Multiply a decimal number by a two digit number

Now, we need to work out 45 times 7.55. []So, we can set out our multiplication like this. So you might notice that here, we don’t have our place values lined up – we have units under hundredths, and tens under tenths. But that doesn’t matter, as long as you remember that if there are 2 decimal places in the question, there will be 2 decimal places in the answer: [][][]so we can write decimal points in line with the decimal point that we have in the question, and then we can just multiply as we normally would if we were doing 755 times 45. So to start with, although what we’re really doing is 5 hundredths times 5, because we’ve put our decimal points in, we can just start with 5 times 5, so that’s [][]25, 5 times 5 is 25, plus 2 is [][]27, and 7 times 5 is 35, plus 2 is []37. []Now we can cross out our working []and write a 0 as the last digit of our second answer line. 5 times 4 is [][]20, 5 times 4 is 20 plus 2 is [][]22 and 7 times 4 is 28, plus 2 is []30. [][][][][]Now if we add up our totals, because we’ve already put our decimal points in, we can see that our final answer is []339.75. So now pause the video and see if you can work out 42 times 4.99. []So we can set out our multiplication like this. So rather than putting our largest number at the top, what we can do when we multiply decimals is put the number with the most digits at the top instead. So, because we have 2 decimal places in our question, there will be 2 decimals place in the answer, [][][]so we can write decimal points in our answer lines, underneath the decimal point that we have in the question. So now, we can just multiply as we normally would if we were doing 499 times 42. So to start with, although what we’re really doing is multiplying 9 hundredths by 2, because we’ve put our decimal points in, we can just start with 9 times 2, so that’s [][]18, 9 times 2 is 18, plus 1 is [][]19, and 4 times 2 is 8, plus 1 is []9. []Now we cross out or working, []write our 0, and 9 times 4 is [][]36, 9 times 4 is 36, plus 3 is [][]39, and 4 times 4 is 16, plus 3 is []19. So if we add up our totals, 8 plus 0 is []8, 9 plus 6 is [][]15, 1 plus 9 plus 9 is [][]19, 1 plus 9 is [][]10, and 1 plus 1 is []2, []so because we’ve already put our decimal point in our answer, we have 209.58.[]
Now, we need to work out 45 times 21.35. []Now, we can set out our multiplication like this. So again, we don’t have our place values lined up, but that doesn’t matter, as long as we remember that if there are 2 decimal places in the question, there will be 2 decimal places in the answer: [][][]so we can write decimal points in our answer lines underneath the decimal point in the question, and then we can just multiply as we normally would if we were doing 2135 times 45. So, we can start with 5 times 5, so that’s [][]25, 3 times 5 is 15, plus 2 is [][]17, 1 times 5 is 5, plus 1 is []6, and 2 times 5 is []10. []Now we can cross out our working, []write a 0 as the final digit our second answer line, and now 5 times 4 is [][]20, 3 times 4 is 12, plus 2 is [][]14, 1 times 4 is 4, plus 1 is []5, and 2 times 4 is []8. So now, adding up our answer lines, 5 plus 0 is []5, 7 plus 0 is []7, 6 plus 4 is [][]10, 1 plus 0 plus 5 is []6 and 1 plus 8 is []9. []So because we already have the decimal point in our answer, we have 960.75.[] So now pause the video and see if you can work out 325.6 times 84. []So we can set out our multiplication like this, putting the number with the most digits at the top. So, because we have 1 decimal place in our question, there will be 1 decimal place in the answer, [][][]so we can write decimal points before the final digit of each of our answer lines. Now that we’ve done that, we can just multiply as we normally would if we were doing 3256 times 84. So to start with, we have 6 times 4, so that’s [][]24, 5 times 4 is 20, plus 2 is [][]22, 2 times 4 is 8, plus 2 is [][]10, and 3 times 4 is 12, plus 1 is []13. []Now we can cross out our working []and write a 0 in our second answer line. Now, 6 times 8 is [][]48, 5 times 8 is 40, plus 4 is [][]44, 2 times 8 is 16, plus 4 is [][]20, and 3 times 8 is 24, plus 2 is []26. So now, adding up our answer lines, 4 plus 0 is []4, 2 plus 8 is [][]10, 1 plus 0 plus 4 is []5, 3 plus 0 is []3, 1 plus 6 is []7 and nothing plus 2 is []2. []So, because we have our decimal point in our answer, we have 27350.4.