ACT Math - How to simplify a fraction

Maria owns an art studio and spent in supplies. She sells her paintings for each. How many paintings does Maria need to sell until she makes a profit?

Explanation

Divide the total money spent by the cost of each painting.

$\frac{$1850}{$150}=12.33333$

Therefore, to make a profit, she needs to sell more than this amount. Since she can't sell a portion of a painting, the answer has to be the next nearest whole number ().

What is the average of $\frac{2}{3}$ and $\frac{5}{6}$ ?

$\frac{3}{4}$

$\frac{11}{12}$

$\frac{4}{5}$

$\frac{6}{7}$

Explanation

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.

Which of the following is the least common denominator for the expression below?

$\frac{1}{d\times e^2\times f}-\frac{1}{d\times f^2}-\frac{1}{d^2\times f}$

$d^2\times e^2\times f^2$

$d\times f$

$d\times e\times f$

$d^2\times e\times f^2$

$d^5\times e^2\times f^4$

Explanation

Finding the least common denominator in rational expressions follows the same procedue as finding the least common denominator in fractions.

The least common denominator for this rational exresspion will use all terms with the highest exponents of each.

The first fraction has as the highest term, the second fraction has as the highest term, and the third fraction has as the highest term. Now we combine these and get the least common denominator to be:

$d^2 \times e^2 \times f^2$

Which of the following is equivalent to $\frac{x}{2}+\frac{x-5}{x+3}$ ?

$\frac{2x-5}{x+5}$

$\frac{x^{2}-5x+10}{2x+6}$

$\frac{x^{2}+5x-10}{2x+6}$

$\frac{x^{2}-5x}{2x+6}$

None of the answers are correct

Explanation

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.

What is $\frac{6}{360}$ in its simplest form?

$\frac{1}{60}$

$\frac{1}{36}$

$\frac{6}{60}$

$\frac{1}{10}$

$\frac{1}{36}$

Explanation

To reach the answer, divide both the numerator and denominator by . After doing that, the answer is $\frac{1}{60}$ .

A train travels at a constant rate of meters per second. How many kilometers does it travel in minutes? $(1\ km=1000\ m)$

Explanation

Set up the conversions as fractions and solve:

$\dpi{100} \small \frac{20m}{1sec}\times \frac{60sec^}{1min}\times \frac{1km}{1000m}\times \frac{10min}{1}$

Simplify: $\frac{8}{64}$

$\frac{1}{8}$

$\frac{8}{64}$

$\frac{4}{64}$

$\frac{2}{8}$

$\frac{4}{8}$

Explanation

To find the answer, divide both the numerator and the denominator by . The result is $\frac{1}{8}$ .

$\frac{34}{5}$

Change to a mixed number

$6\frac{4}{5}$

$4 \frac{6}{5}$

$4 \frac{5}{6}$

$3\frac{4}{5}$

$34\frac{1}{5}$

Explanation

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.

$\frac{34}{5} = 6\ r 4 \ so \6\frac{4}{5}$

Simplify the following fraction until the numerator and denominator share no factors.

$\frac{616}{210}$

$\frac{44}{15}$

$\frac{308}{105}$

$\frac{212}{245}$

$\frac{66}{47}$

Explanation

To simplify a fraction you need to find all the factors that the numerator and denominator have in common. You can see that both share 2 so when you divide both by 2 you get

$\frac{308}{105}$

this is close to the answer but it asks for no common factors, it is hard to see but both of these share 7 as a common factor. When you divide both by 7 you get

$\frac{44}{15}$

Simplify:

$\frac{x^{2}y-5x^{2}y^{2}}{x^{2}y}$

$5+x^{2}y^{2}$

None of the other answers

Explanation

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:

$\frac{y-5y^{2}}{y}$

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

How to simplify a fraction

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