Delta Instruction Manual
Copyright 2009-2010
Lesson 19
LESSON 19
Division, Three Digit by One
LESSON 19
Division, Three Digit by One Digit
The first question we ask when dividing is, “How many groups?” Even though
that is correct, it could be restated. In example 1, we are looking for how many
groups of 3 will go into 900. Since this is the hundreds place, we could look for
the multiple of 3 times 100, or 300, that goes into 900. When dividing into the
hundreds place, this is the place to begin, with 100 times the outside factor (3 in
this case). As we work through the problem, the next place value is the tens. We
should be looking for what times 30 (3 x 10) will go into 36. Then when we come
to the units, we have the easy one: what times 3 (3 x 1) goes into 6.
Example 1
2
10
3 936
−900
36
−30
6
−6
What is the hundreds multiple times 3 that goes into 900?
It is 300. Multiply: 3 x 300 = 900. Place 900 under the
936 and subtract it. 936 minus 900 leaves 36.
What is the tens multiple times 3 that goes into 30?
It is 10. Multiply: 3 x 10 = 30. Place 30 under the 36 and
subtract it. 36 minus 30 leaves 6.
Now what is the units multiple times 3 that goes into 6?
It is 2. Multiply: 3 x 2 = 6. Place 6 under the 6 and
subtract it. There is no remainder.
DIVISION, THREE DIGIT BY ONE DIGIT - LESSON 19
65
2
10
300
3 936
−900
36
−30
8
20
200 r.1
2 457
−400
57
−40
17
−16
1
8
20
200
2 457
−400
57
−40
When you check your answer with
multiplication, notice how the partial
products of the multiplication problem
correspond to the division progression.
6
−6
Example 2
2
× 312
6
30
900
936
17
−16
What is the hundreds multiple times 2 that goes
into 400? It is 200. Multiply: 2 x 200 = 400. Place
400 under the 457 and subtract it. 457 minus 400
is 57.
There is no tens multiple times 2 that makes 50.
What is the tens multiple times 2 that goes into 40?
It is 20. Multiply: 2 x 20 = 40. Place 40 under the
57 and subtract it. 57 minus 40 leaves 17.
Now what is the units multiple times 2 that goes
into 17? It is 8. Multiply: 2 x 8 = 16. Place 16 under
the 17 and subtract it. The remainder is 1.
2
× 228
16
40
400
456
r.1
457
When you check your answer with
multiplication, notice how the partial
products of the multiplication problem
correspond to the division progression.
1
In examples 3 and 4, we encounter two types of problems that can be difficult
if you are just memorizing a formula. However, if we understand what we are
doing, they should be clear. Read them through carefully.
66
LESSON 19 - DIVISION, THREE DIGIT BY ONE DIGIT
DELTA
Example 3
6
10
9 144
−90
54
−54
0
6
10
9 144
−90
54
−54
What is the hundreds multiple times 9 that goes into
100? It is 0. So we move to the tens place.
What is the tens multiple times 9 that goes into 140?
It is 10. Multiply: 9 x 10 = 90. Place 90 under the 144
and subtract it. 144 minus 90 leaves 54.
Now what is the units multiple times 9 that goes
into 54? It is 6. Multiply: 9 x 6 = 54. Place 54 under
the 54 and subtract it. There is no remainder.
9
× 16
54
90
144
When you check your answer with
multiplication, notice how the partial
products of the multiplication problem
correspond to the division progression.
0
Example 4
7
0
100 r.2
3 323
−300
23
−0
23
−21
DELTA
2
What is the hundreds multiple times 3 that goes into
300? It is 100. Multiply: 3 x 100 = 300. Place 300
under the 323 and subtract it. 323 minus 300 is 23.
What is the tens multiple times 3 that goes into 23?
It is 0. There is no answer other than zero, so we put
a zero in the tens place and proceed to the units.
Now what is the units multiple times 3 that goes into
23? It is 7. Multiply: 3 x 7 = 21. Place 21 under the 23
and subtract it. The remainder is 2.
DIVISION, THREE DIGIT BY ONE DIGIT - LESSON 19
67
7
0
100 r.2
3 323
−300
23
−0
68
23
−21
3
× 107
21
0
300
321
r.2
323
When you check your answer with
multiplication, notice how the partial
products of the multiplication problem
correspond to the division progression.
2
LESSON 19 - DIVISION, THREE DIGIT BY ONE DIGIT
DELTA