### All ACT Math Resources

## Example Questions

### Example Question #131 : Fractions

Turn the following from a mixed number to an improper fraction:

**Possible Answers:**

**Correct answer:**

To turn a mixed number into an improper fraction you must recognize the following:

now we need to add 4 and seven ninths, to do that you multiply by a good form of 1

now with the common denominator you can add the fractions to get

### Example Question #1 : Mixed / Improper Fractions

Write as an improper fraction.

**Possible Answers:**

**Correct answer:**

To find the improper fraction value, we must effectively add together 71 and ^{5}/_{7}. To do this, we will give 71 a denominator of 7; therefore, we are transforming ^{71}/_{1} to ^{x}/_{7}. The shortest way to do this is to multiply by ^{7}/_{7} (which really is 1); therefore, 71 = 71 * (^{7}/_{7}) = ^{497}/_{7}.

Now add them: ^{(497 + 5)}/_{7} = ^{502}/_{7}

### Example Question #2 : Mixed / Improper Fractions

Which of the following improper fractions is equivalent to ?

**Possible Answers:**

**Correct answer:**

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction. For our problem, this means that you will multiply by , getting . Next, you add this to the numerator of your fraction, giving you , or . Finally, you place this over your original denominator, giving you:

### Example Question #1 : Mixed / Improper Fractions

Which of the following improper fractions is equivalent to ?

**Possible Answers:**

**Correct answer:**

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction. For our problem, this means that you will multiply by , getting . Next, you add this to the numerator of your fraction, giving you , or . Finally, you place this over your original denominator, giving you:

### Example Question #1 : Mixed / Improper Fractions

Convert to an improper fraction.

**Possible Answers:**

**Correct answer:**

To determine the numerator of the improper fraction, multiply the denominator with the whole number. Then add this with the numerator. The denominator will remain the same.

### Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

Remember that to convert mixed fractions, you can treat it like an addition. Thus

You then find the common denominator of the two which is :

### Example Question #4 : How To Find Out An Improper Fraction From A Mixed Fraction

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

Remember that to convert mixed fractions, you can treat it like an addition. Thus

You then find the common denominator of the two which is :

### Example Question #5 : How To Find Out An Improper Fraction From A Mixed Fraction

Simplify:

**Possible Answers:**

**Correct answer:**

Remember that to convert mixed fractions, you can treat it like an addition. Thus

Now, using the common denominator of , you know:

Another way to do this is to notice that . Then you just add these values to and .

### Example Question #6 : How To Find Out An Improper Fraction From A Mixed Fraction

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

Use your calculator to your advantage. You know that is . This means that the mixed fraction equivalent must be of the form:

Now, you find the fractional portion by multiplying by , which when rounded gives you . (The quickest way to get in your calculator is to subtract from .) Thus, your answer is:

### Example Question #7 : How To Find Out An Improper Fraction From A Mixed Fraction

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

Use your calculator to your advantage. You know that is . This means that the mixed fraction equivalent must be of the form:

Now, you find the fractional portion by multiplying by , which when rounded gives you . (The quickest way to get in your calculator is to subtract from .) Thus, your answer is:

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