-14 \frac{1}{2}+\left(-2 \frac{4}{5}\right)
Answer (2)
To solve − 14 2 1 + ( − 2 5 4 ) , we convert mixed numbers to improper fractions, find a common denominator, add them, and convert back to a mixed number. The final answer is − 17 10 3 .
;
Convert the mixed numbers to improper fractions: − 14 2 1 = − 2 29 and − 2 5 4 = − 5 14 .
Find a common denominator and rewrite the fractions: − 2 29 = − 10 145 and − 5 14 = − 10 28 .
Add the fractions: − 10 145 − 10 28 = − 10 173 .
Convert the improper fraction back to a mixed number: − 10 173 = − 17 10 3 . The final answer is − 17 10 3 .
Explanation
Understanding the Problem We are asked to evaluate the sum of two negative mixed numbers: − 14 2 1 and − 2 5 4 .
Converting to Improper Fractions First, let's convert the mixed numbers to improper fractions.
− 14 2 1 = − 2 14 × 2 + 1 = − 2 28 + 1 = − 2 29
Converting to Improper Fractions − 2 5 4 = − 5 2 × 5 + 4 = − 5 10 + 4 = − 5 14
Adding Improper Fractions Now, let's add the two improper fractions:
− 2 29 + ( − 5 14 ) = − 2 29 − 5 14
Finding Common Denominator To add the fractions, we need a common denominator. The least common multiple of 2 and 5 is 10. So, we rewrite the fractions with a denominator of 10:
− 2 29 = − 2 × 5 29 × 5 = − 10 145
− 5 14 = − 5 × 2 14 × 2 = − 10 28
Adding the Fractions Now we can add the fractions:
− 10 145 − 10 28 = − 10 145 + 28 = − 10 173
Converting Back to Mixed Number Finally, let's convert the improper fraction back to a mixed number:
− 10 173 = − 17 10 3
Final Answer Therefore, − 14 2 1 + ( − 2 5 4 ) = − 17 10 3 .
Examples
Understanding how to add negative mixed numbers is useful in many real-life situations, such as calculating financial balances or measuring temperature changes. For example, if you owe $14.50 to a friend and then borrow an additional $2.80, you can use this skill to calculate your total debt. The ability to work with negative numbers and fractions allows for precise calculations in various practical scenarios.
