[tex]14 - 6 + 21 - 6 = 8 + 15 = 23.[/tex]

[tex]14 - 6 + 21 - 6 \ne 14 + 21 = 35.[/tex]

Do you see your major error now? You were to subtract BC twice, which is the same as subtracting twice BC. Instead you cancelled what you needed to subtract.

[tex]AC - BC + AB - BC = AC + AB - BC - BC = AC + AB - ( BC + BC) =[/tex]

[tex]AC + AB - 2BC.[/tex]

Do you see why you were in error?

Your minor error is much harder to explain. Most people are taught in basic arithmetic to simplify fractions into their APPROXIMATE decimal equivalent right away. This is very bad training. Approximations always introduce errors. Avoid approximations if possible. If you must approximate, do so at the very end of your work because the need for an approximation may disappear by the end.

[tex]\dfrac{4}{3} \ne 1.33 \text { because } 3 * 1.33 = 3.99 \ne 4.[/tex]

If you do not divide both sides of the

equation by 3, you will end up with an answer that looks like

[tex]A = \dfrac{4p}{3q}[/tex] where p and q are algebraic expressions. When you substitute numbers into p, the result may be a multiple of 3, and the threes will cancel, giving you an exact answer.

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