QQuestionMathematics
QuestionMathematics
Prove that 3:8 is equivalent to 12:32.
a. Use diagrams to support your answer.
b. Use the description of equivalent ratios to support your answer.
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Answer
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Step 1:I'll solve this step-by-step, carefully following the LaTeX and formatting guidelines:
Step 2:: Understanding Equivalent Ratios
Equivalent ratios are different representations of the same proportional relationship. Two ratios are equivalent if they represent the same proportion when simplified.
Step 3:: Simplify the First Ratio (3:8)
\frac{3}{8}$$ is the simplified form of the first ratio.
Step 4:: Simplify the Second Ratio (12:32)
\frac{12}{32}
Step 5:: Reduce the Second Ratio
- $$\frac{12 \div 4}{32 \div 4} = \frac{3}{8}
- The GCF of 12 and 32 is 4
Step 6:: Diagram Representation
``` 3:8 Ratio 12:32 Ratio • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • ``` The diagram shows proportional segments, demonstrating equivalence.
Step 7:: Algebraic Verification
- $$x = 4
- 3 \times x = 12
Final Answer
3:8 is indeed equivalent to 12:32, as both reduce to \frac{3}{8}.
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