Multiplication Math Facts Answers

There are a few ways in learning how to do multiplication math facts. These are:

(Bear with us, these Multiplication Math Facts will be uploaded and explained in due course)



How to multiply by ten's - The quick way

Q- What happens when we multiply something by ten?

A- A zero is added on the end of the number.

Q- What happens when we multiply by 100?

A- Two zero's are added on to the end of the number

and so on.


For examples

6×10=60

6×100=600

6×1000=6000

.

.

.

and so on



However, its not mathematically correct to say, "just add the zero's on the end". No, its wrong and we may get done for explaining it that way.

It's a matter of decimal places. So, here's how to explain the decimal place matter...the number 6 has a decimal place on the end of it.


We don't see it because we just don't put it in. There is always a .0000 on the end of numbers.




It's the same as 1 pound, we just don't put the decimal in after we write £1 because we don't need to or we are just simply lazy and can't be bothered.




But we all know very well that £1 is exactly the same as £1.00...isn't that correct?!



So, the numbers 7, 8, 100, 27, 92 all have a dot (decimal) after it. All whole, real numbers do. We just don't put it in.

When we multiply 10, 100, 1000 by these numbers. We all know to add the zero on the end. However, what's happened to the dot? Yes its still there. The dot is on the end.

7.0 multiplied by 10 is now 70.0

8.0 multiplied by 10 is now 80.0

100.0 multiplied by 10 is now 1000.0

27.0 multiplied by 10 is now 270.0

92.0 multiplied by 10 is now 920.0

and so on



Going back to our number 6 example above, putting the decimal place in, this is how it looks:

6.0×10=60.0

6.0×100=600.0

6.0×1000=6000.0

.

.

.

and so on



The decimal place is always moving to the right because quite simply we are multiplying and the number is getting bigger. Not smaller.

So, what happens when we divide by tens?



Examples: Write the answers to these question (answers are at the bottom)

1.

a) 23×100=

b) 23.00×10=

c) 2.3×10=

d) 0.2300×10





How to do Long Multiplication

Example 1

a) 32×4

b) 43×5

c) 312×6

d) 235×4



Example 2

a) 12×23

b) 56×12

c) 749×89



Method

Step 1 - Line up the first set of numbers on the top.

Step 2 - Put the second set of numbers underneath.

Step 3 - Multiply the numbers with each other.

First multiply the bottom unit number with the top unit number. If its a unit number write the number down, otherwise if its a ten's number carry the ten over to the other side and just write the unit number down.

Then multiply the bottom number with the next number (on the ten's column). If its a unit number write it down. If you carried a number along, add it to that number and write it down.

Step 4 - Carry on like this until no more numbers are needed to multiply.

As usual this is best shown with some examples. We have started with some easy examples. Example 2's are slightly harder.




Example 1

a) 32×4

Multiply 4 with 2 to give 8. Then multiply 4 with 3 to give 12. Answer is 128.





b) 43×5

First multiply 5 and 3 to give 15, Carry the one somewhere (in your head, under the 5, anywhere you like) and write the 5 as it is shown.

Then multiply 4 and 5 to give 20 and add it to that 1 you carried along, to give 21. Answer is 215.





c) 312×6

Multiply 6 and 2 to give 12. Write the 2 under the 6 and carry the 1 (in your head, or write it somewhere you will remember).

Then multiply 6 and 1 to give 6 and add it to the 1 that you carried along. This gives us 7, place that next to the 2.

Then multiply 3 and 8 to give 18. That goes next to 7. Final answer is 1872.





d) 235×4

Multiply 5 and 4 to give 20. Write the zero under the 4 and carry the 2.

Next multiply 3 and 4 to give 12. Add 12 to the number carried over to give 14. Write the 4 next to the zero and carry 1 over to the next column to add (keep it in your head or write it somewhere).

Lastly multiply 2 and 4 to give 8. Add the number carried over to give 9. Final answer 940.





Example 2

a) 12×23

Multiply 3 and 2 to give 6. Then multiply 1 and 3 to give 3. Place it next to 6.

Then we multiply the 2 with the top numbers. However, 2 is in the tens column so consequently its as if we were multiplying 20 by the top numbers.

The answers to these answers go in the next row. Put a zero under the 6, some people put a cross. Which ever way it doesn't matter because ultimately we will add these two rows.

Next multiply 2 and 2 and place the 4 next to the zero. Then 2 multiplied by 1 and put it next to the 4.

Then we add 36 and 240. Final answer to this 276.






b) 56×12

First multiply the 6 and 2 to give 12. Write the 2 down and carry the 1 along. Then multiply 6 and 1 to give 6, and add the 1 that was carried along.

Next we multiply the 5 with 12. Only 5 is in the tens column hence it is 50 times 12. (The quick way to multiply by tens is just to add a zero on the end. A more detailed explanation is described above).

So, to start put the zero in first. Then multiply 5 and 2 to give 10.

Write another zero in and carry the 1 along. Multiply 5 and 1 to give 5 and add the 1 that was carried along to give 6.

Then we add 72 and 600 to give a final answer of 672.





c) 749×89

Multiply 9 and 9 to give 81. Write 1 down and carry the 8 along. Next multiply 4 and 9 to give 36 and add 8 to give 44. Write 4 down and carry the 4 along.

Next multiply 7 and 9 to give 63 and add the 4 that was carried along to give 67. Write this number down on the end.

Next we multiply 8 with 749. As we explained before 8 is in the tens column, so really its 80 times 749.

To start put a zero in the units place and multiply 8 with the 9 to give 72. Write 2 down and carry the 7 along.

Next multiply 4 and 8 to give 32 and add the 7 that was carried along to give 39. Write 9 down and carry the 3 along.

Next multiply 7 and 8 to give 56 and add the 3 that was carried along to give 59. Write this number on the end.

Then add 6741 to 59920 to give 66661.






How to do Box Multiplication

The box multiplication method is an excellent way to do long multiplications. If you can multiply by tens easily this method is good to use.


Examples

a) 21×3

b) 324×6

c) 34×45

d) 4563×234


Method

Step 1 - Break up the numbers into hundreds, tens and units.

Step 2 - Create a box and place the tens and units along the top and the other number along the edge of the box.

Step 3 - Multiply the numbers out.

Step 4 - Add up the multiplied numbers


a) 21×3

Break up the 21 into tens and units, 20 and 1.

Draw 2 boxes next to each other

Place 20 above one box and 1 above the other. Put 3 along the side of the box.

Multiply 3 and 20 to give 60 and place it in the the first box. Multiply 3 and 1 to give 3 and place that in the second box.

Add 60 and 3 to give the answer 63.



b) 324×6



Break up 324 into hundreds, tens and units to give 300, 20 and 4. Place these numbers along the top of 3 boxes. Put 6 along the edge of the box.

Multiply 300 and 6 to give 1800. Place this in the first box.

Multiply 20 and 6 to give 120, place this in the second box.

Multiply 4 and 6 to give 24.

Add up answers in the box 1800, 120 and 24 to give 1944



c) 34×45



Break up the numbers into tens and units. 34 into 30 and 4. Place this along the top of 2 boxes. Break up 45 into 40 and 5. Place this along the edge of the boxes.

Multiply out the numbers as shown in the diagram.

Add up the numbers in the box to give the correct answer. 1200+160+150+20=1530



d) 4563×234


Break the numbers into Thousands, hundreds, tens and units. 4563 as 4000, 500, 60 and 3. Place them along the top of the boxes.

Break up 234 into 200, 30 and 4. Put these along the edge of the box.

Multiply the numbers out as its shown above.

Add up all the numbers in the box to give an answer of 1067742.






How to do Egyptian Multiplication Math



This is how the Egyptians used to do multiplication math. This may be a long and tedious way to work out multiplications, but if you know your 2 multiplication tables fairly well, then this may be a good method for you.



Example 1: 11×12

  • Make 2 columns, right and left.

  • Put the number 1 in the left column and keep doubling it until you reach a number that is more than half of the smaller number (8 is more than half of 11).

    LeftRight
    112
    224
    448
    896



  • Put the larger number (12) in the right column and double it until it reaches in line with the number in the left column.

  • From the left column find numbers that will add up to make the smaller number (11).

    The only numbers from this column to make 11 is 1, 2 and 8.

  • Cross out the other number 4, and its corresponding number on the right.






  • Add up the other numbers not crossed out in the right column. This is the answer to the multiplication math problem. 12+24+96=132

    11×12=132



Example 2: 24×36

  • Make 2 columns, right and left.

  • Put the number 1 in the left column and keep doubling it until you reach a number that is more than half of the smaller number (16 is more than half of 24).


    LeftRight
    136
    272
    4144
    8288
    16576



  • Put the larger number (36) in the right column and double it until it reaches in line with the number in the left column.

  • From the left column find numbers that will add up to make the smaller number (24).

    The only numbers from this column to make 24 is 8 and 16.

  • Cross out the other numbers 4, 2 and 1, and its corresponding numbers on the right.



  • Add up the other numbers not crossed out in the right column (288+576=864). This is the answer to the multiplication math problem.

    24×36=864






How To Do Chinese Multiplication Math, also known as the grid method

This is how the Chinese used to do multiplication math facts. This may be a long and tedious way to work out multiplications, but is actually easier to work out if you are doing long complicated sums.

Its also becoming more popular in schools. Long multiplication will probably become a thing of the past.

Example 1: Solve 23×35

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