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Number Theory Level 1

1 2 × 2 3 × 3 4 + x = 1 \large \dfrac12 \times \dfrac23\times \dfrac34 + x = 1

What is x x as a decimal?


The answer is 0.75.

Finn C by Finn C , 18, USA

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4 solutions

Sam Bealing
Jun 9, 2016

1 2 × 2 3 × 34 + x = 1 1 2̸ × 2̸ 3̸ × 3̸ 4 + x = 1 1 4 + x = 1 x = 3 4 \dfrac{1}{2} \times \dfrac{2}{3} \times {3}{4} +x=1 \\ \dfrac{1}{\not{2}} \times \dfrac{\not{2}}{\not{3}} \times \dfrac{\not{3}}{4} +x=1 \\ \dfrac{1}{4}+x=1 \\ x=\dfrac{3}{4}

3 4 = 0.75 \color{#20A900}{\boxed{\boxed{\dfrac{3}{4}=0.75}}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Simple standard approach.

x + 1 4 = 1 x+\dfrac 1 4=1 .

x = 1 − 1 4 = 3 4 = 0.75 x=1-\dfrac 1 4=\dfrac 3 4=0.75 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ashish Menon
Jun 10, 2016

1 2 + 2 3 × 3 4 + x = 1 1 4 + x = 1 x = 1 − 1 4 x = 3 4 x = 0.75 \begin{aligned} \dfrac{1}{2} + \dfrac{2}{3} × \dfrac{3}{4} + x & = 1\\ \\ \dfrac{1}{4} + x & = 1\\ \\ x & = 1 - \dfrac{1}{4}\\ \\ x & = \dfrac{3}{4}\\ \\ x & = \color{#3D99F6}{\boxed{0.75}} \end{aligned}

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Finn C
Jun 9, 2016

Easiest way is when you see this pattern, look at the fraction before x x ( 3 4 \frac{3}{4} ) and you have your answer.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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