Select all ratios equivalent to 1:3.

Understand the Problem

The question is asking to identify and select all the ratios that are equivalent to the ratio of 1:3 from the given options. This involves comparing each provided ratio with the target ratio to determine equivalence.

Answer

$7:21$

Steps to Solve

Understand the target ratio

The target ratio is $1:3$.

Convert ratios to fractions

Convert the target ratio and the provided ratios to fractions for easier comparison:

Target ratio:

$$ \frac{1}{3} $$

Ratio 1: $7:21$

$$ \frac{7}{21} $$

Ratio 2: $3:6$

$$ \frac{3}{6} $$

Ratio 3: $11:18$

$$ \frac{11}{18} $$

Simplify the fractions

Now, simplify the fractions where possible:

For $7:21$:

$$ \frac{7}{21} = \frac{1}{3} $$ (because $7 \div 7 = 1$ and $21 \div 7 = 3$)

For $3:6$:

$$ \frac{3}{6} = \frac{1}{2} $$ (because $3 \div 3 = 1$ and $6 \div 3 = 2$)

For $11:18$:

$$ \frac{11}{18} $$ (it cannot be simplified)

Compare the simplified fractions

Now, compare each simplified fraction with the target ratio:

$ \frac{7}{21} = \frac{1}{3} $ (equivalent)
$ \frac{3}{6} = \frac{1}{2} $ (not equivalent)
$ \frac{11}{18} $ (not equivalent)

The ratios equivalent to $1:3$ are:

$7:21$

More Information

The ratio $1:3$ indicates that for every 1 part of the first quantity, there are 3 parts of the second. Identifying equivalent ratios helps in understanding proportional relationships in mathematics.

Tips

Misunderstanding simplification: A common mistake is incorrectly simplifying ratios. Always divide both sides of the ratio by their greatest common divisor (GCD).
Failure to compare: Sometimes, students don’t compare the simplified fractions to the original ratio, leading to incorrect conclusions.

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

Thank you for voting!