Find the fraction that is equivalent to 5/7 and has a denominator of 28.
Understand the Problem
The question asks for a fraction that is equivalent to 5/7 but has a denominator of 28. We will convert 5/7 to an equivalent fraction with the specified denominator by finding a suitable numerator.
Answer
The equivalent fraction is $\frac{20}{28}$.
Answer for screen readers
The equivalent fraction to $\frac{5}{7}$ with a denominator of 28 is $\frac{20}{28}$.
Steps to Solve
- Identify the Conversion Factor
To convert the fraction $\frac{5}{7}$ to an equivalent fraction with a denominator of 28, we need to determine the factor by which to multiply the denominator.
This can be calculated as:
$$ \text{Conversion factor} = \frac{28}{7} = 4 $$
- Multiply the Denominator and Numerator
Now that we have the conversion factor, we multiply both the numerator and the denominator of the original fraction by this factor to maintain equivalence:
$$ \text{New numerator} = 5 \times 4 = 20 $$
$$ \text{New denominator} = 7 \times 4 = 28 $$
- Write the Equivalent Fraction
The new fraction with the calculated numerator and the specified denominator is:
$$ \frac{20}{28} $$
The equivalent fraction to $\frac{5}{7}$ with a denominator of 28 is $\frac{20}{28}$.
More Information
This fraction can further be simplified if needed. The greatest common divisor of 20 and 28 is 4, so if you divide both the numerator and the denominator by 4, you get $\frac{5}{7}$ again, confirming the equivalence.
Tips
- Failing to multiply both the numerator and the denominator by the same factor, which can lead to an incorrect fraction.
- Not properly identifying the conversion factor, which could result in a denominator that doesn't match.
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