Multiply First, Then Add the Carry
When multiplying multi-digit numbers and a new unit needs to be composed (carried), students must multiply the digits first and then add the carry value afterward, not add the carry before multiplying, as taught in Illustrative Mathematics Grade 5, Chapter 4: Wrapping Up Multiplication and Division with Multi-Digit Numbers. The rule is: (digit x multiplier) + carried value, a key distinction from addition carrying.
Key Concepts
When composing a new unit in multiplication, you must multiply the digits first, then add the carried value to that product. The rule is: (digit $\times$ multiplier) + carried value.
Common Questions
Why must you multiply before adding the carry?
In multiplication, you must multiply the current digits first to get their product, then add the carried value from the previous column; adding the carry first would give the wrong product.
How does carrying in multiplication differ from carrying in addition?
In addition, you add all digits in a column simultaneously; in multiplication, you must first multiply the two relevant digits and only then add any carried amount from the previous step.
What is the rule for carrying in multiplication?
The rule is: (digit x multiplier) + carried value; for example, if you are multiplying the tens digit 4 in 48 by 3 and have a carry of 2, you calculate (4 x 3) + 2 = 12 + 2 = 14.
What is a common error students make with carrying in multiplication?
A common error is adding the carry before multiplying (carry + digit x multiplier) instead of after (digit x multiplier + carry), which produces incorrect results.
Can you show an example of carrying in multiplication?
To multiply 48 x 3: first 3 x 8 = 24, write 4 and carry 2; then for tens place, multiply first 3 x 4 = 12, then add carry 12 + 2 = 14; write 14, giving 144.