As the original numbers are smaller than the base, we add the product of two negative numbers. You can also round up to the base number. Finally, add the product of the difference between the original numbers and the base number.
Reduce the smaller number to reach the nearest round number - our base number, in this case, 40. In this example, the ones digits add up to ten, so our “base” number and the multiplier are round numbers (40 and 50).
The formula works for all numbers, but it doesn’t simplify well unless the numbers are similar. Close together methodĪ similar method works for multiplying numbers that are close together. The ultimate example is when you are squaring a number ending in 5, then round one number up to the nearest 10, the other number down to the nearest 10, and add 25. Where n is the number to be squared, and d is the difference You can re-write a square equation into numbers that are easier to deal with using this formula n^2 = (n+d)(n-d) + d^2 Multiplying by nines can be simplified by multiplying by 10 and subtracting the original number 799 x 9 = 799 x (10 -1) = 7990 – 799 = 7191 The process is a little more complicated for three-digit and greater numbers, but it works in a similar way. For example, 4+8 = 12, write down 2 and carry the 1 into the next column. If the sum is greater than 10, add the tens digit to the next column to the left, and write the ones digit in the answer. Elevensįor a two-digit number, add the digits and put the answer in the middle of the number you are multiplying: 35 x 11 -> 3 _5 -> 3+5 = 8 -> 3 85 Photo by Chris Liverani on Unsplash Multiplication 3. Here is how this is helpful 721–387 # the complement of 87 is 13, so we can swap 387 with 400 – 13 -> 721 - (400 - 13) = 321 -13 = 321 + 13 = 334Īnother method is to write out the larger number so it ends in 99. Notice that the second digits add up to 10, and the first digit adds up to 9.
Here are some examples with the number and its complement compared with 100: 67:33, 45:55, 89:11, 3:97 The complement is the difference between the original number and a round number - say 100, 1000. Using the complement of a number can help make subtraction easier. It’s often easier to work with adding a smaller number, so instead of 131 + 858, swap the numbers 858 + 131 = 858 + 100 + 30 + 1 = 989 2. The first trick is to simplify your problem by breaking it into smaller pieces. Photo by Crissy Jarvis on Unsplash Addition + Subtraction 1.
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