Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

◀ back to index

Question

Answer

$$\dfrac{1}{2}-(\dfrac{1}{4}-\dfrac{2}{3})=\dfrac{11}{12}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}\frac{1}{2}-(\frac{1}{4}-\frac{2}{3})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{2}-(-\frac{5}{12}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{11}{12}\end{aligned} $$
①
Combine like terms
②

Subtract $ \dfrac{-5}{12} $ from $ \dfrac{1}{2} $ to get $ \dfrac{ \color{purple}{ 11 } }{ 12 }$.

To subtract fractions they must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 6 }$.

$$ \begin{aligned} \frac{1}{2} - \frac{-5}{12} & = \frac{ 1 \cdot \color{blue}{ 6 }}{ 2 \cdot \color{blue}{ 6 }} - \frac{ -5 }{ 12 } = \\[1ex] &=\frac{ \color{purple}{ 6 } }{ 12 } - \frac{ \color{purple}{ -5 } }{ 12 }=\frac{ \color{purple}{ 11 } }{ 12 } \end{aligned} $$
This page was created using
Simplify Rational Expressions