Math Help: Tricks to Learn Multiplication

Multiplication Tricks

Single-digit Facts

Understanding how multiplication relates to addition can help you learn your facts faster. To multiply something means to add together a certain number of groups, each of which has a certain number of objects. This means that if you can't remember the answer to a multiplication fact, you can figure it out in your head or on paper using addition.

For instance, if you're asked to solve 3 x 6, you really just need to find the answer to 6 + 6 + 6 or 3 + 3 + 3 + 3 + 3 + 3. Remember that a multiplication fact always gives the same answer no matter what order it's in, so 3 x 6 and 6 x 3 are equal. You might remember that 6 + 6 = 12, and you can quickly add 12 + 6 to get 18. Since 6 + 6 + 6 = 18, this means 3 x 6 = 18.

Let's try this with another example: 6 x 7. This problem is asking for the answer to 6 + 6 + 6 + 6 + 6 + 6 + 6 or 7 + 7 + 7 + 7 + 7 + 7. You might be able to add these up in your head if you proceed carefully (6 + 6 = 12, 12 + 6 = 18, 18 + 6 = 24 and so on). However, it's easy to make a mistake this way, so you can also use one of these methods to solve the problem on paper:

1. Write out either seven groups of six tally marks or six groups of seven tally marks. Then count the total number of marks to get your answer.

2. Draw a square and divide it into six horizontal rows and seven vertical rows, or vice versa. The total number of small squares it's divided into is the answer.

Whichever method you use, you'll find that the answer to both 6 x 7 and 7 x 6 is 42.

2-digit Numbers

You'll also learn to multiply 1-digit numbers by 2-digit numbers that are divisible by ten. For example, you might be asked to solve 3 x 40 or 70 x 5. If you learn and use the tricks described above for solving problems with single-digit numbers, you'll have a solid foundation to master this new skill.

Keep in mind that, even though you're working with larger numbers now, you're still just adding a certain number of groups that are a certain size. For instance, 3 x 40 = 40 + 40 + 40.

However, an even faster way to solve problems like this is to multiply the 1-digit number by the digit in the tens place of the other number, and then add a zero to that answer. For 70 x 5, 7 x 5 = 35. If you add a zero, you get the correct answer: 70 x 5 = 350. Likewise, since 3 x 4 = 12, 3 x 40 = 120.