Mathematical shortcuts are powerful tools that help us solve complex problems quickly and efficiently. Let's see how we can use the difference of squares formula to calculate 47 times 53. Instead of multiplying directly, we can rewrite this as 50 minus 3 times 50 plus 3, which becomes 50 squared minus 3 squared, giving us 2500 minus 9, which equals 2491.
The distributive property is a fundamental tool for mathematical shortcuts. Let's see two examples. First, 23 times 15 can be rewritten as 23 times 10 plus 5, which becomes 23 times 10 plus 23 times 5, giving us 230 plus 115, which equals 345. Similarly, 97 times 8 can be written as 100 minus 3 times 8, which becomes 100 times 8 minus 3 times 8, giving us 800 minus 24, which equals 776.
Squaring numbers near round values becomes much easier with algebraic identities. For 52 squared, we write it as 50 plus 2 squared, which expands to 50 squared plus 2 times 50 times 2 plus 2 squared, giving us 2500 plus 200 plus 4, which equals 2704. Similarly, 98 squared becomes 100 minus 2 squared, which is 100 squared minus 2 times 100 times 2 plus 2 squared, giving us 10000 minus 400 plus 4, which equals 9604.
Percentage calculations become much simpler with mental math tricks. For 15 percent of 80, we can break it down as 10 percent plus 5 percent of 80, which gives us 8 plus 4, equaling 12. For 25 percent of 64, we recognize that 25 percent is one quarter, so we divide 64 by 4 to get 16. For 12 percent of 150, we split it as 10 percent plus 2 percent of 150, giving us 15 plus 3, which equals 18.