Select all ratios equivalent to 5:8.
Understand the Problem
The question is asking us to identify which of the given ratios are equivalent to the ratio of 5:8. To solve this, we will compare each ratio to 5:8 through cross-multiplication or simplification.
Answer
The ratios equivalent to \( 5:8 \) are \( 15:24 \) and \( 10:16 \).
Answer for screen readers
The ratios equivalent to ( 5:8 ) are ( 15:24 ) and ( 10:16 ).
Steps to Solve
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Convert Ratios to Fraction Form
Convert the given ratios to their fractional forms:- For ( 5:8 ), the fraction is ( \frac{5}{8} ).
- For ( 1:2 ), the fraction is ( \frac{1}{2} ).
- For ( 15:24 ), the fraction is ( \frac{15}{24} ).
- For ( 10:16 ), the fraction is ( \frac{10}{16} ).
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Check Equivalent Ratios
To check if two fractions are equivalent, cross-multiply and compare:- Compare ( \frac{5}{8} ) and ( \frac{1}{2} ):
( 5 \times 2 = 10 ) and ( 1 \times 8 = 8 ) (not equivalent). - Compare ( \frac{5}{8} ) and ( \frac{15}{24} ):
( 5 \times 24 = 120 ) and ( 15 \times 8 = 120 ) (equivalent). - Compare ( \frac{5}{8} ) and ( \frac{10}{16} ):
( 5 \times 16 = 80 ) and ( 10 \times 8 = 80 ) (equivalent).
- Compare ( \frac{5}{8} ) and ( \frac{1}{2} ):
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Summary of Results
The ratios equivalent to ( 5:8 ) are ( 15:24 ) and ( 10:16 ).
The ratios equivalent to ( 5:8 ) are ( 15:24 ) and ( 10:16 ).
More Information
The ratio ( 5:8 ) reflects a simple proportional relationship that can be found in various real-world contexts, such as mixing ingredients or scaling recipes. Ratios are often simplified to find equivalent forms.
Tips
A common mistake is forgetting to simplify the ratios before comparing them. Always check if fractions can be reduced to their simplest form for accurate comparisons.
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