Basic Mathematics: Fractions

Algebra Level 1

Which of the following is equal to

5 4 + 1 4 3 4 3 ? \large \frac{\frac{5}{4} + \frac{1}{4} - \frac{3}{4}}{3}?

1 3 \frac13 1 4 \frac14 5 12 \frac5{12} 1 12 \frac1{12}

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3 solutions

Brilliant Mathematics Staff
Aug 1, 2020

We have

5 4 + 1 4 3 4 3 = ( 5 4 + 1 4 3 4 ) × 1 3 = 5 + 1 3 4 × 1 3 = 3 4 × 1 3 = 1 4 . \begin{aligned} \frac{\dfrac{5}{4} + \dfrac{1}{4} - \dfrac{3}{4}}{3} &= \left( \frac{5}{4} + \frac{1}{4} - \frac{3}{4} \right) \times \frac{1}{3} \\ &= \frac{5+1-3}{4} \times \frac{1}{3} \\ &= \frac{3}{4} \times \frac{1}{3} \\ &= \frac{1}{4}. \end{aligned}

Mahdi Raza
Aug 4, 2020

5 4 + 1 4 3 4 3 5 + 1 3 4 × 1 3 3 4 × 1 3 1 4 \dfrac{\dfrac{5}{4} + \dfrac{1}{4} - \dfrac{3}{4}}{3} \implies \dfrac{5 + 1 - 3}{4} \times \dfrac{1}{3} \implies \dfrac{3}{4} \times \dfrac{1}{3} \implies \boxed{\dfrac{1}{4}}

5 4 + 1 4 3 4 3 \frac{\frac{5}{4}+\frac{1}{4}-\frac{3}{4}}{3} \Rightarrow 5 + 1 3 4 3 \frac{\frac{5+1-3}{4}}{3} \Rightarrow 6 3 4 3 \frac{\frac{6-3}{4}}{3} \Rightarrow

3 4 3 \frac{\frac{3}{4}}{3} \Rightarrow 3 4 1 3 \frac{3}{4} * \frac{1}{3} \Rightarrow 1 3 \boxed{\frac{1}{3}}

This is my first explanation

Aaron jabriel Ramos - 2 months, 2 weeks ago

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Great job!

Brilliant Mathematics Staff - 2 months, 2 weeks ago

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