Add these two fractions: [tex]$\frac{2}{5}+\frac{1}{10}=?$[/tex]
Answer (1)
Find a common denominator for the fractions, which is 10.
Convert 5 2 to 10 4 .
Add the fractions: 10 4 + 10 1 = 10 5 .
Simplify the result: 10 5 = 2 1 .
Explanation
Finding a Common Denominator We are asked to add two fractions, 5 2 and 10 1 . To add fractions, we need to find a common denominator. The least common denominator (LCD) is the smallest multiple that both denominators share. In this case, the denominators are 5 and 10.
Converting to Equivalent Fractions The least common multiple of 5 and 10 is 10. So, we will use 10 as the common denominator. We need to convert 5 2 to an equivalent fraction with a denominator of 10. To do this, we multiply both the numerator and the denominator of 5 2 by 2: 5 2 = 5 × 2 2 × 2 = 10 4 .
Adding the Fractions Now we can add the two fractions, since they have the same denominator: 10 4 + 10 1 = 10 4 + 1 = 10 5 .
Simplifying the Result Finally, we simplify the fraction 10 5 by dividing both the numerator and the denominator by their greatest common divisor, which is 5: 10 5 = 10 ÷ 5 5 ÷ 5 = 2 1 .
Examples
Fractions are a fundamental part of everyday life. For example, if you are baking a cake and the recipe calls for 5 2 of a cup of sugar and 10 1 of a cup of flour, you need to add these fractions to know the total amount of dry ingredients. Understanding how to add fractions helps in many real-world situations involving proportions and ratios.
