$-\frac{1}{13}-\frac{10}{39}$
Answer (1)
Find the least common denominator (LCD) of 13 and 39, which is 39.
Rewrite the first fraction with the LCD: − 13 1 = − 39 3 .
Combine the fractions: − 39 3 − 39 10 = 39 − 13 .
Simplify the resulting fraction: 39 − 13 = − 3 1 .
The final answer is − 3 1 .
Explanation
Finding a Common Denominator We are asked to simplify the expression − 13 1 − 39 10 . To do this, we need to find a common denominator for the two fractions.
Rewriting the First Fraction The least common denominator (LCD) of 13 and 39 is 39, since 39 = 3 × 13 . We can rewrite the first fraction with a denominator of 39 by multiplying both the numerator and denominator by 3: − 13 1 = − 13 × 3 1 × 3 = − 39 3 .
Combining the Fractions Now we can rewrite the original expression as − 39 3 − 39 10 . Since the fractions now have the same denominator, we can combine them by subtracting the numerators: − 39 3 − 39 10 = 39 − 3 − 10 = 39 − 13 .
Simplifying the Fraction Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 13: 39 − 13 = 39 ÷ 13 − 13 ÷ 13 = 3 − 1 = − 3 1 .
Final Answer Therefore, the simplified expression is − 3 1 .
Examples
Fractions are used in everyday life, such as when splitting a pizza or measuring ingredients for a recipe. Understanding how to add and subtract fractions is essential for accurate calculations in these situations. For example, if you have 3 1 of a cup of flour and need 3 2 of a cup, you need to know how much more flour to add. This problem demonstrates the basic principles of fraction arithmetic, which is a fundamental skill in cooking, baking, and many other practical applications.
