Improper fractions can be a little confusing when you're learning about mixed numbers. But once you understand the idea, they’re not that scary!

So, what are improper fractions? An improper fraction is when the top number (called the numerator) is bigger than the bottom number (called the denominator). For instance, $\frac{9}{4}$ is an improper fraction because 9 is greater than 4.

Changing Mixed Numbers to Improper Fractions

Before you do any math with mixed numbers, it helps to change them into improper fractions. A mixed number has both a whole number and a fraction in it, like $2\frac{1}{3}$. Here's how to turn it into an improper fraction:

1. Multiply the whole number by the denominator:
   • For $2\frac{1}{3}$, you multiply $2 \times 3 = 6$.
2. Add that result to the numerator:
   • Now you add the $1$ from the fraction: $6 + 1 = 7$.
3. Put this sum over the original denominator:
   • You get $\frac{7}{3}$.

So, $2\frac{1}{3}$ becomes $\frac{7}{3}$.

Doing Math with Improper Fractions

Once you have your numbers as improper fractions, it's easier to add, subtract, multiply, or divide them.

1. Adding Example

Let’s add $2\frac{1}{3}$ and $1\frac{2}{5}$.

• First, change both mixed numbers to improper fractions:

  • $2\frac{1}{3} = \frac{7}{3}$
  • $1\frac{2}{5} = \frac{7}{5}$

• Now, we need a common denominator. The least common multiple of 3 and 5 is 15.

• Change both fractions to have this common denominator:

  • $\frac{7}{3} = \frac{35}{15}$
  • $\frac{7}{5} = \frac{21}{15}$

• Now add them: $\frac{35}{15} + \frac{21}{15} = \frac{56}{15}$

• If you want, you can change it back to a mixed number, and that gives you $3\frac{11}{15}$.

2. Subtracting Example

Subtracting works in a similar way. Let’s look at $4\frac{1}{2}$ and $2\frac{2}{3}$:

• Change them to improper fractions: $4\frac{1}{2} = \frac{9}{2}, \quad 2\frac{2}{3} = \frac{8}{3}$

• The common denominator for 2 and 3 is 6.

• Change both fractions: $\frac{9}{2} = \frac{27}{6}, \quad \frac{8}{3} = \frac{16}{6}$

• Now subtract: $\frac{27}{6} - \frac{16}{6} = \frac{11}{6}$

This can be written as $1\frac{5}{6}$.

Conclusion

Improper fractions and mixed numbers might seem tough at first, but with practice, you’ll find it easy to switch between them and do math. So grab a pencil and some practice sheets! The more you practice adding, subtracting, multiplying, or dividing, the better you’ll get. Happy calculating!