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.

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