Lorelei Evaluates The Expression $\frac{121}{(12-10) / 101}$ To Determine How Many Different Groups Of Ten She Can Make Out Of Twelve Items. Her Solution:1. Subtract Within Parentheses And Simplify: $\frac{61}{(2) 151}$2. Expand:

Introduction

In this article, we will delve into the world of mathematics and evaluate an expression presented by Lorelei. The expression in question is $\frac{121}{(12-10) / 101}$, which is used to determine how many different groups of ten she can make out of twelve items. We will follow Lorelei's solution step-by-step and provide a detailed analysis of each step.

Step 1: Subtract within Parentheses and Simplify

Lorelei's first step is to subtract within the parentheses and simplify the expression. The expression within the parentheses is $12-10$, which equals $2$. Therefore, the expression becomes $\frac{121}{2/101}$.

(12-10) = 2
\frac{121}{(12-10) / 101} = \frac{121}{2/101}

Step 2: Expand

The next step is to expand the expression. To do this, we need to multiply the numerator by the reciprocal of the denominator. The reciprocal of $\frac{2}{101}$ is $\frac{101}{2}$. Therefore, the expression becomes $121 \times \frac{101}{2}$.

\frac{121}{2/101} = 121 \times \frac{101}{2}

Step 3: Multiply

Now, we need to multiply $121$ by $\frac{101}{2}$. To do this, we can multiply the numerators and denominators separately. The numerator is $121 \times 101$, which equals $12221$. The denominator is $2$.

121 \times \frac{101}{2} = \frac{121 \times 101}{2}

Step 4: Simplify

The final step is to simplify the expression. We can simplify the fraction by dividing the numerator by the denominator. However, in this case, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of $12221$ and $2$ is $1$. Therefore, the expression remains the same.

\frac{12221}{2} = 6110.5

Conclusion

In conclusion, Lorelei's solution to the expression $\frac{121}{(12-10) / 101}$ is $6110.5$. This means that she can make $6110.5$ groups of ten out of twelve items. However, since we cannot have a fraction of a group, we need to round down to the nearest whole number. Therefore, Lorelei can make $6110$ groups of ten out of twelve items.

Discussion

The expression $\frac{121}{(12-10) / 101}$ is a simple algebraic expression that can be evaluated using basic arithmetic operations. However, the solution to this expression is not as straightforward as it seems. The expression involves a fraction within a fraction, which can be confusing for some students. Therefore, it is essential to break down the expression into smaller steps and simplify each step before moving on to the next one.

Real-World Application

The expression $\frac{121}{(12-10) / 101}$ has a real-world application in mathematics. It can be used to determine how many different groups of ten can be made out of a certain number of items. For example, if we have $12$ items and we want to know how many groups of ten we can make, we can use the expression $\frac{121}{(12-10) / 101}$ to find the answer.

Mathematical Concepts

The expression $\frac{121}{(12-10) / 101}$ involves several mathematical concepts, including fractions, algebraic expressions, and arithmetic operations. It also involves the concept of simplifying fractions, which is an essential skill in mathematics.

Conclusion

In conclusion, the expression $\frac{121}{(12-10) / 101}$ is a simple algebraic expression that can be evaluated using basic arithmetic operations. However, the solution to this expression is not as straightforward as it seems. The expression involves a fraction within a fraction, which can be confusing for some students. Therefore, it is essential to break down the expression into smaller steps and simplify each step before moving on to the next one.