$1 \frac{3}{5}-\left(-7 \frac{4}{5}\right)$
Answer (2)
Convert mixed numbers to improper fractions: 1 5 3 = 5 8 and − 7 5 4 = − 5 39 .
Rewrite the expression: 5 8 − ( − 5 39 ) = 5 8 + 5 39 .
Add the fractions: 5 8 + 5 39 = 5 47 .
Convert the improper fraction back to a mixed number: 5 47 = 9 5 2 . The final answer is 9 5 2 .
Explanation
Understanding the Problem We are asked to evaluate the expression 1 5 3 − ( − 7 5 4 ) . This involves mixed numbers and subtraction of a negative number.
Converting Mixed Numbers to Improper Fractions First, let's convert the mixed number 1 5 3 to an improper fraction. To do this, we multiply the whole number (1) by the denominator (5) and add the numerator (3): 1 × 5 + 3 = 8 . So, 1 5 3 = 5 8 .
Converting Mixed Numbers to Improper Fractions Next, let's convert the mixed number − 7 5 4 to an improper fraction. We multiply the whole number (7) by the denominator (5) and add the numerator (4): 7 × 5 + 4 = 39 . Since the original number is negative, we have − 7 5 4 = − 5 39 .
Rewriting the Expression Now, we can rewrite the expression as the addition of two fractions: 5 8 − ( − 5 39 ) . Subtracting a negative number is the same as adding the positive number, so we have 5 8 + 5 39 .
Adding the Fractions Since the two fractions have a common denominator of 5, we can add the numerators: 8 + 39 = 47 . So, 5 8 + 5 39 = 5 47 .
Converting Back to a Mixed Number Finally, let's convert the improper fraction 5 47 back to a mixed number. We divide 47 by 5: 47 ÷ 5 = 9 with a remainder of 2. So, 5 47 = 9 5 2 .
Final Answer Therefore, 1 5 3 − ( − 7 5 4 ) = 9 5 2 .
Examples
Understanding how to add and subtract mixed numbers is useful in everyday situations, such as when you're cooking and need to combine different amounts of ingredients. For example, if a recipe calls for 1 5 3 cups of flour and you want to increase the recipe, you might need to add another 7 5 4 cups of flour. Knowing how to perform this calculation ensures that you get the right amount of ingredients for your recipe, leading to a delicious outcome. This skill is also helpful in scenarios like measuring distances, calculating time, or managing finances, where you often encounter mixed numbers.
To solve the expression 1 5 3 − ( − 7 5 4 ) , first convert the mixed numbers into improper fractions as 5 8 and − 5 39 . Then, rewrite the expression as 5 8 + 5 39 = 5 47 , which converts back to a mixed number giving the final answer of 9 5 2 .
;
