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# Improper Fractions

If you've worked with fractions that look like $\frac{9}{7}$ or $\frac{17}{3}$ , you've encountered improper fractions. Unlike a proper fraction, which has a numerator that is smaller than the denominator, an improper fraction has an equal or larger numerator than the denominator. Let's take a closer look at improper fractions and their relationship with mixed numbers.

## Improper fractions and mixed numbers

Improper fractions are another way of writing mixed numbers:

As you can see, the improper fraction $\frac{7}{6}$ is actually the mixed number $1\frac{1}{6}$ .

Since both mixed numbers and improper fractions are common in math problems, knowing how to convert one to the other is important.

### Converting improper fractions into mixed numbers

Let's convert the improper fraction $\frac{19}{9}$ into a mixed number. First, divide the denominator into the numerator. Then, write the fraction as a sum of the whole part plus the remaining fraction.

$\frac{19}{9}=2+\frac{1}{9}=2\frac{1}{9}$

### Converting mixed numbers into improper fractions

Now, let's convert the mixed number $7\frac{2}{3}$ into an improper fraction. First, write the mixed number as a sum of a whole number and a proper fraction. Then, write the two parts with a common denominator. Finally, add the fractions.

$7+\frac{2}{3}=\frac{21}{3}+\frac{2}{3}=\frac{23}{3}$

## Practice questions on improper fractions

a. Turn $1\frac{3}{5}$ into an improper fraction.

$1+\frac{3}{5}=\frac{5}{5}+\frac{3}{5}=\frac{8}{5}$

b. Turn $\frac{26}{7}$ into a mixed number.

$\frac{26}{7}=3+\frac{5}{7}=3\frac{5}{7}$

c. Turn $2\frac{5}{6}$ into an improper fraction

$2+\frac{5}{6}=\frac{12}{6}+\frac{5}{6}=\frac{17}{6}$

d. Turn $\frac{33}{4}$ into a mixed number.

$\frac{33}{4}=8+\frac{1}{4}=8\frac{1}{4}$

## Get a better understanding of improper fractions

If your student wants help understanding improper fractions or needs assistance with converting them into mixed numbers, tutoring is a great option. A skilled private educator can help your student understand assignments and even refresh their knowledge while preparing for a test. Discover the perks of tutoring and how your student can benefit by reaching out to the Educational Directors at Varsity Tutors today.

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