B' Long Multiplication'

1
B. Long Multiplication.

• There are several methods to multiply numbers,
  (without using a
• calculator). Two methods will be shown.
• Method 1. Multiply 231 by 19.

2 3 1
Multiply from the bottom right.
1 9
Write the numbers in a column. Be careful to
space the figures out.

9
7
2 0
9 3 27
2
9 2 18
9 1 9
18 2 20
2
B. Long Multiplication.

• There are several methods to multiply numbers,
  (without using a
• calculator). Two methods will be shown.
• Method 1. Multiply 231 by 19.

2 3 1
Multiply from the next figure to the left.
1 9

9
7
2 0
The 1 has a value of 10. So 0 must be put in the
units column.
2
0
Why?
3
B. Long Multiplication.

• There are several methods to multiply numbers,
  (without using a
• calculator). Two methods will be shown.
• Method 1. Multiply 231 by 19.

2 3 1
Multiply from the next figure to the left.
1 9

9
7
2 0
1 3 3
1 1 1
1 2 2
2
2
0
1
3
4
B. Long Multiplication.

• There are several methods to multiply numbers,
  (without using a
• calculator). Two methods will be shown.
• Method 1. Multiply 231 by 19.

That was as easy as falling off a log!
2 3 1
1 9

9
7
2 0
2
2
0

1
3
Now add the products
8
9
3
4
5
B. Long Multiplication.

• There are several methods to multiply numbers,
  (without using a
• calculator). Two methods will be shown.
• Method 1. Multiply 231 by 19.

A quick way to see if the answer is reasonable
can be made by estimation.
231 can be rounded down to one significant figure.
2 3 1
0 0
231 is closer to 200.
Key terms
6
B. Long Multiplication.

• There are several methods to multiply numbers,
  (without using a
• calculator). Two methods will be shown.
• Method 1. Multiply 231 by 19.

A quick to see if the answer 4389 is reasonable
can be made by estimation.
2 3 1
0 0
19 can be rounded up to one significant figure.
19 is closer to 20.
1 9
2 0
7
B. Long Multiplication.

• There are several methods to multiply numbers,
  (without using a
• calculator). Two methods will be shown.
• Method 1. Multiply 231 by 19.

A quick to see if the answer 4389 is reasonable
can be made by estimation.
2 3 1
0 0
Multiply together.
1 9
2 0

2 2 4
4
0 0 0
Followed by three 0s
8
B. Long multiplication continued

• Method 2. Gelosia, box multiplication.
• Multiply 231 by 19.
• Many students find this method easier to carry
  out, but it does
• require a little more preparation.

Draw a rectangle 6 cm by 2 cm. Divide the
rectangle into 1 cm squares.
Down right to left!
Now divide the squares diagonally.
9
B. Long multiplication continued

• Method 2. Gelosia, box multiplication.
• Multiply 231 by 19.
• Many students find this method easier to carry
  out, but it does
• require a little more preparation.

2
3
1
Place the numbers across the top and down the
right side.
1
9
10
B. Long multiplication continued

• Method 2. Gelosia, box multiplication.
• Multiply 231 by 19.
• Many students find this method easier to carry
  out, but it does
• require a little more preparation.

Note only 10s go in the top triangle.
2
3
1
Multiply the 1 highlighted with each figure
across the top.
0
0
0
1
1
2
3
9
1 3 03
1 1 01
1 2 02
11
B. Long multiplication continued

• Method 2. Gelosia, box multiplication.
• Multiply 231 by 19.
• Many students find this method easier to carry
  out, but it does
• require a little more preparation.

2
3
1
Multiply the 9 highlighted with each figure
across the top.
0
0
0
1
1
2
3
0
2
1
9
9 3 27
9 1 09
9 2 18
9
7
8
12
B. Long multiplication continued

• Method 2. Gelosia, box multiplication.
• Multiply 231 by 19.
• Many students find this method easier to carry
  out, but it does
• require a little more preparation.

2
3
1
Add up the figures along the diagonal paths from
the right.
0
0
0
0
1
1
2
3
0
2
1
9
4
9
7
8
1
carry
3
9
8