Читать книгу All the Math You'll Ever Need - Steve Slavin - Страница 18

Multiplication is repeated addition. For instance, you probably know 4 × 3 is 12 because you searched your memory for that multiplication fact. There's nothing wrong with that.

Another way to calculate 4 × 3 is to think of it as adding four threes, or adding three fours.

What about 5 × 7? Maybe you know it's 35, but you could always do this:

You do multiplication instead of addition because it's shorter—sometimes much shorter. Suppose you needed to multiply 78 × 95. If you set this up as an addition problem, you'd have to write 78 copies of 95 before you could even start adding.

Let's set this up as a regular multiplication problem and take a look at the expanded form.

The key to this multiplication is you have to multiply 8 × 5 and 8 × 90 and then multiply 70 × 5 and 70 × 90, and add up all the results. Don't get discouraged, because there is a condensed form.

The first set of numbers we'd multiply would be 8 × 5. You probably know, or can figure out, that's 40. (We'll focus on all the multiplication facts you should memorize in Chapter 3, “Focus on Multiplication.”) Then we'd multiply 8 × 90, which just means multiplying 8 × 9 and putting a zero at the end. Whenever you multiply a number that ends in zero, you can deal with the non-zero parts and add the zero at the end. (See Chapter 5, “Mental Math” for more on that shortcut.) 8 × 9 =72 so 8 × 90 = 720. Next would come 70 × 5. 7 × 5 = 35 so 70 × 5 =350. The last multiplication would be 70 × 90. Multiply 7 × 9 = 63, and then add a zero for the 70 and another zero for the 90. 70 × 90 = 6,300. Add up 6,300 + 350 + 720 + 40 to get 7,410.

Here's how to write it more compactly. Multiply 8 × 5 = 40, put down the 0 and carry the 4. 8 × 9 = 72 and the 4 we carried makes 76. Write the 76 in front of that 0 you put down and you see 760. This 760 is the 40 and the 720 combined. Now, you need to multiply 95 by 70, which means multiply by 7 and add a zero. So put the zero down first, under the 0 of the 760. Then 7 × 5 = 35. Put down the 5 to the left of the 0 and carry the 3. 7 × 9 = 63 plus the 3 you carried is 66. Write the 66 in front of the 50 and you've got 6,650, which is the 350 and 6300 combined. Add the two lines, and you're done.

As you can see, a long multiplication problem can be broken down into a series of simple multiplication problems. It's important to have basic multiplication facts in memory, so you don't have to spend time doing the repeated addition every time. You'll learn more about that in the next chapter.