Evaluate the following as a reduced fraction: [tex]$\frac{\sqrt{8+1}+1^2}{10 \cdot 12-7}$[/tex]
Answer (1)
Simplify the numerator: 8 + 1 + 1 2 = 9 + 1 = 3 + 1 = 4 .
Simplify the denominator: 10 ⋅ 12 − 7 = 120 − 7 = 113 .
Write the expression as a fraction: 113 4 .
The reduced fraction is: 113 4 .
Explanation
Problem Analysis We are asked to evaluate the expression 10 ⋅ 12 − 7 8 + 1 + 1 2 as a reduced fraction. To do this, we will simplify the numerator and denominator separately, and then reduce the resulting fraction.
Simplifying the Numerator First, let's simplify the numerator. We have 8 + 1 + 1 2 = 9 + 1 = 3 + 1 = 4 .
Simplifying the Denominator Next, let's simplify the denominator. We have 10 ⋅ 12 − 7 = 120 − 7 = 113 .
Reducing the Fraction Now, we can write the expression as a fraction: 113 4 . Since 4 and 113 have no common factors other than 1, the fraction is already in its simplest form.
Final Answer Therefore, the expression evaluates to 113 4 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to simplify fractions helps in making these calculations easier and more accurate. For example, if you need to divide a pizza into equal slices among a group of people, you're using fractions. Simplifying the fraction representing each person's share ensures everyone gets the right amount.
