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The method of subtraction of items of size is strictly just like that of subtraction of bizarre numbers.
Find out how the
values of size are organized in several columns for the subtraction of
size.
1. Subtract 12 m 36 cm from 48 m 57 cm
Answer:
Case 1:
Minuend and subtrahend are each transformed into smaller items.
12 m 36 cm = (12 × 100) cm + 36 cm = (1200 + 36) cm = 1236 cm
48 m 57 cm = (48 × 100) cm + 57 cm = (4800 + 57) cm = 4857 cm
Now subtract
48 m 57 cm = 4857 cm
– 12 m 36 cm = – 1236 cm
3621 cm
= 3600 cm + 21 cm
= 36 m 21 cm
Subsequently, 48 m 57 cm – 12 m 36 cm = 36 m 21 cm
Case 2:
As minuend is bigger than subtrahend, the minuend is positioned above the subtrahend. Then m and cm are organized in several columns.
Now subtract
m cm
48 57
– 12 36
36 21
(i) Subtracting cm, 57 cm – 36 cm = 21 cm.
It’s positioned underneath cm column.
(ii) Subtracting m, 48 m – 12 m = 36 m.
It’s positioned underneath m column.
Therefore, distinction = 36 m 21 cm
2. Subtract 37 m 50 cm from 53 m 30 cm.
Answer:
Case 1:
Minuend and subtrahend are each transformed into smaller items.
53 m 30 cm = (53 × 100) cm + 33 cm = (5300 + 30) cm = 5330 cm
37 m 50 cm = (37 × 100) cm + 50 cm = (3700 + 50) cm = 3750 cm
Now subtract
5330 cm
– 3750 cm
1580 cm
= 1500 cm + 80 cm
= 15 m 80 cm
Subsequently, 53 m 30 cm – 37 m 50 cm = 15 m 80 cm.
Case 2:
As minuend is bigger than subtrahend, the minuend is positioned above the subtrahend. Then m and cm are organized in several columns. Minuend 53 m 30 cm is positioned above subtrahend 37 m 50 cm.
m cm
1 100
53 30
– 37 50
15 80
(i) 50 cm > 30 cm. So, 50 cm can’t be subtracted from 30 cm.
1 m or 100 cm is borrowed from 53 m leaving 52 m making 30 cm to 130 cm.
Now 130 – 50 = 80. It’s positioned underneath cm column.
(ii) Now within the m column, 53 – 1 = 52 m. 52 m – 37 m = 15 m.
It’s positioned underneath m column.
Therefore, the distinction is 15 m 80 cm.
3. Subtract 56 m 65 cm from 62 m 7 cm.
|
Answer: Allow us to subtract. Step I: Organize the numbers vertically. Step II: Write the lengths to be subtracted in m and cm as proven. Step III: First, subtract centimetres from proper after which subtract the metres. |
 |
Thus, 62 m 7 cm – 56 m 65 cm = 5 m 42 cm
4. Subtract 37 m 6 cm from 70 m.
Answer:
Case 1:
We’ve, 70 m – 37 m 6 cm
Minuend and
subtrahend are each transformed into smaller items.
70 m =
(70 × 100) cm = 7000 cm
37 m 6 cm =
(37 × 100) cm + 6 cm = (3700 + 6) cm = 3706 cm
Now subtract
7000 cm
– 3706 cm
3294 cm
= 3200 cm + 94 cm
= 32 m 94 cm
Subsequently, 70 m – 37 m 6 cm = 32 m 94 cm.
Case 2:
As minuend is bigger than
subtrahend, the minuend is positioned above the subtrahend. Then m and cm
are organized in several columns. Minuend 70 m 00 cm is positioned above subtrahend 37 m 06 cm.
m cm
1 100
70 00
– 37 06
32 94
(i) 06 cm > 0 cm. So, 6 cm can’t be subtracted from 0 cm.
1 m or 100 cm is borrowed from 70 m leaving 69 m in m column.
(ii) Now 100 cm – 06 cm = 94 cm. It’s positioned underneath cm column.
(iii) Now within the m column, 69 m – 37 m = 32 m.
It’s positioned underneath m column.
Therefore, the distinction is 32 m 94 cm.
5. Subtract 45 km 282 m from 63 km 70 m.
Answer:
Case 1:
Minuend and
subtrahend are each transformed into smaller items (conversion technique).
63 km 70 m =
(63 × 1000) m + 70 m = (63000 + 70) m = 63070 m
45 km 282 m =
(45 × 1000) m + 282 m = (45000 + 282) m = 45282 m
Now subtract
63070 m
– 45282 m
17788 m
= 17000 m + 788 m
= 17 km 788 m
Subsequently, 63 km 70 m – 45 km 282 m = 17 km 788 m.
Case 2:
As
minuend is bigger than subtrahend, the minuend is positioned above the
subtrahend. Then km and m are organized in several columns. Minuend 63 km 70 m is positioned above subtrahend 45 km 282 m (with out conversion).
km m
1 1000
63 070
– 45 282
17 788
(i) 282 m > 70 m. So, 282 m can’t be subtracted from 70 m.
1 km or 1000 m is borrowed from 63 km leaving 62 km making 70 m to 1070 m (Since, 1 km = 1000 m and 70 m = 1070 m).
Now 1070 m – 282 m = 788 m. It’s positioned underneath m column.
(ii) Now within the km column, 63 – 1 = 62 km. 62 km – 45 km = 17 km.
It’s positioned underneath km column.
Therefore, the distinction is 17 km 788 m.
6. Subtract 75 km 345 m from 200 km 20 m.
Answer:
As
minuend is bigger than subtrahend, the minuend is positioned above the
subtrahend. Then km and m are organized in several columns. Minuend 200 km 20 m is positioned above subtrahend 75 km 345 m.
km m
1 1000
200 020
– 275 345
124 675
(i) 345 m > 20 m. So, 345 m can’t be subtracted from 20 m.
1 km or 1000 m is borrowed from 200 km leaving 199 km making 020 m to 1020 m.
Now 1020 m – 345 m = 675 m. It’s positioned underneath m column.
(ii) Now within the km column, 200 – 1 = 199 km. 199 km – 75 km = 124 km.
It’s positioned underneath km column.
Therefore, the distinction is 124 km 675 m.
7. Subtract 8 m 7 dm 5 cm from 26 m 4 dm 8 cm.
Answer:
As
minuend is bigger than subtrahend, the minuend is positioned above the
subtrahend. Then m, dm and cm are organized in several columns. Minuend 26 m 4 dm 8 cm is positioned above subtrahend 8 m 7 dm 5 cm.
m dm cm
1 10
26 4 8
– 8 7 5
17 7 3
(i) 8 cm – 5 cm = 3 cm. It’s positioned underneath cm column.
(ii) 7 dm > 4 dm. So, 7 dm can’t be subtracted from 4 dm.
1 m or 10 dm is borrowed from 26 m leaving 25 m making 4 dm to 14 dm.
Now 14 dm – 7 dm = 7 dm. It’s positioned underneath dm column.
(iii) Now within the m column, 26 – 1 = 25 m. 25 m – 8 m = 17 m.
It’s positioned underneath m column.
Therefore, the distinction is 17 m 7 dm 3 cm.
Questions and Solutions on Subtraction of Size:
1. Subtract the next:
(i) 81 m 9 cm – 52 m 52 cm
(ii) 28 m 98 cm – 16 m 20 cm
(iii) 352 m 917 cm – 148 m 79 cm
(iv) 938 m 33 cm – 619 m 57 cm
(v) 394 m 68 cm – 45 m 79 cm
(vi) 180 m 90 cm – 42 m 33 cm
Reply:
1. (i) 28 m 57 cm
(ii) 12 m 78 cm
(iii) 203 m 38 cm
(iv) 318 m 76 cm
(v) 348 m 89 cm
(vi) 138 m 57 cm
2. Subtract the next:
(i) 81 m 09 cm from 145 m 56 cm
(ii) 14 m 82 cm from 67 m 40 cm
(iii) 174 m 259 cm from 512 m 36 cm
(iv) 79 m 56 cm from 140 m 23 cm
(v) 180 m 90 cm from 287 m 46 cm
Reply:
2. (i) 64 m 47 cm
(ii) 52 m 58 cm
(iii) 338 m 11 cm
(iv) 60 m 67 cm
(v) 106 m 56 cm
● Associated
Ideas
● Conversion
of Customary Unit of Size
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