Video: Estimating and Proving Using the Standard Algorithm to Multiply Multidigit Whole Numbers

Use your rounding skills to estimate 42 × 399. [A] 1600 [B] 12000 [C] 16000 [D] 18000 [E] 20000. Use the standard algorithm to find the exact answer. Hint: Use your estimate to check your answer.

06:21

Video Transcript

Use your rounding skills to estimate 42 multiplied by 399. Is the answer 1600, 12000, 16000, 18000, or 20000? And then, use the standard algorithm to find the exact answer. Hint: use your estimate to check your answer.

This question is based around a multiplication, 42 multiplied by 399. And the two parts to the question ask us to calculate the answer in two different ways. Firstly, we’re asked to estimate the answer. And then secondly, we need to find the exact answer. Let’s look at the first part to begin with. We’re asked to use our rounding skills to estimate the answer to the calculation. Instead of calculating 42 multiplied by 399, we need to round those numbers to make it easier to work out. Firstly, we can round 42 down to 40. This is a multiple of 10. And this makes it easier for us to work with. And then 399 is only one away from 400. So we can round that up 42 multiplied by 399 is approximately equal to 40 multiplied by 400. The symbol for approximately is this squiggly equal sign.

Now that we’ve rounded both numbers we can estimate the answer to 42 multiplied by 399. We know four times four equals 16. And we can use this fact to help us four times 400 must be worth 1600, which is the same as 1600. And so 40 times 400 will be 10 times greater than this. The answer is 16000. We rounded 42 to 40 and 399 to 400. When we multiplied both numbers together, we found that the answer was 16000. In the second part of our problem, we’re asked to use the standard algorithm or the standard written method to find the exact answer to the calculation. And as a hint, we’re also told to use our estimate to check our answer. So we hope it’s going to be somewhere around 16000.

To begin with we need to multiply 399 by the two digits in 42. Nine times two equals 18. Nine tens times two equals 18 tens. We got one ten underneath, so that makes 19 tens. And finally, 300 multiplied by two equals 600 plus the one we’ve exchanged seven hundreds. 399 multiplied by two equals 798. Now we need to multiply 399 by the four digit of 42. This represents four tens. Multiplying a number by 40 is the same as multiplying it by 10 and then by four. When we multiply any number by 10, the digits move one place to the left. So if we write a zero as a placeholder in the ones place, we’ve shifted all the digits to the left to start with. We’ve already multiplied our answer by 10. Now, all we need to do is to multiply each digit by four.

Firstly, nine times four, we know 10 times four equals 40. So nine times four equals four less than 40 or 36. We’ve got another nine in the next column. So we know nine times four equals 36 again, but we’ve got three underneath. So we can change that answer to 39. And finally, three multiplied by four equals 12 plus the three that we’ve exchanged equals 15. 399 multiplied by 40 equals 15960. Now, all we need to do is to add the two parts of our multiplication to find the overall total. Eight plus zero equals eight. Nine tens plus six tens equals 15 tens. Seven hundreds plus nine hundreds plus the one 100 underneath equals 17 hundreds. Five thousands plus the one 1000 underneath equals six thousands. And we’ve got nothing to add to the one lot of 10000 that we have.

We use the standard algorithm to find the exact answer which is 16758. Remember the estimate that we started off with. We can now use this to check that our answer is correct. If you remember we estimated that the answer to the calculation would be around about 16000. Well, the answer we’ve come up with is 16758. It looks like we might be right. We used rounding skills to estimate the answer to 42 multiplied by 399. And the answer was 16000. We then used the standard algorithm to find the exact answer which we said was 16758.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.