Multiplication of Number Bases

Would you like to know how to multiply number bases in Mathematics?

In this lesson,

You will see and learn step-by-step method for the multiplication of number base.


ALSO SEE: Steps For The Subtraction of Number Base


Take note.

A link for you to practice past questions on number base is included at the end of this lesson.

Question on multiplication of number base

Let’s take an example:

QUESTION

Multiply 3145 by 245

1. Position the numbers

Arrange the numbers the same way you would arrange them in your normal multiplication.

WORKINGEXPLANATION
3145
×245
______
You can decide not to include the base beside the numbers but remember it in your subsequent the steps.

2. Start your multiplication

Start from the back as you would do in your normal multiplication.

WORKINGEXPLANATION
314
×24
_____
___1
4 × 4 = 16

The answer 16 is BIGGER THAN our base 5, so we use repeated division to break 16 down to (3, 1).

Write down the last digit (1) and carry (3) over to the next multiplication.

3. Continue your multiplication

WORKINGEXPLANATION
31³4
× 2 4
______
___21
4 × 1 = 4
4 + 3 (carried over) = 7

The answer 7 is BIGGER THAN our base 5, so we use repeated division to break 7 down to (1, 2).

Write down the last digit (2) and carry (1) over to the next multiplication.

4. Finish your multiplication with the first number

WORKINGEXPLANATION
3¹14
× 2 4
______
2321
4 × 3 = 12
12 + 1 (carried over) = 13

The answer 13 is BIGGER THAN our base 5, so we use repeated division to break 13 down to (2, 3).

Write down the entire number (2, 3) because there is no next multiplication to carry anything over to.

5. Move to the 2nd number

WORKINGEXPLANATION
314
×24
______
2321
___3
2 × 4 = 8

The answer 8 is BIGGER THAN our base 5, so we use repeated division to break 8 down to (1, 3).

Write down the last digit (3) and carry (1) over to the next multiplication.

6. Continue your multiplication

WORKINGEXPLANATION
31¹4
×2 4
______
,2321
__33
2 × 1 = 2
2 + 1 (carried over) = 3

The answer 3 is SMALLER THAN our base 5, so there is no need to break it down.

7. Finish your multiplication with the second number

WORKINGEXPLANATION
314
×24
______
_,2321
1133
2 × 3 = 6

The answer 6 is BIGGER THAN our base 5, so we use repeated division to break 6 down to (1, 1).

Write down the entire number (1, 1) because there is no next multiplication to carry anything over to.

8. Add your results together

After multiplying all the numbers, follow the steps in the addition of number base to add all your result together.

WORKINGEXPLANATION
314
×24
______
_,2¹3¹21
1 1 3 3
________
14 2 0 1
1 + nothing = 1

2 + 3 = 5
The answer 5 is EQUAL TO our base 5, so we break 5 down to (1, 0). Write 0, carry 1.

3 + 3 = 6 (+1) =7
The answer 7 is BIGGER THAN our base 5, so we break 7 down to (1, 2). Write 2, carry 1.

2 + 1 = 3 (+1) = 4

1 + nothing = 1

FINAL ANSWER:

3145 × 245

= 14201

Test yourself

Click on the link below to practice past questions on Number Base now.

  • PRACTICE QUESTIONS

GOOD LUCK.

Do you have something to ask on this multiplication of number base? Comment below and a staff or fellow Topper will reply you.

Let others know

Leave a Comment

Your email address will not be published. Required fields are marked *

Copyrighted. Why not share this post instead?