{"id":10578,"date":"2017-08-30T19:04:04","date_gmt":"2017-08-30T19:04:04","guid":{"rendered":"https:\/\/www.manhattanprep.com\/gre\/?p=10578"},"modified":"2019-08-30T16:38:36","modified_gmt":"2019-08-30T16:38:36","slug":"mental-math-magic-part-2","status":"publish","type":"post","link":"https:\/\/www.manhattanprep.com\/gre\/blog\/mental-math-magic-part-2\/","title":{"rendered":"Mental Math Magic (Part 2)"},"content":{"rendered":"

\"Manhattan<\/p>\n

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<\/i><\/b>In my <\/span>last article<\/span><\/a>, I gave you some time-saving basic arithmetic to memorize and a few tools to calculate more efficiently, using a combination of your brain and your scratch paper.<\/span><\/p>\n

Today I\u2019m going to throw few fun mental math \u201ctricks\u201d your way. Again, you could always pop out your calculator or do long division and multiplication on your scratch paper, but learning to multiply numbers in your head can be a massive time saver, as well as a good way to double-check what you do put into the calculator. <\/span><\/p>\n

Multiplying by 5<\/strong><\/h4>\n

Start with the simple fact that 5 is half of 10:<\/span><\/p>\n

5 x 2 = 10, and therefore 5 = 10\/2.<\/span><\/p>\n

If you want to multiply by 5 easily in your head, try multiplying by 10 and dividing by 2. Or a bit easier: find half of it and then and multiply by 10. <\/span><\/p>\n

8 x 5 = ?<\/span><\/p>\n

Think: half of 8 is 4, and 4 times 10 is 40. So 8 x 5 = 40! You should have that memorized, but it\u2019s a good example to start.<\/span><\/p>\n

240 x 5 = ?<\/span><\/p>\n

Half of 240 is 120, and 120 x 10 is 1200, so 240 x 5 = 1200.<\/span><\/p>\n

Try it on your own, and if you must, use a calculator to check your work: <\/span><\/p>\n

210 x 5 = ?
\n<\/span>54 x 5 = ?
\n<\/span>62 x 5 = ?<\/span><\/p>\n

By the way, this method works with odd numbers, too!<\/span><\/p>\n

19 x 5 = ?<\/span><\/p>\n

Half of 19 is 9.5, and 9.5 x 10 = 95. So 19 x 5 = 95.<\/span><\/p>\n

37 x 5 = ?<\/span><\/p>\n

Half of 37 is 18.5, and 18.5 x 10 = 185, so 39 x 5 = 185.<\/span><\/p>\n

Dividing by 5<\/strong><\/h4>\n

By the same principle, dividing by 5 is the same as multiplying by 2\/10. So to divide by 5, double the number and then divide by 10.<\/span><\/p>\n

210 \/ 5 = ?<\/span><\/p>\n

Double 210 is 420. Divide by 10 = 42. So 210 divided by 5 is 42!<\/span><\/p>\n

300 \/ 5 = 60<\/span><\/p>\n

This works with numbers that don\u2019t end in 0, too!<\/span><\/p>\n

76 \/ 5 = ?<\/span><\/p>\n

Double 76 to get 152, divided by 10 is 15.2, so 76 \/ 5 = 15.2!<\/span><\/p>\n

43 \/ 5 \u00a0= ?<\/span><\/p>\n

Double 43 to get 86, divided by 10 is 8.6, so 43 \/ 5 = 8.6.<\/span><\/p>\n

Work these a few times, and be careful not to get the methods mixed up! Think before you start: Is it 10\/2 or 2\/10?<\/span><\/p>\n

Multiplying by 9<\/strong><\/h4>\n

Here\u2019s a trick I learned in 3<\/span>rd<\/span> grade:<\/span><\/p>\n

Hold your hands up in front of you, palms facing you. If you want to multiply any number (from 1 to 10) by 9, just hold down that finger. The number of fingers to the left of your held-down finger is the 10\u2019s digit. The number to the right is the units digit. <\/span><\/p>\n

9 x 3 = ?<\/span><\/p>\n

Hold down your third finger. You\u2019ll have 2 fingers to the left, 7 fingers to the right. So 9 x 3 = 27.<\/span><\/p>\n

9 x 6 = ?<\/span><\/p>\n

Hold down your 6<\/span>th<\/span> finger. You\u2019ll have 5 to the left, 4 to the right, so 9 x 6 = 54.<\/span><\/p>\n

Once you do this a few times, you\u2019ll be able to visualize the approach and knock out your multiples of 9 with ease.<\/span><\/p>\n