The problem asks us to find the value of the expression $\frac{c+d}{c-d}$ given the relationship $\frac{c}{d} = 1 \div \frac{3}{4}$.
Ratio Calculation
First, let's simplify the given ratio $\frac{c}{d}$: $ \frac{c}{d} = 1 \div \frac{3}{4} $ Dividing by a fraction is the same as multiplying by its reciprocal: $ \frac{c}{d} = 1 \times \frac{4}{3} $ $ \frac{c}{d} = \frac{4}{3} $ So, the ratio of $c$ to $d$ is $4:3$.
Finding the Expression $\frac{c+d}{c-d}$
We need to calculate $\frac{c+d}{c-d}$. We can use the property of ratios known as Componendo and Dividendo. This property states that if $\frac{a}{b} = \frac{p}{q}$, then $\frac{a+b}{a-b} = \frac{p+q}{p-q}$.
Applying Componendo and Dividendo to our ratio $\frac{c}{d} = \frac{4}{3}$: $ \frac{c+d}{c-d} = \frac{4+3}{4-3} $ $ \frac{c+d}{c-d} = \frac{7}{1} $ $ \frac{c+d}{c-d} = 7 $
Alternatively, we can substitute $c = \frac{4}{3}d$ into the expression:
$ \frac{c+d}{c-d} = \frac{(\frac{4}{3}d) + d}{(\frac{4}{3}d) - d} $ Factor out $d$ from the numerator and denominator: $ = \frac{d(\frac{4}{3} + 1)}{d(\frac{4}{3} - 1)} $ Cancel out $d$ (assuming $d \neq 0$): $ = \frac{\frac{4}{3} + \frac{3}{3}}{\frac{4}{3} - \frac{3}{3}} $ $ = \frac{\frac{7}{3}}{\frac{1}{3}} $ Simplify the complex fraction: $ = \frac{7}{3} \times \frac{3}{1} $ $ = 7 $ Both methods yield the same result.Similar Questions
- If $0.02x = 0.5y$, then find the value of $\frac{x-y}{x+y}$ is:
Important Questions from Componendo or Dividendo
If \(\frac{x}{y} = \frac{5}{3}\), then \(\frac{x + y}{x - y}\) is equal to
- If $0.02x = 0.5y$, then find the value of $\frac{x-y}{x+y}$ is:
If \(\frac b a = 0.7,\) find the value of \(\frac {a-b}{a+b} + \frac {11}{34}.\)
If \({\rm{x}} = \frac{{\sqrt {{\rm{a}} + {\rm{b\;}}} -{\rm{\;}}\sqrt {{\rm{a}} - {\rm{b}}} }}{{\sqrt {{\rm{a}} + {\rm{b}}} {\rm{\;}} + {\rm{\;}}\sqrt {{\rm{a}} - {\rm{b\;}}} }}\) , then what is bx 2– 2ax + b equal to (b ≠ 0)?
For \(x = \frac{{4\sqrt 6 }}{{\sqrt 2 + \sqrt 3 }},\)what is the value of \(\frac{{x + 2\sqrt 2 }}{{x - 2\sqrt 2 }} + \frac{{x\; + \;2\sqrt 3 }}{{x - 2\sqrt 3 }}?\)
