Multiplication and Division:

Multiplication

While we can memorize single digit multiplication, we can’t memorize all multiplication problems. Instead, we use single digit multiplication and some steps to solve large multiplication problems. The following video will teach these steps. If you have a different method of doing multiplication, you can use the method you are comfortable with.

Scripture Connection

In Matthew 18: 22, Jesus taught Peter about forgiveness. Peter asks if he should forgive his brother seven times but Jesus replies, “I say not unto thee, Until seven times: but Until seventy times seven.” We might think this gives us permission to stop forgiving someone after forgiving them 490 times, but Elder Bruce R. McConkie explained that this really means “there is no limit to the number of times men should forgive their brethren.” (The Mortal Messiah: From Bethlehem to Calvary, 4 vols. [1979-81], 3:91).

Video Source (04:19 mins) | Transcript

Steps for Multiplication

  1. Put number with most digits on top of the number with fewer digits.
  2. Start with the bottom number furthest to the right. Multiply it to all the digits in the top number one by one starting at the right and going left.
    3. This image shows 32 times 8. The number 32 is written at the top. The 8 is written directly under the 2 in the ones place value. There is a horizontal line stretching below the numbers signifying the answer will go below it. There is also a multiplication symbol to the left of the numbers.
  3. If the numbers in the first column multiplied together are greater than 9, then carry the first digit of their solution into the next column. (Example: 8 × 2 = 16. Carry the 1 into the tens column and write the 6 below the ones column in the solution area.)
    4. This image is the same as the previous one except there is now a number 6 in the solution area below the horizontal line in the ones column. There is also a 1 at the very top of the tens column above the number 3.
  4. Continue by multiplying the bottom rightmost number to the number in the next place value to the left in the top number and add any number that was carried into that column to this solution.
  5. Continue following this pattern of multiplying the rightmost number in the bottom to all the digits in the top and writing the solution in the solution area and carrying anything greater than 9 to the next column.
    6. This image is the same as the previous one except that down in the solution area below the horizontal line there is now a 5 in the tens column and a 2 in the hundreds column. The final solution is thus 256.

Multiplying multiple digits follows the same pattern as multiplying a single digit, as shown in the video above, it just takes a few more steps. The following video shows these steps and works through an example.

Video Source (07:12 mins) | Transcript

If you are multiplying by more than one digit just follow the same steps as when working with one digit, but include the following:

  1. After multiplying all the digits in the top number by the bottom right digit, move to the next digit to the left in the bottom number and repeat the process, but be sure to start a new solution line and include a 0 in the rightmost column of the solution line.
    2. Image shows 534 times 127 with 3738 in the solution area by carrying 2 in both tens and hundreds column.Image shows 534 times 127 with 3738 in the solution area by carrying 2 in both tens and hundreds column. Start a new solution line and include a zero in the rightmost column of the solution line.
  2. When you have repeated this process for all the digits in the bottom number, add the lines in the solution together.
    3. This is the same as the previous image except now the solution area contains three rows of numbers. The top solution is 3738. The middle solution is 10680, and the bottom solution row is 53400. These numbers are stacked according to place value with all the ones in the ones column and so forth. To the left of the solution rows is an addition symbol. There is horizontal row below these solution rows indicating a new solution area. Below this second horizontal line is the addition of the solution rows. It contains the number 67818.

This works because what we are really doing is multiplying each place value in the bottom number by each place value in the top number and adding them together.

This image shows two rows of numbers with arrows between them. The top row is 500 + 30 + 4. This is the expanded representation of 534. The bottom row is 100+20+7 which is the expanded version of the number 127. There are orange arrows from the number 100 to each number in the top row. This represents 100 times 500, 100 times 30, and 100 times 4. Similarly there are arrows from the 20 to each number in the top row. These arrows represent 20 times 500, 20 times 30, and 20 times 4. Finally, there are arrows from the number seven to each number in the top row. These represent 7 times 500, 7 times 30, and 7 times 4.

If you’re trying to do the practice problems and it’s taking a very long time, it might be helpful for you to review and memorize your single-digit multiplication (1 × 1 to 9 × 9). If you have all of the single-digit multiplication problems memorized, it will make these problems a lot easier. It will also make the math in future lessons easier.

Additional Resources

(Additional videos and practice problems can be found on the left side of the screen after selecting the above Khan Academy links.)

Practice Problems

Evaluate the following expression:

  1. 22 × 3 = ?
  2. 70 × 5 = ?
  3. 75 × 48 = ?
  4. 542 × 14 = ?
  5. 294 × 400 = ?
  6. 876 × 204 = ?
  7. 807 × 655 = ?

Solutions

  1. 66 (Written Solution)
  2. 350 (Written Solution)
  3. 3,600 (Solution Video | Transcript)
  4. 7,588
  5. 117,600
  6. 178,704 (Solution Video | Transcript)
  7. 528,585