Sure, let's solve the problem step by step.
1. Understanding the Problem:
- We are given two numbers that are in the ratio of [tex]\(2:5\)[/tex].
- The bigger number is given as 20.
- We need to find the smaller number.
2. Set Up the Ratio:
- Let's denote the smaller number as [tex]\( x \)[/tex].
- According to the given ratio [tex]\(2:5\)[/tex], the smaller number ([tex]\( x \)[/tex]) is to the bigger number (20) as 2 is to 5.
- This can be written as: [tex]\[ \frac{x}{20} = \frac{2}{5} \][/tex]
3. Solve the Equation:
- To find [tex]\( x \)[/tex], we need to solve the proportion. We do this by cross-multiplying.
- Cross-multiplying gives us: [tex]\[ x \cdot 5 = 20 \cdot 2 \][/tex]
4. Simplify and Solve for [tex]\( x \)[/tex]:
- Simplifying the equation above: [tex]\[ 5x = 40 \][/tex]
- Now, solve for [tex]\( x \)[/tex] by dividing both sides by 5: [tex]\[ x = \frac{40}{5} \][/tex]
- Simplifying further gives us: [tex]\[ x = 8 \][/tex]
5. Conclusion:
- The smaller number is [tex]\( \boxed{8} \)[/tex].
