is 45.

Come across Problem 21.

Example seven. How much is one-half of $9.70?

Respond. Half of $ix.00 (8 + 1) is $iv .50. One-half of $.70 is $ .35. Therefore one-half of $ix.70 is $4 .85.

Example 8. The famous number π ("pi") is approximately three.fourteen. How

much is one-half of π; that is,

π
two

Reply. Ignore the decimal point in 3.14. So half of 300 is 150; one-half of 14 is 7; therefore half of 314 is 157. On replacing the decimal point,

π
2

1.57.

10.	How can nosotros have a fourth or 25% of a number?

	Take half of half.

parts

To separate a number in Half means to divide it into two equal parts. To divide information technology into Fourths, or quarters, means to separate it into 4 equal parts. And we can exercise that by taking one-half of each Half.

A quarter is half of a one-half. Compare Lesson xv.

Example 9. How much is a quaternary, or a quarter, of threescore?

Answer. Half of 60 is 30. Half of 30 is xv.

Instance 10. How much is 25% of 180?

Answer. 25% means a fourth. (Lesson 15.) Half of 180 is 90. One-half of ninety is 45.

Example 11. How much is 25% of 112?

Answer. Half of 112 = One-half of 100 + Half of 12 = 56.

Respond.One-half of 56 = Half of 50 + One-half of 6 = 25 + 3 = 28.

Example 12. How much is 25% of $9.60?

Answer. One-half of $9.60 = $4.50 + $.30 = $iv.eighty. Half of $4.80 = $ii.40

11.	How can we multiply past 5?

	5 × 123

	Take half of the multiplication past 10.

Since 5 is half of 10, then v times a number volition exist one-half of 10 times that number.

Example thirteen. 5 × 123 = Half of ten × 123

Case 13 5 × 123 = Half of 1230 (Lesson 4, Question 1.)

Example 13. v × 123 = 615.

Example 14. 5 × $1.50 = Half of $fifteen

Instance fourteen. 5 × $ane.50 = $7.50.

Example 15. 5 × $46.lxxx = Half of $468

Instance fifteen. 5 × $46.80 = $234.

12.	How can we take 5% of a number?

	Take one-half of 10%.

Instance 16. How much is 5% of $162?

Answer. 10% is $16.20. (Lesson four, Question 7.) Therefore, five% is $8.ten.

To write .05 and multiply, is a written method for those who do not understand percentage.

Example 17. How much is 5% of $475?

Respond. 10% is $47 . 50. Therefore, five% is $23.50 + $. 25 = $23.75.

13.	How can we multiply past 15?

15 × 8

	Multiply by 10, and add half.

For, fifteen = 10 + Half of 10.

Example 18. fifteen × eight = 80 + Half of eighty

Instance 18. xv × 8 = 80 + xl

Example xviii. fifteen × 8 = 120.

Instance nineteen. 15 × 42 = four 20 + ii 10.

Case 19. fifteen × 42 = 6 iii0.

fourteen.	How can we have xv% of a number?

	Take 10% and add half.

Example 20. How much is 15% of $70??

Answer. 15%	=	10% + Half of 10%

	=	$seven.00 + $iii.50

	=	$10.50.

Example 21. If you lot tip at the charge per unit of xv%, and the bill is $twoscore, how much practice you leave?

Reply. xv%	=	ten% + One-half of 10%

	=	$4.00 + $2.00

	=	$six.00.

At this point, delight "turn" the folio and do some Problems.

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