# Solve (x/1100)-(x/16850) = 1?

I know the answer is 1177, but how do I properly solve for it?

This is not homework; I'm trying to relearn math by using the book, Mathematics for the Non-mathematician, but it moves way too fast.

Relevance

To solve this equation, you must know first what are fractions.

Some examples of fractions are, 2/3, 1/2, x/1100, etc.

Now you must know how to subtract fractions. You can subtract fractions only when the denominators' (the numbers in the bottom) value are the same.

In this equation we have,

x/1100 - x/16850 = 1

The denominator of the fractions are 1100 and 16850 respectively.

As said before, you can only subtract fractions when the denominators are equal.

To equal the denominators of the fractions we just make 1100 x 16850, which gives us a value of 18535000.

So we substitute the denominators by 18535000. And then we have:

x/18535000 - x/18535000 = 1

But it's not over: x/18535000 is not the same thing as x/1100. So what now?

To get x/1100 to x/18535000, you have multiplied the fraction by 1/16850. So you have to multiply x by 16850, because 16850x/18535000 and x/1100 are the same fraction.

Same thing with the second fraction that is still x/18535000. You have multiplied 1/16850 by 1/1100 to get 1/18535000. That means you have to multiply x by 1100, because 1100x/18535000 and x/16850 are the same fractions.

Doing this, our new equation is:

16850x/18535000 - 1100x/18535000 = 1

Now to subtract fractions we subtract the numerators ( the numbers at top) and conserve the denominator. So we get:

16850x - 1100x / 18535000 = 1

15750x/18535000 = 1/1

an "n" number is the same thing as an "n/1" fraction, because n/1 = n

Multiplying in cross:

18535000*1 = 15750x*1

18535000 = 15750x

x = 1176.8254 which is approximately 1177.

• Factor 1100 and 16850 to determine the LCD.

LCD = common factors * other factors

1100 = 11 * 100 = 11 * 2 * 50

16850 = 50 * 337

LCD = 50 * 11 * 2 * 337

Now, multiply everything by LCD.

337x - 22x = 50 * 11 * 2 * 337

315x = 50 * 11 * 2 * 337

x = (50 * 11 * 2 * 337)/(5 * 63)

x = (10 * 11 * 2 * 337)/63 = 74140/63

This is the exact answer; rounding gives 1177.

• (x/1100) - (x/16850) = 1

The following simplification holds true:

(a/b) - (c/d) = (ad - bc)/(bd)

Using the same for the left hand side of the given equation, we have:

(16850x - 1100x)/(1100*16850) = 1

=> 15750x = 1100*16850

=> x = (1100*16850)/15750

=> x = 1176.825397

Depending on what you are trying to find by solving that equation, either the accurate or the approximate answer could be correct.

For example, if you are trying to find arsenic levels in water, or GPS calculations by space shuttle software, then the precise answer (1176.825397) would be required. On the other hand, if you are trying to find out number of hours one should work, or total capacity of a parking lot, or number of balls to be filled in urns, then the approximate answer of 1177 might work. It really depends on what the problem is and what you are trying to find.