Fractions - ACT Math

With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:

Now we can see that the equation can all be divided by y, leaving the answer to be:

_x_2 – _y_2 can be also expressed as (x + y)(x – y).

Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).

This simplifies to (x – y).

This problem is solved the same way ½ + 1/3 is solved. For example, ½ + 1/3 = 3/6 + 2/6 = 5/6. Find a common denominator then convert each fraction into an equivalent fraction using that common denominator. The final step is to add the two new fractions and simplify.

To average, we have to add the values and divide by two. To do this we need to find a common denomenator of 6. We then add and divide by 2, yielding 4.5/6. This reduces to 3/4.

Following this equation, you divide 4 by 8 to get 1/2. When a variable is raised to an exponent, and you are dividing, you subtract the exponents, so 6 – 3 = 3.

125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.

120 goes into 6000 evenly 50 times, so we get 1/50 as our simplified fraction.

(2_x_ + 4)/(x + 2)

To simplify you must first factor the top polynomial to 2(x + 2). You may then eliminate the identical (x + 2) from the top and bottom leaving 2.

Set up the conversions as fractions and solve:

To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified

Factor both the numerator and the denominator:

After reducing the fraction, all that remains is:

Notice that the term appears frequently. Let's try to factor that out:

Now multiply both the numerator and denominator by the conjugate of the denominator:

To convert from a fraction to a mixed number we must find out how many times the denominator goes into the numerator using division and the remainder becomes the new fraction.

The numerator and denominator are both divisible by 12. Thus, we divide both by 12 to get our final answer.

If we instead divide by another common factor, we may need to complete the process again to make sure that we have completely reduced the fraction.

In mathematical words we get the following:

is one third of , so in its simplest form is . To reach this answer, divide both and by .

To reach the answer, divide both the numerator and denominator by . After doing that, the answer is .

To find the answer, divide both the numerator and the denominator by . The result is .

We first find out how much each person must run. Thus we take 110/5 to get 22 yards. However, Jim must run twice the amount of a normal competitor, so we multiply by 2 to get 44 yards.

The best approach to this equation is to evaluate each of the equations and inequalities. The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.

1/2 is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.

√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.

Finally, the fraction 1/3 has repeating 3s which makes it larger than 3/10 so it is true.

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.