Mixed to Improper Fractions Calculator

Published on: May 12, 2024
Final Answer: Free • Full Steps: Free

This Mixed to Improper Fractions Calculator helps you turn a whole number and a fraction into a single top-heavy fraction, and shows the working clearly at every step. Multiply the whole number by the bottom number to see how many pieces those whole ones are worth, then add the top number to get the total. That total goes over the same bottom number. Following the same pattern every time is what makes converting fractions easy to picture, check, and repeat on your own with any mixed number.

Step-by-step method

  1. Set up the problem.
  2. Multiply the whole number by the bottom number.
  3. Add the top number to that, and put the total over the same bottom number.
  4. Put the minus sign back if the mixed number was negative.
  5. Do a simplifying of fractions at the end if you can.
See Example 1 Hide Example 1

Problem

\(4\tfrac{1}{2}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Multiply the whole number by the bottom number.
  3. Add the top number to that, and put the total over the same bottom number.
  4. Put the minus sign back if the mixed number was negative.
  5. Do a simplifying of fractions at the end if you can.

Step 1

Step 1 - Setup the problem.

In this problem: We convert \(4\tfrac{1}{2}\) into an improper fraction.

\(4\tfrac{1}{2}\)

Step 2

Step 2 - Multiply the whole number by the denominator.

In this problem: The whole number times the bottom number gives \(4 \times 2 = 8\).

\(4 \times 2 = 8\)

Step 3

Step 3 - Add the numerator.

In this problem: Adding the top number gives \(8 + 1 = 9\), which goes on top.

\(8 + 1 = 9\)

Step 4

Step 4 - Apply the sign.

In this problem: The mixed number was positive, so the answer stays \(\frac{9}{2}\).

\(\frac{9}{2}\)

Step 5

Step 5 - Simplify the fraction.

In this problem: The only number that divides both \(9\) and \(2\) is \(1\), so nothing changes.

\(\frac{9}{2}\)

Final Answer

\(4\tfrac{1}{2} = \frac{9}{2}\)
See Example 2 Hide Example 2

Problem

\(-3\tfrac{2}{5}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Multiply the whole number by the bottom number.
  3. Add the top number to that, and put the total over the same bottom number.
  4. Put the minus sign back if the mixed number was negative.
  5. Do a simplifying of fractions at the end if you can.

Step 1

Step 1 - Setup the problem.

In this problem: We convert \(-3\tfrac{2}{5}\) into an improper fraction.

\(-3\tfrac{2}{5}\)

Step 2

Step 2 - Multiply the whole number by the denominator.

In this problem: The whole number times the bottom number gives \(3 \times 5 = 15\).

\(3 \times 5 = 15\)

Step 3

Step 3 - Add the numerator.

In this problem: Adding the top number gives \(15 + 2 = 17\), which goes on top.

\(15 + 2 = 17\)

Step 4

Step 4 - Apply the sign.

In this problem: The mixed number was negative, so the answer is \(-\frac{17}{5}\).

\(\frac{17}{5} \;\rightarrow\; -\frac{17}{5}\)

Step 5

Step 5 - Simplify the fraction.

In this problem: The only number that divides both \(-17\) and \(5\) is \(1\), so nothing changes.

\(-\frac{17}{5}\)

Final Answer

\(-3\tfrac{2}{5} = -\frac{17}{5}\)