Multiplication of number bases that are NOT binary, or numbers from base 3 upward, follow the same steps as the multiplication of binary numbers.
In this lesson, you will learn step-by-step method for the multiplication of number bases that are not binary.
BONUS: A link to practice questions on number bases is included at the end of this lesson.
Question on multiplication of number bases that are not binary
Let’s take an example:
Question:
Multiply 3145 by 245
STEP 1.
Position the numbers
Arrange the numbers the same way you would arrange them in your normal multiplication.
| WORKING | EXPLANATION |
| 3145 ×245 ______ | You can decide not to include the base beside the numbers but remember the base for the steps below. |
STEP 2.
Start your multiplication
Start from the back as you would do in your normal multiplication.
| WORKING | EXPLANATION |
| 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. |
STEP 3.
Continue your multiplication
| WORKING | EXPLANATION |
| 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. |
STEP 4.
Finish your multiplication with the 1st number
| WORKING | EXPLANATION |
| 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. |
STEP 5.
Move to the 2nd number
| WORKING | EXPLANATION |
| 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. |
STEP 6.
Continue your multiplication
| WORKING | EXPLANATION |
| 31¹4 ×2 4 ______ ,2321 __33 | 2 × 1 = 2 2 + 1 (carried over) = 3 The answer 3 is smaller than our number base 5, so there is no need for breaking it down. |
STEP 7.
Finish your multiplication with the 2nd number
| WORKING | EXPLANATION |
| 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. |
STEP 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.
| WORKING | EXPLANATION |
| 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
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