### All ACT Math Resources

## Example Questions

### Example Question #1 : Simplifying Fractions

Simplify the following fraction:

**Possible Answers:**

**Correct answer:**

Find the largest number that divides into both and

### Example Question #2 : Simplifying Fractions

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

**Possible Answers:**

**Correct answer:**

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

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

### Example Question #3 : Simplifying Fractions

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

**Possible Answers:**

**Correct answer:**

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:

### Example Question #4 : Simplifying Fractions

Simplify the following fraction:

**Possible Answers:**

**Correct answer:**

To simplify a fraction, find the gcf (gcd) of the numerator and denominator and divide both by the gcf (gcd). the gcf of and is so:

### Example Question #5 : Simplifying Fractions

Simplify the following fraction:

**Possible Answers:**

**Correct answer:**

The first and easiest simplification for this fraction is to divide numerator and denominator by . This gives you:

Next, notice that the two fractions do not both contain factors of . This is because the denominator's digits, when added up come to , which is not divisible by . This means is not divisible by . Now, is . There is no shared between these numbers. However, if you try, you will see that they are both divisible by , which gives you:

This is simplest form.

### Example Question #6 : Simplifying Fractions

Simplify the following fraction:

**Possible Answers:**

**Correct answer:**

First, begin by noticing that both numerator and denominator contain a . Dividing this out gives you:

Now, and . Since each of these are true, we know that both numerator and denominator contain a . Dividing this out, you get:

This is the simplest possible form of the fraction.

### Example Question #7 : Simplifying Fractions

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?

**Possible Answers:**

**Correct answer:**

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

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 ().