What Is Half Of 42
Lesson 16 Department ii
HOW TO Have HALF
OF Whatever NUMBER
Dorsum to Section i
| vii. | Which natural numbers are called the fifty-fifty numbers? |
| Numbers that can be divided into two equal parts. | |
8 is an even number because nosotros can divide information technology "evenly" into ii four's.
four is one-half of 8.
9 is not an fifty-fifty number. There is an "odd" 1:
Therefore we call 9 an odd number. Nosotros cannot take half of a natural number that is odd. We cannot take half of 9 people.
The fifty-fifty numbers, then, are the numbers divisible past 2: ii, 4, 6, 8, then on. The odd numbers are ane, iii, 5, 7, and then on.
If you do not know half of some even number, y'all can find it by decomposing information technology mentally into two even numbers whose half you do know. We saw how to do that in Section 1, Example 8.
Example 1. How much is half of 54?
| Answer. One-half of 54 | = | One-half of 50 + Half of 4 |
| = | 25 + 2 | |
| = | 27. | |
Equally for odd numbers, note that every odd number is equal to an even number plus 1.
3 = ii + one.
5 = 4 + 1.
7 = half dozen + 1.
9 = eight + i.
And and then on.
Over again, if a natural number is odd, then we cannot accept one-half of information technology. Therefore, nosotros volition now presume that nosotros are not necessarily dealing with natural numbers, and that 1 is at present a continuous unit -- a unit nosotros use to measure -- and that has a one-half: 1 infinitesimal, ane centimeter, 1 pound, and so on. (Lesson twenty.)
| viii. | What number is half of 1? |
| ½ ("I-half") | |
½ must be 1 half of something. Information technology is one one-half of one.
Half of $1, of grade, is $.50.
| 9. | How can we take half of an odd number? |
| Half of vii | |
| Have one-half of its even part, and add half of ane. | |
Example 2. How much is one-half of 7?
Respond. vii = half-dozen + 1. One-half of half-dozen is 3; one-half of 1 is ½; therefore half of 7
is 3½.
Half of $7.00 is $3.50.
Example 3. A scarf that usually sells for $17 is being sold at half toll. What do you pay?
Answer. 17 = 16 + ane. Half of sixteen is viii. Therefore, half of $17 is $8 .50.
Example 4. How much is half of 25%?
Respond. 12½%.
25 = 24 + 1. Half of 24 is 12. Half of 1 is ½.
And so if you knew that 25% means a quarter, then you at present know that 12½% means an 8th.
(See Lesson 27, Example 7.)
Example 5 How much is half of $27.40?
Respond. Nosotros will take half of $27 and add it to half of $.40.
Since 27 = 26 + 1, then
Half of $27 is $thirteen .50.
Half of $.40 is $ .20.
Therefore, half of $27.forty is $13 .70.
Case 6. How much is half of xc?
Reply. 90 = 80 + 10. Half of eighty is 40; half of ten is five; therefore half of 90 is 45.
See Problem 21.
Instance 7. How much is half of $nine.70?
Answer. One-half of $nine.00 (8 + 1) is $4 .50. Half of $.seventy is $ .35. Therefore half of $9.70 is $4 .85.
Case 8. The famous number π ("pi") is approximately three.14. How
| much is half of π; that is, | π ii | ? |
Answer. Ignore the decimal point in 3.14. Then half of 300 is 150; one-half of 14 is 7; therefore half of 314 is 157. On replacing the decimal point,
| π ii |  1.57. |
| 10. | How can we accept a fourth or 25% of a number? |
| Have one-half of one-half. | |
To divide a number in Half means to divide it into two equal parts. To dissever it into Fourths, or quarters, means to divide information technology into four equal parts. And we can do that by taking half of each Half.
A quarter is half of a half. Compare Lesson 15.
Instance 9. How much is a 4th, or a quarter, of threescore?
Reply. Half of 60 is 30. Half of 30 is 15.
Instance 10. How much is 25% of 180?
Answer. 25% ways a fourth. (Lesson 15.) Half of 180 is 90. Half of xc is 45.
Example 11. How much is 25% of 112?
Reply. One-half of 112 = Half of 100 + Half of 12 = 56.
Reply.Half of 56 = Half of 50 + One-half of vi = 25 + iii = 28.
Example 12. How much is 25% of $9.60?
Reply. One-half of $9.60 = $iv.50 + $.thirty = $4.lxxx. One-half of $four.80 = $2.xl
| xi. | How tin we multiply by five? |
| v × 123 | |
| Have half of the multiplication by ten. | |
Since 5 is half of 10, then five times a number will be one-half of 10 times that number.
Example 13. 5 × 123 = Half of 10 × 123
Case 13 v × 123 = Half of 1230 (Lesson 4, Question 1.)
Example 13. five × 123 = 615.
Case xiv. 5 × $1.50 = One-half of $15
Example 14. 5 × $1.50 = $vii.50.
Case fifteen. 5 × $46.lxxx = Half of $468
Example 15. five × $46.fourscore = $234.
| 12. | How can we have 5% of a number? |
| Take half of 10%. | |
Example sixteen. How much is 5% of $162?
Answer. 10% is $16.xx. (Lesson 4, Question vii.) Therefore, 5% is $8.10.
To write .05 and multiply, is a written method for those who practise not understand percentage.
Example 17. How much is v% of $475?
Respond. 10% is $47 . 50. Therefore, 5% is $23.50 + $. 25 = $23.75.
| 13. | How can we multiply by fifteen? |
| 15 × eight | |
| Multiply by x, and add half. | |
For, 15 = x + Half of 10.
Case 18. 15 × viii = 80 + Half of 80
Instance 18. 15 × eight = eighty + 40
Instance 18. 15 × 8 = 120.
Example 19. 15 × 42 = 4 ii0 + 2 10.
Example 19. 15 × 42 = 6 three0.
| 14. | How can nosotros take xv% of a number? |
| Take ten% and add one-half. | |
Example twenty. How much is 15% of $seventy??
| Reply. xv% | = | ten% + Half of 10% |
| = | $seven.00 + $three.50 | |
| = | $ten.50. | |
Instance 21. If y'all tip at the rate of 15%, and the bill is $40, how much do you leave?
| Respond. fifteen% | = | 10% + Half of 10% |
| = | $four.00 + $2.00 | |
| = | $six.00. | |
At this betoken, please "turn" the page and do some Problems.
or
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What Is Half Of 42,
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