Work out $\frac{1}{8}+\frac{3}{4}$. Give your answer in its simplest form.
Answer (1)
Find a common denominator for the fractions: The least common multiple of 8 and 4 is 8.
Convert 4 3 to an equivalent fraction with a denominator of 8: 4 3 = 8 6 .
Add the fractions: 8 1 + 8 6 = 8 7 .
The fraction 8 7 is already in its simplest form, so the final answer is 8 7 .
Explanation
Understanding the problem We need to calculate the sum of two fractions: 8 1 and 4 3 . The problem asks us to give the answer in its simplest form.
Finding a common denominator To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 8 and 4 is 8. So, we will convert the second fraction to have a denominator of 8.
Converting fractions To convert 4 3 to an equivalent fraction with a denominator of 8, we multiply both the numerator and the denominator by 2: 4 3 = 4 × 2 3 × 2 = 8 6 .
Adding the fractions Now we can add the two fractions: 8 1 + 8 6 = 8 1 + 6 = 8 7 .
Simplifying the result Now, we need to check if the resulting fraction 8 7 can be simplified. Since 7 is a prime number and it does not divide 8, the fraction is already in its simplest form. Therefore, the final answer is 8 7 .
Final Answer The sum of 8 1 and 4 3 in its simplest form is 8 7 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 8 1 cup of sugar and 4 3 cup of flour, you need to add these fractions to determine the total amount of dry ingredients. Understanding how to add fractions is essential for accurate measurements and successful cooking.
