To solve for the other number given that the difference between two numbers is [tex]\(\frac{1}{72}\)[/tex] and the smaller number is [tex]\(\frac{7}{36}\)[/tex], follow these steps:
1. Identify the given values:
- The difference between the two numbers is [tex]\(\frac{1}{72}\)[/tex].
- The smaller number is [tex]\(\frac{7}{36}\)[/tex].
2. Convert the given fractions to decimal form for easier calculations:
- The difference [tex]\(\frac{1}{72}\)[/tex] converts to approximately [tex]\(0.013888888888888888\)[/tex].
- The smaller number [tex]\(\frac{7}{36}\)[/tex] converts to approximately [tex]\(0.19444444444444445\)[/tex].
3. Set up the equation to find the larger number:
- Let the larger number be [tex]\(x\)[/tex].
- Given that the difference between the larger number and the smaller number is [tex]\(\frac{1}{72}\)[/tex], we can write the equation:
[tex]\[
x - 0.19444444444444445 = 0.013888888888888888
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Add the decimal form of the smaller number to the difference:
[tex]\[
x = 0.19444444444444445 + 0.013888888888888888
\][/tex]
- Perform the addition to find [tex]\(x\)[/tex]:
[tex]\[
x = 0.20833333333333334
\][/tex]
5. Convert the larger number back to a fraction, if needed:
- The larger number [tex]\(0.20833333333333334\)[/tex] corresponds to [tex]\(\frac{5}{24}\)[/tex] as a fraction. (Note: this step assumes we are working in decimals, but typically you can leave the answer in decimal form as well if not explicitly asked for fractions).
Conclusion: The other (larger) number is approximately [tex]\(0.20833333333333334\)[/tex], or [tex]\(\frac{5}{24}\)[/tex] in fractional form.
