Download Lesson 1: SUBTRACTION IS FINDING THE DIFFERENCE

Lesson 1: SUBTRACTION IS FINDING THE DIFFERENCE
FACT 1:
Subtraction is finding the difference.
(a) We may do that by taking the smaller number out of the larger number.
(b) We may also do that by counting from smaller to the larger number.
FACT 2:
Subtraction is the same level of operation as addition.
(a) We may subtract quantities of the same unit only. We cannot subtract
quantities of different units.
We may take 2 bananas out of 5 bananas. But we cannot take 2 bananas out of
5 apples.
(b) To subtract quantities of different units, you must change them to some
common units first.
We may change 2 bananas and 5 apples to 2 fruits and 5 fruits. We may then
correctly take 2 fruits out of 5 fruits.
1. Subtract 2 marbles from 9 marbles. What is the difference?
2. Amy had 6 cats. 2 of the cats ran away. How many cats Amy is left with?
3. What is the difference between 18 inches and 25 inches?
(NOTE: Count from 18 to 25. How much is more are 25 from 18?)
Lesson 2: SUBTRACTION IS “REVERSE ADDITION”
FACT 1:
Subtraction is opposite of addition.
To determine
We may ask,
11 – 6
6 + what?
=
=
what?
11
We then count from 6 to 11. This gives us a count of 5. This is the difference.
FACT 2:
For single-digit differences, count from smaller to the larger number.
(a) To subtract 5 from 9, we start from 5 and count up to 9. There are 4 counts. This
is the difference.
(b) To subtract 28 from 33, we start from 28 and count up to 33. There are 5 counts.
This is the difference.
FACT 3:
For double-digit differences, count from smaller to the “next ten”, and from
“next ten” to the larger number. This can be done mentally.
(a) To subtract 17 from 43, we start from 17 and count up to 20 (the next “ten”).
From 20 we count to 43. The total count “3 + 23” or 26. This is the difference.
(b) To subtract 25 from 82, we use a similar diagram. The difference is 57.
4. Find the difference by mental subtraction.
(a) 42 – 23
(f) 32 – 28
(k) 84 – 45
(b) 37 – 14
(g) 59 – 53
(l) 63 – 38
(c) 89 – 48
(h) 71 – 63
(m) 82 – 28
(d) 69 – 46
(i) 39 – 23
(n) 87 – 75
(e) 73 – 49
(j) 66 – 66
(o) 83 – 44
(Check your answers using a calculator)
Lesson 3: SUBTRACTING BY COLUMNS (Traditional)
FACT 1:
Arrange the digits in columns by their place values. Subtract the columns from
right to left using regrouping.
Subtract 387 from 623:
7 is more than 3; regroup 1 from 10’s column to have 13 ones; 13 minus
7 equal 6, put down 6.
(b) For 10's: 1 is left in 10’s column; regroup 1 from 100’s column to have 11 tens; 11
minus 8 equal 3, put down 3.
(c) For 100's: 5 is left in 100’s column; 5 minus 3 equal 2; put down 2.
(d) The difference is 236.
(a) For 1's:
FACT 2:
Verify the difference by reverse addition.
Subtract 369
FACT 3:
from 657.
If there is 0 in a column we may have to regroup from farther left.
9 is more than 5; regroup 1 from 10’s column. Since there are zeroes in
10’s and 100’s columns, Regroup starting from 1000’s columns as
shown above. 15 minus 9 equal 6; put down 6.
For 10's: 9 is left in 10’s column; 9 minus 0 equal 9, put down 9.
For 100's: 9 is left in 100’s column; 9 minus 5 equal 4; put down 4.
For 1000's: 1 is left in 100’s column; put down 1.
The difference is 1496.
(a) For 1's:
(b)
(c)
(d)
(e)
FACT 4:
We may subtract large numbers the same way.
(a) Subtract: 4,001,030,352 – 1,946,327,115.
Note that when there are several zeroes following each other in the larger number,
regrouping takes place far from the left.
(b) Subtract: 5,082,359,777 – 3,193,461,857.
1. Subtract the following by columns. (Check your answers using a calculator)
Lesson 4: SUBTRACTING BY COLUMNS (Reverse Addition)
FACT 1:
To do reverse addition, write the smaller number at the top, set up space for
difference underneath it, and place the larger number in the place of the sum.
Subtract 387 from 623:
(a) For ONEs: Ask 7 plus what is “13” (not “3” because 3 is smaller than 7). Put down
6 in the difference.
(b) For TENs: Carry over 1 from “13” to the next column. 1 and 8 are 9. Ask 9 plus
what is “12”? Put down 3 in the difference.
(c) For 100's:
Carry over 1 to the next column. 1 and 3 are 4. Ask 4 plus what is “6”?
Put down 2 in the difference.
(d) The overall difference is 236.
FACT 2:
We may subtract large numbers through reverse addition as follows.
(c) Subtract: 4,001,030,352 – 1,946,327,115.
Note that when there are several zeroes following each other in the larger number,
there is no confusion of repeated regrouping as is the case with traditional method.
(d) Subtract: 5,082,359,777 – 3,193,461,857.
1. Subtract by “reverse addition”. (Check your answers using a calculator)
(a) 36,251 – 14,532
(d) 400,315 – 291,827
(g) 5,423,234,015 – 3,567,888,146
(b) 30,000 – 24,762
(e) 549,321 – 485,789
(h) 9,876,543,210 – 6,012,345,678
(c) 77,004 – 45,675
(f) 707,303 – 596,276
(i) 5,937,123,472 – 4,999,847,503