So, since it’s the same as “3 groups of 4,” you can view the problem as 4+4+4{\displaystyle 4+4+4}. Or, if you prefer, view it as 3+3+3+3{\displaystyle 3+3+3+3}
4+4+4=12{\displaystyle 4+4+4=12}; therefore, 4∗3=12{\displaystyle 43=12} Alternatively, 3+3+3+3=12{\displaystyle 3+3+3+3=12}, so 4∗3=12{\displaystyle 43=12}
For an even quicker method for multiplying smaller numbers, practice your multiplication tables (or times tables).
In the sample problem 187∗54{\displaystyle 187*54}, 187 goes on the top line, with 54 below it. The 5 should be in line beneath the 8, and the 4 right beneath the 7.
In the sample problem 187∗54{\displaystyle 187*54}, 187 goes on the top line, with 54 below it. The 5 should be in line beneath the 8, and the 4 right beneath the 7.
In the sample problem 187∗54{\displaystyle 18754}, the digits in the ones place are 4 and 7, and 4∗7=28{\displaystyle 47=28}. Write the number 8 from the number 28 directly below the 4 (with the line between them), and “carry” the 2 from the number 28 by writing a small 2 over top of the 8 in 187.
In 187∗54{\displaystyle 18754}, 4 is in the ones place in the bottom number (54), and 8 is in the tens place in the top number (187). Compute 4∗8=32{\displaystyle 48=32}, then remember to add 2 because of the number you “carried” from the previous computation—so, 32+2=34{\displaystyle 32+2=34} Place the 4 from the number 34 below the line under the 8, next to the number 8 that you wrote down in the previous step. Carry the 3 from the number 34 over the 1 in the number 187.
In 187∗54{\displaystyle 18754}, the ones place for the bottom number (54) is still 4, while the hundreds place for the top number (187) is 1. Calculate 4∗1=4{\displaystyle 41=4}, then add the 3 you carried from the previous calculation to get 4+3=7{\displaystyle 4+3=7} Write the 7 just to the left of the 48 below the line. It should now read 748 below the line, because you have just calculated 187∗4=748{\displaystyle 187*4=748}. Note that if the top number had 4 or more digits, you would just repeat the process until you multiplied the number in the ones place of the bottom number with all of the digits in the top number, continuing to move from right to left.
For 187∗54{\displaystyle 187*54}, start a new line directly below the 748, and write 0{\displaystyle 0} directly below the 8 in 748. This zero is a placeholder that shows you are moving on to multiply the tens place value. If you’re multiplying larger numbers, you keep adding another zero to the right every time you add another number row below the drawn line. So, the third number row would have 00{\displaystyle 00} to the far right, the fourth number row would have 000{\displaystyle 000}, and so on.
In 187∗54{\displaystyle 18754}, the tens place in 54 is occupied by 5, and the ones place in 187 is occupied by 7. Therefore, calculate 5∗7=35{\displaystyle 57=35}. Write down the 5 from 35 to the left of the zero (on the second row below the drawn line), and carry the 3 from the 35 above the 8 in the top number (187).
In 187∗54{\displaystyle 18754}, multiply the 5 from 54 by the 8 from 187: 5∗8=40{\displaystyle 58=40}. Then, remember to add the 3 you carried from the previous calculation to get 40+3=43{\displaystyle 40+3=43} Write down the 3 from 43 to the left of the 5 (giving you 350 on the bottom row), and carry the 4 from the 43 above the 1 in the top number.
For 187∗54{\displaystyle 18754}, multiply the 5 from 54 by the 1 from 187. Finish this easy equation (5∗1=5{\displaystyle 51=5}), then add the 4 that you carried from the previous computation (5+4=9{\displaystyle 5+4=9}). Write 9 down next to the 3 to give you 9350 on the bottom row. You have done long multiplication to calculate 5∗187=9350{\displaystyle 5*187=9350}.
Add the digits in the far right columns, 8+0=8{\displaystyle 8+0=8}, draw another horizontal line below 9350, and write 8 to the far right just below the zero in 9350. Add the digits in the second column from the right, 4+5=9{\displaystyle 4+5=9}, and write 9 to the left of the 8 in the bottom row. Add the digits in the third column from the right, 7+3=10{\displaystyle 7+3=10}, write 0{\displaystyle 0} just to the left of 98, and carry the 1 to above the 9 in 9350. Add the 9 in the fourth column from the right with the 1 you carried to get 9+1=10{\displaystyle 9+1=10}. Write 10 to the left of 098 in the bottom row. Congratulations! 10098{\displaystyle 10098} is the answer to 187∗54{\displaystyle 187*54}.
This shortcut method works best when the smaller number is between 10 and 19. If the smaller number is between 20 and 99, you’ll have to do some extra work to figure out the tens component. As a result, you’ll probably find it easier to just do traditional long multiplication. You can also use this method with a 3-digit smaller number as well—in that case, you’ll need to break it up into hundreds, tens, and ones. For example, 162 would become 100, 60, and 2. Once again, though, doing standard long multiplication will likely be easier.
320∗10{\displaystyle 32010} 320∗7{\displaystyle 3207}
Likewise, when you multiply by 100{\displaystyle 100}, you add 2 zeros, you add 3 zeros when multiplying by 1000{\displaystyle 1000}, and so on.
Write down 320{\displaystyle 320}, then write 7{\displaystyle 7} just beneath it, aligned directly below the zero. Draw a 3-digit long line under the 7{\displaystyle 7}. Multiply 7{\displaystyle 7} and each digit of the larger number separately, working from right to left. Since 7∗0=0{\displaystyle 70=0}, write a zero under the line, aligned below the 7{\displaystyle 7}. Since 7∗2=14{\displaystyle 72=14}, write a 4{\displaystyle 4} just to the left of the zero under the line, and write a small 1{\displaystyle 1} just above the 3{\displaystyle 3} in 320{\displaystyle 320}. This is your reminder to add 1{\displaystyle 1}. Multiply 7∗3=21{\displaystyle 73=21}, then add 1{\displaystyle 1} (as indicated by your reminder). Write 22{\displaystyle 22} just to the left of the 3{\displaystyle 3} and zero under the line. Your answer is under the line: 320∗7=2240{\displaystyle 3207=2240}
Write 2240{\displaystyle 2240} underneath 3200{\displaystyle 3200}, with the right-side zeros aligned. Draw a line underneath 2240{\displaystyle 2240}. Add each column separately, and write the sum below the line: 0+0=0{\displaystyle 0+0=0} 0+4=4{\displaystyle 0+4=4} 2+2=4{\displaystyle 2+2=4} 3+2=5{\displaystyle 3+2=5} The answer is 5440{\displaystyle 5440}.
