Copy and complete this equality to find three equivalent fractions.

Understand the Problem

The question is asking to find three fractions that are equivalent to 1/3, given the second fraction's numerator is 3 and the denominator is 15. We need to find the appropriate denominators for equivalent fractions.

Answer

The equivalent fractions are $\frac{1}{3}$, $\frac{3}{9}$, and $\frac{5}{15}$.

Steps to Solve

Identify the Fraction Measures
We start with the fraction $\frac{1}{3}$. To find equivalent fractions, we need to scale this fraction by a common multiplier.
Find Equivalent Fraction for $\frac{3}{?}$
To find the denominator for the fraction $\frac{3}{?}$ that is equivalent to $\frac{1}{3}$, we can set up the proportion: $$ \frac{1}{3} = \frac{3}{x} $$
Cross-multiplying gives us: $$ 1 \cdot x = 3 \cdot 3 $$ This simplifies to: $$ x = 9 $$
So, $\frac{3}{9}$ is equivalent to $\frac{1}{3}$.
Calculate Equivalent Fraction for $\frac{?}{15}$
Next, we set up the equation for the fraction $\frac{?}{15}$: $$ \frac{1}{3} = \frac{y}{15} $$
Cross-multiplying again gives: $$ 1 \cdot 15 = 3 \cdot y $$
This simplifies to: $$ 15 = 3y $$
Dividing both sides by 3 yields: $$ y = 5 $$
Thus, $\frac{5}{15}$ is also equivalent to $\frac{1}{3}$.
List All Equivalent Fractions
Summarizing the equivalent fractions:

First fraction: $\frac{1}{3}$
Second fraction: $\frac{3}{9}$
Third fraction: $\frac{5}{15}$

The three equivalent fractions are $\frac{1}{3}$, $\frac{3}{9}$, and $\frac{5}{15}$.

More Information

Equivalent fractions represent the same value but are expressed with different numerators and denominators. Any fractions that can be scaled up or down to match each other are considered equivalent.

Tips

Forgetting to Cross-Multiply: Make sure to use cross-multiplication correctly when finding equivalent fractions.
Incorrect Scaling: Always ensure the fractions you are generating maintain the same ratio as the original.

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