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Welcome to Mathnasium’s MathsTricks series. Today we are multiplying numbers that are near one hundred.
We can use mental maths to quickly multiply numbers that are slightly smaller or larger than one hundred using three simple steps:
Step 1: Subtract each of the numbers from 100.
Step 2: “Cross-subtract” and write the answer.
Step 3: Multiply the two differences from Step 1 and write the answer beside the number from Step 2. (If the product is negative, add it to one hundred times the number from Step 2.)
Follow the examples below to find each product.
Step 1: Subtract each of the numbers from 100.
100 minus 103 is -3.
100 minus 107 is -7.
103 minus the second difference of -7 is 110.
Alternatively, 107 minus the first difference of -3 is also 110.
The product of the two differences is -3 x -7 = 21.
The first part of the final answer is the difference from Step 2: 11000.
The last part of the final answer is the product from Step 3: 11021.
Answer: 11,021.
Example 2: Find 102 x 94.
100 minus 102 is -2.
100 minus 94 is 6.
102 minus the second difference of 6 is 96.
Alternatively, 94 minus the first difference of -2 is also 96.
The product of the two differences is 6 x -2 = -12.
The first part of the final answer is the difference from Step 2: 9600.
The last part of the final answer is the product from Step 3. Since this product is negative, we add it to one hundred times the number from Step 2:
9600 + (-12) = 9,588.
Answer: 9,588.
Now, with this strategy, you are ready to use mental maths to multiply any two numbers near 100. Click here for more practice problems, then check your answers here.
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