Which expression is equivalent to the following complex fraction 2-1/y – In mathematics, complex fractions arise when one fraction is contained within another. One common task is finding equivalent expressions for complex fractions, which can simplify calculations and make them more manageable. This article explores the process of simplifying the complex fraction 2-1/y, determining its equivalent expression, and discussing its practical applications.
Complex fractions are composed of a numerator and denominator, both of which are fractions themselves. The numerator is the fraction above the division line, while the denominator is the fraction below the line. In the case of 2-1/y, the numerator is 2, and the denominator is 1/y.
Complex Fractions
A complex fraction is a fraction that has a fraction in its numerator or denominator. The numerator and denominator of a complex fraction can be either simple fractions or whole numbers.
For example, the following are complex fractions:
- $\frac1/21/3$
- $\frac21/3$
- $\frac1/2 + 1/31/4$
Equivalent Expressions for Complex Fractions, Which expression is equivalent to the following complex fraction 2-1/y
A complex fraction can be simplified by multiplying the numerator and denominator by the least common multiple (LCM) of the denominators of the fractions in the numerator and denominator.
For example, to simplify the complex fraction $\frac1/21/3$, we would multiply the numerator and denominator by 6, which is the LCM of 2 and 3:
$$\frac1/21/3 = \frac1/2 \times 61/3 \times 6 = \frac32$$
Simplifying the Complex Fraction 2-1/y
To simplify the complex fraction $2-\frac1y$, we would multiply the numerator and denominator by $y$:
$$2-\frac1y = \frac2yy
- \frac1y = \frac2y
- 1y$$
Equivalent Expression for the Simplified Fraction
The equivalent expression for the simplified fraction $\frac2y – 1y$ is $2 – \frac1y$.
This is because we can divide the numerator and denominator of $\frac2y – 1y$ by $y$ to get $2 – \frac1y$:
$$\frac2y
- 1y = \frac(2y
- 1) \div yy \div y = \frac2y/y
- 1/yy/y = 2
- \frac1y$$
Examples of Equivalent Expressions
The following table shows some examples of complex fractions and their equivalent expressions:
| Complex Fraction | Simplified Fraction | Equivalent Expression |
|---|---|---|
| $\frac1/21/3$ | $\frac32$ | $1\frac12$ |
| $\frac21/3$ | $6$ | $5\frac13$ |
| $\frac1/2 + 1/31/4$ | $\frac56$ | $0.833$ |
Applications of Equivalent Expressions
Equivalent expressions for complex fractions are useful in a variety of applications, such as:
- Simplifying algebraic expressions
- Solving equations
- Finding the area of a figure
- Calculating the volume of a solid
Clarifying Questions: Which Expression Is Equivalent To The Following Complex Fraction 2-1/y
What is a complex fraction?
A complex fraction is a fraction that has another fraction in its numerator or denominator.
How do you simplify a complex fraction?
To simplify a complex fraction, multiply the numerator and denominator by the least common multiple (LCM) of the denominators of the fractions in the numerator and denominator.
What is the equivalent expression for 2-1/y?
The equivalent expression for 2-1/y is (2y-1)/y.
