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 Post subject: How to read a computer-written math formulas?Posted: Thu Nov 17, 2011 6:07 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
2x² – 9x²/4 × 2 = 2x² – 9x²/4

How can 4 × 2 = 2. Wouldn't this equal 8?

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 Post subject: Re: How to read a computer-written math formulas?Posted: Thu Nov 17, 2011 6:35 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Very often, when we deal with math formulas on a computer, they are written in one line. So a fraction appears as 4/3 or 9x/4.

In this case we originally had (3x/2)² × 2, which means fraction 3x/2 squared and then multiplied by 2.
(3x/2)² results in 9x/4, in other words it is (9/4) × x. Then we multiply it by 2 and get (9/2) × x, which is the same as 9x/2.

The notation "2x² – 9x²/4 × 2" means

Furthermore, when we deal with division ("/") and multiplication ("×") in line, parentheses play the key role.
For example, how should we read the following formula?
12/3×4×2
According to the rules of mathematical operations division and multiplication have equal priorities. So we just do calculations from left to right:
12/3 = 4. Then 4 × 4 = 16. Then 16 × 2 = 32. So the result is 12/3×4×2 = 32.

If we wanted to notate a fraction, we would have to put parentheses (round brackets):
12/(3×4×2)
In this case we get a single fraction: 12 divided by the product of 3, 4, and 2.
12/(3×4×2) = 12/24 = 1/2.

To summarize, when you see formulas written in line, pay attention to parentheses and priority of mathematical operations.

In our materials we use spaces to emphasize formulas as well, but all formulas would have the same meaning as if there were no spaces. For example, we write 4/3 + 2. If it is written somewhere 4/3+2 - it will still mean the sum of fraction 4/3 and integer 2, because addition has lower priority than multiplication.
We write 12/3 × 4 × 2. If it is written somewhere 12/3×4×2, it will still mean the same, 32.

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