Select all ratios equivalent to 1:3.

Question image

Understand the Problem

The question is asking to identify whether the ratios 5:15, 4:12, and 6:18 are equivalent to the ratio 1:3. To do this, we need to simplify each ratio and compare them to see if they equal 1:3.

Answer

$5:15$, $4:12$, $6:18$ are all equivalent to $1:3$.
Answer for screen readers

The ratios equivalent to $1:3$ are:

  • $5:15$
  • $4:12$
  • $6:18$

Steps to Solve

  1. Simplifying the Ratios

We need to simplify each of the given ratios to see if they are equivalent to $1:3$.

  1. Simplifying Ratio 5:15

For the ratio $5:15$, we divide both parts by their greatest common divisor (GCD), which is 5:

$$ \frac{5}{5} : \frac{15}{5} = 1:3 $$

  1. Simplifying Ratio 4:12

For the ratio $4:12$, we divide by the GCD, which is 4:

$$ \frac{4}{4} : \frac{12}{4} = 1:3 $$

  1. Simplifying Ratio 6:18

For the ratio $6:18$, we divide by the GCD, which is 6:

$$ \frac{6}{6} : \frac{18}{6} = 1:3 $$

  1. Comparison

Now, we compare the simplified ratios:

  • $5:15$ simplifies to $1:3$
  • $4:12$ simplifies to $1:3$
  • $6:18$ simplifies to $1:3$

All three ratios are equivalent to $1:3$.

The ratios equivalent to $1:3$ are:

  • $5:15$
  • $4:12$
  • $6:18$

More Information

All three ratios simplify to $1:3$, demonstrating that each of them maintains the same proportion despite different numerical values. This is a useful concept in various math applications, especially in ratios and proportions.

Tips

  • Not simplifying correctly: Always ensure you divide by the GCD. Confirm each simplification step.
  • Overlooking equivalent forms: Remember that different ratios can express the same relationship when simplified properly.
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