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Converting Between Improper Fractions and Mixed Numbers
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An important part of learning about fractions is becoming comfortable understanding what they mean. Being able to convert between improper fractions and mixed numbers is a great way to be able to understand fractions and recognize how large or small a fraction is. Here are some math terms that will help you to understand this lesson better:

1. Proper Fraction = A fraction whose numerator is smaller than the denominator. Example: $$\dfrac{3}{4}$$
2. Improper Fraction = A fraction whose numerator is larger than the denominator. Example: $$\dfrac{4}{3}$$
3. Mixed Number = An integer combined with a proper fraction showing how many wholes and how many parts are in the number. Example: $$\displaystyle 2\frac{1}{3}$$ means 2 whole and $$\dfrac{1}{3}$$ pieces, pronounced two and one-third.

The following video will show how this conversion can be done:

Converting between Improper Fractions and Mixed Numbers

When converting from a Mixed Number to an Improper Fraction:

• Multiply the integer by the denominator and add the numerator to get the new numerator.
• Keep the denominator the same.
• Example: $$\displaystyle2\frac{1}{3}=\left ( \frac{2}{1}\times\frac{3}{3} \right )+\frac{1}{3}=\frac{2\times3}{3}+\frac{1}{3}=\frac{6}{3}+\frac{1}{3}=\frac{7}{3}$$

When converting from an Improper Fraction to a Mixed Number:

• Divide the numerator by the denominator.
• Keep the remainder as the numerator of the new fraction part.
• The denominator stays the same.
• Example: $$\displaystyle \frac{11}{5}=11\div5=2\;$$ with 1 divided by 5 left over $$\displaystyle =2\frac{1}{5}$$

There are additional resource videos to the left of the screen on each of these links above.

### Practice Problems

Convert the following mixed number to an improper fraction:
1. $$\displaystyle 1\frac{3}{4}$$ (
Solution
Solution: $$\dfrac{7}{4}$$
Details:

Step 1: Rewrite the whole number as a fraction with the same denominator as the fraction. Right now we have $$\displaystyle 1\frac{3}{4}$$, which is the same as $$\displaystyle 1+\frac{3}{4}$$. To write this as an improper fraction, we will change 1 to a fraction with a denominator of 4. We know that we need a denominator of 4 because $$\dfrac{3}{4}$$ has a denominator of 4. $$\dfrac{4}{4}$$ is equal to 1 because 4 divided by 4 equals 1.

We now have the following:
$$\displaystyle \frac{4}{4}+\frac{3}{4}$$ $$\displaystyle \frac{4}{4}+\frac{3}{4}=\frac{7}{4}$$

The first circle has 4 shaded sections or 1 whole, and the second has 3 out of 4 shaded sections. When we count how many parts are shaded, we have a total of 7 sections of size $$\dfrac{1}{4}$$.
)
2. $$\displaystyle 5\frac{1}{8}$$ (
Video Solution
Solution: $$\dfrac{41}{8}$$
Details:

(Video Source | Transcript)
)
3. $$\displaystyle 3\frac{2}{5}$$ (
Solution
Solution:
$$\dfrac{17}{5}$$
)
4. $$\dfrac{11}{4}$$ (
Video Solution
Solution: $$\displaystyle 2\frac{3}{4}$$
Details:

(Video Source | Transcript)
)
5. $$\dfrac{13}{6}$$ (
Solution
Solution: $$\displaystyle 2\frac{1}{6}$$
Details: To convert $$\dfrac{13}{6}$$ into a mixed number we start by dividing 13 by 6: We know that 6 times 2 equals 12: Subtract 12 which gives us a remainder of 1: This means that 6 divides into 13 two times with a remainder of 1. So $$\dfrac{13}{6}$$ is equivalent to 2 wholes with a remainder of $$\dfrac{1}{6}$$ of a whole, or $$\displaystyle 2\frac{1}{6}$$.
We can also represent this visually: )
6. $$\dfrac{32}{3}$$ (
Solution
Solution:
$$\displaystyle 10\frac{2}{3}$$
)

## Need More Help?

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