Squaring rounding method
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This document provides an introduction to rounding methods and tricks for squaring numbers. It explains how to square numbers by rounding them to the nearest multiple of 10 or 100 and then using the properties of exponents. Several examples are shown of squaring two-digit numbers like 45, 73, 58, 105, and 428. The key steps are to round the number to the nearest decade, express the square as the rounded number multiplied by itself plus the difference squared. This technique breaks down the square into easier to calculate components. In the examples, the rounded square is calculated first before adding the difference squared at the end.
Squaring rounding method
- 1. Extra Math: Methods, Tips And Tricks Series. By Puwork Utara May 2012
- 3. Foreword Compare the Illustration 1 and Illustration 2.. Illustration 1 -3 +3 40 41 42 43 44 45 46 47 48 49 50 45 is 3 more than 42 but 3 less than 48, or, 45 – 3 = 42 and comparatively, 45 + 3 = 48 Illustration 2 -5 +5 40 41 42 43 44 45 46 47 48 49 50 45 is 5 more than 40 but 5 less than 50, or, 45 – 5 = 40 and, comparatively, 45 + 5 = 50 Calculation using Rounding Method, Illustration 2 is more useful and practical. You can see “why” on next slides…
- 4. Example 1: 45 X 45 Figure out…. Where is 45..to be rounded -5 +5 40 41 42 43 44 45 46 47 48 49 50 45..is nearest to either 40 or 50 How to Square -5 40 45 2 ( 40 X 50 ) + 5 2 = 2025 +5 50 Briefly.. 45 2 = ( 40 X 50 ) + 5 2 Simplified = 2000 + 25 = 2025
- 5. Example 2: 73 X 73 Figure out…. Where is 73... -3 +3 70 71 72 73 74 75 76 77 78 79 70 In this case, 73..is nearest to 70. How to Square -3 70 73 2 ( 70 X 76 ) + 3 2 = 5329 +3 76 Briefly.. 73 2 = ( 70 X 76 ) + 3 2 Simplified = 5320 + 09 = 5329
- 6. Example 3: 58 X 58 Where is 58..?. Yep! 58..is nearest to 60. In Diagrammed Solution +2 60 58 2 ( 60 X 56 ) + 2 2 = 3364 -2 56 Simplified Solution 582 = ( 60 X 56 ) + 2 2 = 3360 + 04 = 3364
- 7. Example 4: 105 X 105 Where is 105..?. Yep! 105..is 5 away from 100 Diagrammatically -5 100 105 2 ( 100 x 110 ) + 5 2 = 11025 +5 110 Simplified 105 2 ( 100 x 110 ) + 5 2 = = 11000 + 25 = 11025
- 8. Example 5: 428 X 428 Yep! 428..is nearest to 400, or 428 is (-28) away from 400 Diagrammatically - 28 400 4282 ( 400 x 456 ) + 28 2 = 182400 + 784 +28 456 -8 20 28 2 ( 20 X 36) + 8 2 = 784 +8 36 Simplified Solution 2 4282 = ( 400 x 456 ) + 28 = 182400 + 784 = 183184
- 9. Why this tricks work out ?
- 10. But why this tricks work out ? To figure out -5 +5 40 41 42 43 44 45 46 47 48 49 50 An example to be deduced. 45 = 40 + 5 and also 45 = 50 - 5 So, 45 X 45 = ( 40 + 5 )( 50 – 5 ) = 40(50) - 40(5) + 5(50) - 5(5) Expanded Rearranged = 40(50) + 5(50) - 40(5) - 5(5) = 40(50) + 5( 50 - 40 - 5 ) Refactorised = 40(50) + 5( 5 ) Simplified = 2000 + 25 = 2025 Final Answer
- 11. End Show Thanks! GOOD LUCK !