You're absolutely right! The solution shown in the image is correct. Let's break down the problem and the solution step-by-step for a clear understanding.
---
The Problem:
We are given the proportion (a statement that two ratios are equal):
\[\frac{6}{15} = \frac{x}{20}\]
Our goal is to find the value of \(x\) that makes this equation true.
---
Step 1: Use Cross-Multiplication
When you have a proportion \(\frac{a}{b} = \frac{c}{d}\), you can solve it by
cross-multiplying. This means multiplying the numerator of one fraction by the denominator of the other fraction, and setting those products equal.
In your case:
- Multiply the top-left number (\(6\)) by the bottom-right number (\(20\)).
- Multiply the bottom-left number (\(15\)) by the top-right number (\(x\)).
This gives us:
\[15 \cdot x = 6 \cdot 20\]
This is exactly what the image shows: “Set the Product of the Diagonals Equal to Each Other.”
---
Step 2: Simplify the Equation
Now, calculate the right side of the equation:
\[6 \cdot 20 = 120\]
So the equation becomes:
\[15x = 120\]
---
Step 3: Solve for \(x\)
To isolate \(x\), divide both sides of the equation by 15:
\[\frac{15x}{15} = \frac{120}{15}\]
\[x = 8\]
---
Step 4: Verify the Answer (Optional but Good Practice)
Plug \(x = 8\) back into the original proportion to check if it’s true:
\[\frac{6}{15} \stackrel{?}{=} \frac{8}{20}\]
Simplify both fractions:
- \(\frac{6}{15} = \frac{2}{5}\) (divide numerator and denominator by 3)
- \(\frac{8}{20} = \frac{2}{5}\) (divide numerator and denominator by 4)
Since both sides equal \(\frac{2}{5}\), the solution is correct!
---
✔ Final Answer:
\(x = 8\)
And yes —
GOOD TEACHER! 👏 The method shown is a standard, reliable way to solve proportions using cross-multiplication.
Parent Tip: Review the logic above to help your child master the concept of ratio and proportions worksheet.
