Simplifying Fractions: 1/3 + 1/5 ÷ 4/5
When dealing with fractions, it's essential to understand how to perform various operations, including addition, subtraction, multiplication, and division. In this article, we'll explore how to simplify the expression 1/3 + 1/5 ÷ 4/5.
Step 1: Divide 1/5 by 4/5
To divide a fraction by another fraction, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply:
$\frac{1}{5} ÷ \frac{4}{5} = \frac{1}{5} × \frac{5}{4} = \frac{1}{4}$
Step 2: Add 1/3 to the Result
Now, let's add 1/3 to the result:
$\frac{1}{3} + \frac{1}{4}$
To add these fractions, we need a common denominator, which is 12. So, we'll convert both fractions to have a denominator of 12:
$\frac{1}{3} = \frac{4}{12}$ $\frac{1}{4} = \frac{3}{12}$
Now, we can add:
$\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$
Result
So, the simplified form of 1/3 + 1/5 ÷ 4/5 is:
$\frac{7}{12}$
In conclusion, by following the correct order of operations and applying the rules of fraction division and addition, we've successfully simplified the expression 1/3 + 1/5 ÷ 4/5 to its simplest form, which is 7/12.
