Select all ratios equivalent to 5:8.

Question image

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

  1. 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} ).
  2. 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).
  3. 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.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!
Use Quizgecko on...
Browser
Browser