# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/14

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Problem 14

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## Exercise 14

### Question

export const metadata = {
  title: "Problem 14",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

The correct order of the numbers below from smallest to largest is...

<MathContainer>
  <BlockMath math="1.45; \frac{17}{14}; 123\%; \sqrt{12}; \frac{5}{3}" />
</MathContainer>


### Choices

- [x] $$\frac{17}{14}; 123\%; 1.45; \frac{5}{3}; \sqrt{12}$$
- [ ] $$\frac{17}{14}; 123\%; 1.45; \sqrt{12}; \frac{5}{3}$$
- [ ] $$\frac{5}{3}; \frac{17}{14}; 123\%; 1.45; \sqrt{12}$$
- [ ] $$\frac{5}{3}; 123\%; 1.45; \sqrt{12}; \frac{17}{14}$$
- [ ] $$123\%; \frac{5}{3}; 1.45; \sqrt{12}; \frac{17}{14}$$

### Answer & Explanation

export const metadata = {
  title: "Solution 14",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

#### Converting to Fractions

To determine the order from smallest to largest, we convert all numbers into fractions with a common denominator.

<MathContainer>
  <BlockMath math="1.45 = \frac{145}{100}" />
  <BlockMath math="\frac{17}{14}" />
  <BlockMath math="123\% = \frac{123}{100}" />
  <BlockMath math="\frac{5}{3}" />
  <BlockMath math="\sqrt{12} \approx 3.46" />
</MathContainer>

#### Finding a Common Denominator

We use <InlineMath math="2100" /> as the common denominator (LCM of <InlineMath math="100" />, <InlineMath math="14" />, and <InlineMath math="3" />).

<MathContainer>
  <BlockMath math="1.45 = \frac{145 \times 21}{2100} = \frac{3045}{2100}" />
  <BlockMath math="\frac{17}{14} = \frac{17 \times 150}{2100} = \frac{2550}{2100}" />
  <BlockMath math="123\% = \frac{123 \times 21}{2100} = \frac{2583}{2100}" />
  <BlockMath math="\frac{5}{3} = \frac{5 \times 700}{2100} = \frac{3500}{2100}" />
</MathContainer>

For <InlineMath math="\sqrt{12}" />, since its value is approximately <InlineMath math="3.46" />, if converted to a fraction over 2100, it would be very large (much larger than the others which are all below 2).

<MathContainer>
  <BlockMath math="\sqrt{12} \approx \frac{7274}{2100}" />
</MathContainer>

#### Conclusion

Based on the numerators with the common denominator:
<MathContainer>
  <BlockMath math="2550 < 2583 < 3045 < 3500 < 7274" />
</MathContainer>

So the order is:
<MathContainer>
  <BlockMath math="\frac{2550}{2100}; \frac{2583}{2100}; \frac{3045}{2100}; \frac{3500}{2100}; \sqrt{12}" />
</MathContainer>

Returning to the original forms:
<MathContainer>
  <BlockMath math="\frac{17}{14}; 123\%; 1.45; \frac{5}{3}; \sqrt{12}" />
</MathContainer>


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