To write the fraction [tex]\(\frac{3}{5}\)[/tex] as an equivalent fraction with denominator 35, follow these steps:
1. Identify the original fraction: The given fraction is [tex]\(\frac{3}{5}\)[/tex].
2. Determine the new denominator: We want to find an equivalent fraction with a denominator of 35.
3. Find the multiplier: To change the denominator from 5 to 35, we need to determine the factor that 5 must be multiplied by to get 35. We recognize that [tex]\(35\)[/tex] is [tex]\(5 \times 7\)[/tex]. Therefore, the multiplier is 7.
4. Multiply the numerator and the denominator: To keep the fraction equivalent, we must multiply both the numerator and the denominator by the same number (which is 7 in this case).
- Multiply the numerator by 7:
[tex]\[
3 \times 7 = 21
\][/tex]
- Multiply the denominator by 7:
[tex]\[
5 \times 7 = 35
\][/tex]
5. Write the new fraction: After performing the multiplication, the new fraction with the denominator of 35 is:
[tex]\[
\frac{21}{35}
\][/tex]
Therefore, the fraction [tex]\(\frac{3}{5}\)[/tex] written as an equivalent fraction with a denominator of 35 is [tex]\(\frac{21}{35}\)[/tex].
