Transcript Multiply 469 by 36

Multiplication Past Paper
Questions.
This demonstrates a Past Paper question using several
different methods to find the answer.
Working correctly through any of the following
methods will get full marks for the question.
Further practice can be obtained using the relevant
activities in the Multiplication section of the Moodle.
Multiply 469 by 36
Traditional Method.
469 x
36
Write the question with the
bigger number above the
smaller number
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
4
First multiply the top row by
the units of the second row.
5
9 x 6 = 54: 4 goes in the 1st
column and the 5 is carried
over to the next column.
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
14
First multiply the top row by
the units of the second row.
4 5
6 x 6 = 36: add the 5 that has
been carried over to make 41.
The 1 goes in the 2nd column
and the 4 is carried over to
the next column
[3]
Multiply 469 by 36
Traditional Method.
2
469 x
36
814
First multiply the top row by
the units of the second row.
4 5
6 x 4 = 24: add the 4 that has
been carried over to make 28.
The 8 goes in the 3rd column
and the 2 is carried over to
the next column
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
2
First multiply the top row by
the units of the second row.
4 5
Carry the 2 down
1 mark to get this far.
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
0
2
4 5
Next multiply the top row by
the tens of the second row.
Remember to add the 0 to the
units column.
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
70
2
Next multiply the top row by
the tens of the second row.
4 5
3 x 9 = 27: the 7 goes in the
2nd column and the 2 is
carried over to the 3rd
column.
2
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
070
2
2
Next multiply the top row by
the tens of the second row.
4 5
2
3 x 6 = 18: add to this the 2
that was carried over and we
have 20. The 0 goes in the
3rd column and the 2 is
carried over to the 4th
column.
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
4070
2
1
2
Next multiply the top row by
the tens of the second row.
4 5
2
3 x 4 = 12: add to this the 2
that was carried over and we
have 14. The 4 goes in the
4th column and the 1 is
carried over to the 5th
column.
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
1 4070
1
2
4 5
2
2
Carry the 1 up.
Another mark for getting this
far.
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
1 4070
4
2
1
2
Now add the two rows of
numbers together.
4 5
4+0=4
2
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
1 4070
84
2
1
2
Now add the two rows of
numbers together.
4 5
1+7=8
2
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
1 4070
884
2
1
2
Now add the two rows of
numbers together.
4 5
8+0=8
2
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
1 4070
6884
2
1
2
Now add the two rows of
numbers together.
4 5
2+4=6
2
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
1 4070
1 6884
2
1
2
Now add the two rows of
numbers together.
4 5
0+1=1
2
[3]
Multiply 469 by 36
Traditional Method.
469 x
36
2814
1 4070
1 6884
1
2
4 5
2
2
We now have the answer.
Final mark for a correct
addition.
[3]
Multiply 469 by 36
Multiplication Grid.
x
Draw the multiplication grid and write the numbers across the
top and down the side.
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
9
30
6
Draw the multiplication grid and write the numbers across the
top and down the side.
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
9
30
6
Cross multiply each number in the top row by each number
up the side.
400 x 30 = 12000 (4 x 3 = 12 and there are three 0’s in total)
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
9
30 12000
6
Cross multiply each number in the top row by each number
up the side.
400 x 30 = 12000 (4 x 3 = 12 and there are three 0’s in total)
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30 12000 1800
6
2400
360
9
270
54
Do the same for the other cells.
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30 12000 1800
6
2400
360
9
270
54
Do the same for the other cells.
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30 12000 1800
6
2400
360
9
270
54
Do the same for the other cells.
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30 12000 1800
6
2400
360
9
270
54
Do the same for the other cells.
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30 12000 1800
6
2400
360
9
270
54
Do the same for the other cells.
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30 12000 1800
6
2400
360
9
270 14070
54
2814
16884
Add up the rows to complete the final column.
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30 12000 1800
6
2400
360
9
270 14070
54
2814
16884
Add up the rows to complete the final column.
12000 + 1800 + 270 = 14070
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30 12000 1800
6
2400
360
9
270 14070
54
2814
16884
Add up the rows to complete the final column.
2400 + 360 + 54 = 2814
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30 12000 1800
6
2400
360
9
270 14070
54
2814
16884
Add up the final column to get your answer.
14070 + 2814 = 16884
[3]
Multiply 469 by 36
Multiplication Grid.
x
400
60
30
12000 1800
6
2400 360
9
270 14070
54
2814
16884
Answer = 16884
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
9
Draw the table and write the
numbers across the top and
down the side.
Remember to write the
digits in the vertical column
upwards from the bottom to
the top.
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
9
Cross multiply every digit
in the horizontal column by
every digit in the vertical
column.
6 x 4 = 24
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
2
6
4
9
Cross multiply every digit
in the horizontal column by
every digit in the vertical
column.
6 x 4 = 24
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
2
6
4
3
9
6
Cross multiply every digit
in the horizontal column by
every digit in the vertical
column.
6 x 6 = 36
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
2
6
4
3
9
6
5
4
Cross multiply every digit
in the horizontal column by
every digit in the vertical
column.
6 x 9 = 54
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
2
3
2
1
9
6
5
4
Cross multiply every digit
in the horizontal column by
every digit in the vertical
column.
3 x 4 = 12
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
9
6
2
3
5
2
8
1
1
4
Cross multiply every digit
in the horizontal column by
every digit in the vertical
column.
3 x 6 = 18
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
9
6
4
2
3
5
2
8
7
1
1
2
Cross multiply every digit
in the horizontal column by
every digit in the vertical
column.
3 x 9 = 27
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
Next add the digits
diagonally.
9
6
4
2
3
5
2
8
7
1
1
2
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
9
6
44
2
3
5
2
8
7
1
1
2
Next add the digits
diagonally.
4=4
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
9
44
2
3
5
2
8
7
8
1
1
2
Next add the digits diagonally.
6
1
6 + 5 + 7 = 18.
Write 8 next to the last digit
and carry the 1 under where
the next answer will be.
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
9
6
44
2
3
5
2
8
7
8
1
1
2
8
1
1
Next add the digits diagonally.
4 + 3 + 8 + 2 = 17 plus the
remainder from the previous
sum.
17+1 = 18
Write 8 under the last digit and
carry the 1 under where the
next answer will be.
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
9
6
44
2
3
5
2
8
7
8
1
1
2
6
8
1
1
Next add the digits diagonally.
2 + 2 + 1 = 5 plus the
remainder from the previous
sum
5 + 1 = 6.
Write 8 under the last digit and
carry the 1 under where the
next answer will be.
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
9
6
44
2
3
5
2
8
7
8
1
1
2
1
6
8
1
1
Next add the digits diagonally.
Finally
1 = 1 and there is no remainder
to add.
[3]
Multiply 469 by 36
Chinese Method.
x
6
3
4
6
4
9
6
44
2
3
5
2
8
7
8
1
1
2
1
6
8
1
1
Read the answer in the
direction of the arrows.
(Do not include the
remainders).
The answer is 16884
[3]
Multiply 469 by 36
Egyptian Method (Double and Half).
1
469
Write down 1 in the left
hand column and 469 in
the right hand column.
[3]
Multiply 469 by 36
Egyptian Method (Double and Half).
1
469
2
938
469 + 469 = 938
Double the number in each
column.
1+1=2
469 + 469 = 938.
Write these answers
underneath in the 2nd row.
[3]
Multiply 469 by 36
Egyptian Method (Double and Half).
1
469
469 + 469 = 938
2
938
938 + 938 = 1876
4
1876
Double the number in each
column again.
2+2=4
938 + 938 = 1876.
Write these answers
underneath in the 3nd row.
[3]
Multiply 469 by 36
Egyptian Method (Double and Half).
1
469
469 + 469 = 938
2
938
938 + 938 = 1876
4
1876
1876 + 1876 = 3752
8
3752
Double the number in each
column again.
4+4=8
1876 + 1876 = 3752.
Write these answers
underneath in the 4th row.
[3]
Multiply 469 by 36
Egyptian Method (Double and Half).
1
469
469 + 469 = 938
2
938
938 + 938 = 1876
4
1876
1876 + 1876 = 3752
8
3752
3752 + 3752 = 7504
16
7504
7504 + 7504 = 15008
Continue until, when you
double the number in the
left hand column, you get
to a number greater than
the one you are going to
multiply it by 9 (in this
case 36).
32 15008
[3]
Multiply 469 by 36
Egyptian Method (Double and Half).
1
469
469 + 469 = 938
2
938
938 + 938 = 1876
4
1876
1876 + 1876 = 3752
8
3752
3752 + 3752 = 7504
16
7504
7504 + 7504 = 15008
Continue until, when you
double the number in the
left hand column, you get
to a number greater than
the one you are going to
multiply it by 9 (in this
case 36).
32 15008
[3]
Multiply 469 by 36
Egyptian Method (Double and Half).
1
469
469 + 469 = 938
2
938
938 + 938 = 1876
4
1876
1876 + 1876 = 3752
8
3752
3752 + 3752 = 7504
16
7504
7504 + 7504 = 15008
Now decide how you can
make 36 by adding the
numbers in the left hand
column.
36 = 32 + 4.
32 15008
[3]
Multiply 469 by 36
Egyptian Method (Double and Half).
1
469
469 + 469 = 938
2
938
938 + 938 = 1876
4
1876
1876 + 1876 = 3752
8
3752
3752 + 3752 = 7504
16
7504
32 15008
7504 + 7504 = 15008
Now decide how you can
make 36 by adding the
numbers in the left habd
column.
36 = 32 + 4.
Highlight these two
numbers and the matching
numbers in the other
column.
[3]
Multiply 469 by 36
Egyptian Method (Double and Half).
1
469
469 + 469 = 938
2
938
938 + 938 = 1876
Now add together the
other two highlighted
numbers.
4
1876
1876 + 1876 = 3752
1876 + 15008 = 16884
8
3752
3752 + 3752 = 7504
16
7504 7504 + 7504 = 15008
32
15008
36
16884
Answer = 16884.
[3]
For further practice using any of
the explained methods then
please see the relevant Excel
sheet in the Moodle.