ACT Math : How to find out a mixed fraction from an improper fraction

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

Convert \dpi{100} \small \frac{21}{4} to a mixed number.

Possible Answers:

\dpi{100} \small \frac{4}{5}

\dpi{100} \small 5\frac{1}{2}

\dpi{100} \small 4\frac{1}{4}

\dpi{100} \small 5\frac{1}{4}

\dpi{100} \small 20\frac{1}{4}

Correct answer:

\dpi{100} \small 5\frac{1}{4}

Explanation:

4 goes into 21 five times. 5 becomes your whole number. There is a remainder of 1 and your denominator remains the same, so your fraction is \dpi{100} \small \frac{1}{4}.

\dpi{100} \small 5\frac{1}{4}

Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

What is \frac{23}{4} written as a mixed number?

Possible Answers:

5\frac{3}{4}

4\frac{1}{4}

5\frac{1}{2}

2\frac{1}{4}

Correct answer:

5\frac{3}{4}

Explanation:

 goes into  five times with a remainder of

The denominator does not change. 

Example Question #67 : Fractions

Which of the following is the mixed fraction equivalent to ?

Possible Answers:

Correct answer:

Explanation:

To begin, notice that using your calculator, you can find:

Now, the closest even multiple of  that is less than  is .  Therefore, you know that your number is:

This is the same as:

, or simply, .  This is your mixed fraction.

Example Question #3 : How To Find Out A Mixed Fraction From An Improper Fraction

Which of the following is equivalent to ?

Possible Answers:

Correct answer:

Explanation:

Although there are many ways to convert improper fractions into mixed fractions, the easiest way is to use your calculator to your advantage.  Begin by dividing  by .  This gives you . Therefore, you can eliminate all the options that have do not have  for their first portion. Next, multiply  by the denominator (), and get .  This means that you have  and , or .  Thus, your answer is .

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

What does  equal, expressed as a mixed number?

Possible Answers:

Correct answer:

Explanation:

Simplify the two fractions, then find a common denominator, then solve.

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

Convert the improper fraction to a mixed number. Reduce all fractions if possible.

Possible Answers:

Correct answer:

Explanation:

To convert a mixed number into a fraction, first divide the denominator into the numerator and record the remainder:

.

the result is the mixed number, with the remainder being put as the numerator over the old denominator:
 when we reduce.

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