Add.
$\frac{-1}{4}+\frac{3}{5}=$
Answer (1)
Find the least common denominator (LCD) of 4 and 5, which is 20.
Rewrite the fractions with the LCD: 4 − 1 = 20 − 5 and 5 3 = 20 12 .
Add the fractions: 20 − 5 + 20 12 = 20 7 .
The final answer is 20 7 .
Explanation
Finding a Common Denominator We are asked to add two fractions, 4 − 1 and 5 3 . To add fractions, they must have a common denominator. Let's find the least common denominator (LCD) of 4 and 5.
Rewriting Fractions The least common multiple (LCM) of 4 and 5 is 20. So, the LCD is 20. Now we rewrite each fraction with the denominator of 20.
Converting to Equivalent Fractions To rewrite 4 − 1 with a denominator of 20, we multiply both the numerator and the denominator by 5: 4 − 1 = 4 × 5 − 1 × 5 = 20 − 5 . To rewrite 5 3 with a denominator of 20, we multiply both the numerator and the denominator by 4: 5 3 = 5 × 4 3 × 4 = 20 12 .
Adding the Fractions Now we can add the two fractions: 20 − 5 + 20 12 = 20 − 5 + 12 = 20 7 .
Final Answer The resulting fraction is 20 7 . Since 7 and 20 have no common factors other than 1, the fraction is already in its simplest form. Therefore, the sum of the two fractions is 20 7 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have a pizza cut into 8 slices and you eat 2 slices, you have eaten 8 2 or 4 1 of the pizza. Adding and subtracting fractions is essential for calculating quantities in various real-world scenarios.
