Question
12:59 AM Wed Feb 5 5. [-/1 Points] DETAILS MY NOTES TGEIALG6 1.2.037. \( 0 / 10 \) Subr Build the fraction to an equivalent fraction with the indicated denominator. \[ \frac{2}{5}, \text { denominator } 45 \] \( \square \) Need Help? Read it Watch It SUBMIT ANSWER
Ask by Reese Mccarthy. in the United States
Feb 05,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equivalent fraction of \(\frac{2}{5}\) with a denominator of 45 is \(\frac{18}{45}\).
Solution
To convert the fraction \(\frac{2}{5}\) to an equivalent fraction with a denominator of 45, we can follow these steps:
1. **Identify the current denominator and the target denominator**:
- Current denominator: \(5\)
- Target denominator: \(45\)
2. **Determine the factor needed to convert the current denominator to the target denominator**:
- We need to find a number \(k\) such that:
\[
5 \cdot k = 45
\]
- Solving for \(k\):
\[
k = \frac{45}{5} = 9
\]
3. **Multiply both the numerator and the denominator of the original fraction by this factor**:
- Multiply the numerator \(2\) by \(9\):
\[
2 \cdot 9 = 18
\]
- Multiply the denominator \(5\) by \(9\):
\[
5 \cdot 9 = 45
\]
4. **Write the equivalent fraction**:
- The equivalent fraction is:
\[
\frac{18}{45}
\]
Thus, the equivalent fraction of \(\frac{2}{5}\) with a denominator of \(45\) is \(\frac{18}{45}\).
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Simplify this solution The Deep Dive
To convert the fraction \(\frac{2}{5}\) to an equivalent fraction with a denominator of 45, you need to find a common multiplier. Multiply both the numerator and denominator by 9, because \(5 \times 9 = 45\). Thus, you get: \[ \frac{2 \times 9}{5 \times 9} = \frac{18}{45} \] So, \(\frac{2}{5}\) is equivalent to \(\frac{18}{45}\). Now, it’s like magic! Equivalent fractions are the same but simply dressed differently. The trick involves keeping the balance; whatever you do to the top (numerator) you also have to do to the bottom (denominator). So remember, whether you are simplifying or expanding fractions, always maintain that equality!
