THE MEANING OF DIVISION
PROBLEMS: SECTION 2
Decomposing the dividend
15. To find the quotient, decompose the dividend into obvious
15. multiples of the divisor.
| a) | 96 3 |
= | 90 3 |
+ | 6 3 |
= | 32 | b) | 63 3 |
= | 60 3 |
+ | 3 3 |
= | 21 | |
| c) | 128 4 |
= | 120 4 |
+ | 8 4 |
= | 32 | d) | 186 6 |
= | 180 6 |
+ | 6 6 |
= | 31 | |
| e) | 265 5 |
= | 250 5 |
+ | 15 5 |
= | 53 | |||||||||
16. Decompose the dividend into multiples of the divisor. Find the
16. quotient.
| a) | 78 3 |
= | 60 3 |
+ | 18 3 |
= | 26 | b) | 92 4 |
= | 80 4 |
+ | 12 4 |
= | 23 |
| c) | 85 5 |
= | 50 5 |
+ | 35 5 |
= | 17 | d) | 91 7 |
= | 70 7 |
+ | 21 7 |
= | 13 |
| e) | 96 8 |
= | 80 8 |
+ | 16 8 |
= | 12 | f) | 56 4 |
= | 40 4 |
+ | 16 4 |
= | 14 |
| g) | 45 3 |
= | 30 3 |
+ | 15 3 |
= | 15 | h) | 84 6 |
= | 60 6 |
+ | 24 6 |
= | 14 |
17. Decompose each dividend into multiples of the divisor, and find the
17. quotient. (Try the divisor into the first two digits of the dividend.)
24. Check your answer: Multiply the quotient times the divisor.
| a) | 237 3 |
= | 210 3 |
+ | 27 3 |
= | 79 | b) | 184 4 |
= | 160 4 |
+ | 24 4 |
= | 46 |
| c) | 185 5 |
= | 150 5 |
+ | 35 5 |
= | 37 | d) | 378 6 |
= | 360 6 |
+ | 18 6 |
= | 63 |
| e) | 441 7 |
= | 63 | f) | 456 8 |
= | 57 | ||||||||
| g) | 105 7 |
= | 15 | h) | 512 8 |
= | 64 | ||||||||
| i) | 432 9 |
= | 450 9 |
− | 18 9 |
= | 48 | j) | 267 3 |
= |
270 3 |
− | 3 3 |
= | 89 |
| k) | 136 4 |
= | 34 | l) | 396 9 |
= | 44 | ||||||||
| m) | 385 5 |
= | 77 | n) | 276 6 |
= | 46 | ||||||||
18. Inexact division. Write each quotient as a mixed number.
| a) | 7 5 |
= | 1 | 2 5 |
b) | 26 3 |
= | 8 | 2 3 |
c) | 23 9 |
= | 2 | 5 9 |
d) | 31 8 |
= | 3 | 7 8 |
|||
| e) | 46 7 |
= | 6 | 4 7 |
f) | 39 4 |
= | 9 | 3 4 |
g) | 65 12 |
= | 5 | 5 12 |
h) | 53 6 |
= | 8 | 5 6 |
|||
Can you do these mentally? Decompose the dividend.
19. How many 7's are there in 644? 92. 644 = 630 + 14.
20. What number times 9 is 351? 39. 351 = 360 − 9.
21. How many 8-inch boards could you cut from a piece that is 120
27. inches? 15. 120 = 80 + 40.
22. In 5 hours, Arlene was able to drive 315 miles. How far did she
30. travel in 1 hour? That is, what was her speed? Miles per hours.
27. 63 mph. 315 = 300 + 15.
23. Helen took 6 exams, and the total of all her grades was 510. What
32. was her average grade? 85. 510 = 480 + 30.
24. Joe borrowed $408, and agreed to pay it back in one year in equal
32. monthly payments. How much will he pay each month?
32. $34. 408 = 360 + 48. Divide each by 12.
25. 4 jackets that cost the same, together cost $304. How much did each
27. one cost? $76. 304 = 280 + 24.
26. You have $425 from which you plan to make payments of $35 each.
26. How many payments will you be able to make? 12.
27. 425 = 350 + 70 + 5 = 12 × 35 + 5.
27. A club wants to raise $1400. If it sells tickets at $5 each, how many 27. tickets must it sell? 280. 1400 = 1000 + 400.
28. Divide $882 equally among 9 people. $98 each. 882 = 900 − 18.
The problems following the next Lesson will include calculator problems.
Go on to the next Section.
or
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Copyright © 2021 Lawrence Spector
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