A negative exponent in the numerator of a fraction can be rewritten with a positive exponent in the denominator. The same is true for a negative exponent in the denominator. Thus,.

Whenis multiplied by, the numerators and denominators cancel out, and you are left with 1.

Another way to represent this question is:

In the one's column,and增加产生一个数与两个place. In the ten's column, we can see that a one must carry in order to get a digit in the hundred's place. Together, we can combine these deductions to see that the sum ofandmust be twelve (a one in the ten's place and a two in the one's place).

In the one's column:

The one carries to the ten's column.

In the ten's column:

The three goes into the answer and the one carries to the hundred's place. The final answer is 132. From this, we can see thatbecause.

Using this information, we can solve for.

You can check your answer by returning to the original addition and plugging in the values ofand.

First we want to simplify the expression:.

为了简化这个复杂的分数的方法之一是find the least common multiple of all the denominators, i.e. the least common denominator (LCD). If we find this, then we can multiply every fraction by the LCD and thereby be left with only whole numbers. This will make more sense in a little bit.

The denominators we are dealing with are 2, 3, 4, 5, and 6. We want to find the smallest multiple that these numbers have in common. First, it will help us to notice that 6 is a multiple of both 2 and 3. Thus, if we find the least common multiple of 4, 5, and 6, it will automatically be a multiple of both 2 and 3. Let's list out the first several multiples of 4, 5, and 6.

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

The smallest multiple that 4, 5, and 6 have in common is 60. Thus, the least common multiple of 4, 5, and 6 is 60. This also means that the least common multiple of 2, 3, 4, 5, and 6 is 60. Therefore, the LCD of all the fractions is 60.

让's think of the expression we want to simplify as one big fraction. The numerator contains the fractions 1/4, 1/3, and –1/5. The denominator of the fraction is 1/2, –1/6 and 1. Remember that if we have a fraction, we can multiply the numerator and denominator by the same number without changing the value of the fraction. In other words,x/y= (xz)/(yz）.这将帮助我们,因为我们可以用numerator (which consists of 1/4, 1/3, and –1/5) by 60, and then mutiply the denominator (which consists of 1/2, –1/6, and 1) by 60, thereby ridding us of fractions in the numerator and denominator. This process is shown below:

==

=

This means thata/b= 23/80. We are told thataandbare both positive and that their greatest common factor is 1. In other words,a/bmust be the simplified form of 23/80. When a fraction is in simplest form, the greatest common factor of the numerator and denominator equals one. Since 23/80 is simplified,a= 23, andb= 80. The sum ofaandbis thus 23 + 80 = 103.

The answer is 103.

To simply a fraction with variables, subtract exponents of like bases:

This leaves us with the expression:

Next, we know that to change negative exponents in the numerator into positive exponents, we place them in the denominator. Thus, our expression simplifies to:

Theandvariables with negative exponents can be rewritten with positive exponents by moving them from the denominator to the numerator, and vice versa. Therefore, the expression can be rewritten as

.

The exponents on the denominator can then be subtracted from the exponent in the numerator to give

The expression can be rewritten as

Now the expression can be combined by adding and subtracting exponents

We can combine the expression into

The combined expression can then be simplified to

The expression can be rewritten as

We can now move the variables to the numerator and combine alike variables

This becomes

The numerator of this expression can be factored, giving the expression

Thewill cancel itself out leaving,

The expression can be factored to the expression

Thein the numerator and denominator will then cancel each other out to give,