Editing NumbersNear10

= Numbers Near 10 = To help multiply two numbers near 10 in your head, this article will provide a convenient shortcut. Practice by selecting numbers of your own and work through each category until you're confident you understand the process and are getting the correct answer each time. == Both Numbers Above 10 == To start off, we'll work with an equation in which both numbers are above 10. For this section's example, we'll multiply 14 * 13. First, we subtract 10 from both 14 and 13: 14 - 10 = 4[[BR]] 13 - 10 = 3 Next, you're going to add either number's difference from the opposing number from the equation. In this example, you can either add 4 to 13 or 3 to 14 (you'll get the same answer either way): 4 + 13 = 17[[BR]] '''or'''[[BR]] 3 + 14 = 17 This number is then multiplied by 10 (the reference point we've been using): 17 * 10 = 170 The two differences are then multiplied together: 3 * 4 = 12 Finally, you add this number to the previous answer: 170 + 12 = 182 Thus, the answer to 14 * 13 is 182! Let's try another example, this time with 12 * 15. We start by subtracting 10 from both numbers: 12 - 10 = 2[[BR]] 15 - 10 = 5 Next, we add either number's difference to the opposing number: 2 + 15 = 17[[BR]] '''or'''[[BR]] 5 + 12 = 17 This number is multiplied by 10: 17 * 10 = 170 The two differences are multiplied (2 * 5 = 10) and then added to the previous answer: 170 + 10 = 180 This gives us 15 * 12 = 180. == Both Numbers Below 10 == The process for multiplying two numbers below 10 is the same as above, except that you start dealing with negative numbers. For this example, we'll use 6 * 8. First, we subtract 10 from both numbers: 6 - 10 = -4[[BR]] 8 - 10 = -2 Next, one numbers difference is added to the other number (notice that the addition of a negative number is effectively a subtraction): -4 + 8 = +4[[BR]] '''or'''[[BR]] -2 + 6 = +4 This number is then multiplied by 10: 4 * 10 = 40 Finally, the two differences are multiplied together (-4 * -2 = +8) and added to the previous answer: 40 + 8 = 48 == Numbers Above AND Below 10 == When you're multiplying two numbers in which one is above 10 and the other is below 10, the process is the same as the above, except that negative numbers play a bigger role. In this section, we'll use 8 * 13 as the example. We start by subtracting 10 from both sides: 8 - 10 = -2[[BR]] 13 - 10 = 3 Next, add either number's difference to the opposing number: 3 + 8 = 11[[BR]] '''or'''[[BR]] -2 + 13 = 11 Multiply this number by 10: 11 * 10 = 110 In this next step, it's important to take signs into consideration. As before, we multiply the differences of the two numbers: -2 * 3 = -6 Finally, we add this answer to the previous answer: -6 + 110 = 104 This gives us the answer of 8 * 13 as 104.

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