Divid in Half Divide in Half Again
Lesson xvi Section two
HOW TO TAKE One-half
OF ANY NUMBER
Back to Section i
| 7. | Which natural numbers are chosen the fifty-fifty numbers? |
| Numbers that can be divided into two equal parts. | |
8 is an even number considering we tin can divide information technology "evenly" into 2 4's.
iv is half of 8.
9 is not an even number. There is an "odd" 1:
Therefore we call 9 an odd number. We cannot take 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: 2, 4, vi, 8, and so on. The odd numbers are ane, 3, v, seven, and so on.
If you do not know one-half of some even number, you can observe it by decomposing it mentally into two even numbers whose one-half you practise know. We saw how to practice that in Section 1, Example 8.
Case 1. How much is one-half of 54?
| Answer. Half of 54 | = | Half of 50 + Half of iv |
| = | 25 + 2 | |
| = | 27. | |
As for odd numbers, note that every odd number is equal to an fifty-fifty number plus 1.
three = ii + 1.
five = iv + 1.
7 = 6 + one.
9 = 8 + i.
And so on.
Once more, if a natural number is odd, so we cannot take half of it. Therefore, we volition now assume that we are not necessarily dealing with natural numbers, and that one is now a continuous unit of measurement -- a unit we utilise to mensurate -- and that has a half: ane minute, 1 centimeter, 1 pound, and then on. (Lesson 20.)
| 8. | What number is one-half of i? |
| ½ ("1-half") | |
½ must be i half of something. It is one half of 1.
Half of $ane, of course, is $.50.
| 9. | How can we accept one-half of an odd number? |
| Half of 7 | |
| Take half of its even role, and add together half of one. | |
Example 2. How much is one-half of 7?
Answer. 7 = 6 + 1. One-half of 6 is 3; half of 1 is ½; therefore half of 7
is 3½.
Half of $7.00 is $3.50.
Case iii. A scarf that normally sells for $17 is being sold at half price. What practise you pay?
Answer. 17 = 16 + 1. Half of sixteen is 8. Therefore, half of $17 is $eight .fifty.
Case 4. How much is half of 25%?
Respond. 12½%.
25 = 24 + 1. Half of 24 is 12. One-half of 1 is ½.
And then if you knew that 25% means a quarter, and then you now know that 12½% means an 8th.
(Encounter Lesson 27, Example 7.)
Example 5 How much is half of $27.xl?
Respond. We will take half of $27 and add it to half of $.40.
Since 27 = 26 + 1, then
One-half of $27 is $13 .l.
Half of $.forty is $ .20.
Therefore, half of $27.twoscore is $thirteen .70.
Example six. How much is one-half of xc?
Answer. 90 = fourscore + x. Half of 80 is forty; one-half of 10 is 5; therefore half of ninety is 45.
See Problem 21.
Example 7. How much is half of $9.seventy?
Respond. One-half of $9.00 (eight + ane) is $iv .l. Half of $.70 is $ .35. Therefore half of $9.70 is $4 .85.
Example 8. The famous number π ("pi") is approximately 3.14. How
| much is half of π; that is, | π 2 | ? |
Answer. Ignore the decimal point in 3.14. Then half of 300 is 150; one-half of 14 is seven; therefore half of 314 is 157. On replacing the decimal point,
| π 2 |  one.57. |
| x. | How can nosotros accept a fourth or 25% of a number? |
| Take half of half. | |
To divide a number in One-half means to divide it into 2 equal parts. To separate information technology into Fourths, or quarters, means to carve up information technology into 4 equal parts. And we can do that by taking half of each One-half.
A quarter is one-half of a one-half. Compare Lesson 15.
Example 9. How much is a fourth, or a quarter, of sixty?
Answer. Half of sixty is 30. Half of 30 is xv.
Instance 10. How much is 25% of 180?
Reply. 25% means a fourth. (Lesson 15.) One-half of 180 is 90. One-half of 90 is 45.
Instance 11. How much is 25% of 112?
Respond. Half of 112 = Half of 100 + Half of 12 = 56.
Answer.Half of 56 = Half of fifty + One-half of half-dozen = 25 + 3 = 28.
Instance 12. How much is 25% of $9.sixty?
Answer. Half of $9.60 = $4.50 + $.30 = $4.80. Half of $4.80 = $2.40
| 11. | How tin nosotros multiply by v? |
| 5 × 123 | |
| Take half of the multiplication by 10. | |
Since five is half of x, then v times a number volition be half of x times that number.
Example 13. v × 123 = One-half of 10 × 123
Instance 13 5 × 123 = One-half of 1230 (Lesson iv, Question ane.)
Example 13. five × 123 = 615.
Example 14. 5 × $1.fifty = Half of $xv
Example 14. 5 × $1.fifty = $seven.50.
Case 15. 5 × $46.lxxx = Half of $468
Example fifteen. v × $46.eighty = $234.
| 12. | How can we accept 5% of a number? |
| Have half of 10%. | |
Example 16. How much is v% of $162?
Reply. 10% is $16.20. (Lesson four, Question 7.) Therefore, 5% is $8.ten.
To write .05 and multiply, is a written method for those who exercise non sympathize percent.
Example 17. How much is 5% of $475?
Answer. 10% is $47 . 50. Therefore, 5% is $23.50 + $. 25 = $23.75.
| thirteen. | How tin can we multiply by xv? |
| 15 × 8 | |
| Multiply by 10, and add half. | |
For, 15 = 10 + Half of 10.
Instance 18. 15 × 8 = 80 + Half of 80
Example 18. fifteen × 8 = 80 + 40
Example eighteen. 15 × 8 = 120.
Example 19. 15 × 42 = four 20 + 2 ane0.
Example 19. fifteen × 42 = 6 three0.
| 14. | How can we accept 15% of a number? |
| Take 10% and add together one-half. | |
Example 20. How much is 15% of $lxx??
| Answer. fifteen% | = | x% + One-half of 10% |
| = | $vii.00 + $iii.fifty | |
| = | $x.50. | |
Instance 21. If yous tip at the rate of fifteen%, and the bill is $40, how much practice you lot leave?
| Answer. xv% | = | x% + Half of 10% |
| = | $4.00 + $ii.00 | |
| = | $six.00. | |
At this point, delight "turn" the page and do some Problems.
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