To solve the problem of finding the other number when the product of two numbers is [tex]\(\frac{16}{3}\)[/tex] and one of the numbers is [tex]\(\frac{26}{3}\)[/tex], follow these steps:
1. Understand the Problem:
- We are given the product of two numbers, which is [tex]\(\frac{16}{3}\)[/tex].
- We are also given one of the numbers, which is [tex]\(\frac{26}{3}\)[/tex].
- We need to find the other number.
2. Set Up the Equation:
- Let [tex]\( x \)[/tex] be the other number.
- The product of the given number and this unknown number should equal the given product, that is:
[tex]\[
\frac{26}{3} \times x = \frac{16}{3}
\][/tex]
3. Isolate the Unknown Number:
- To find [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(\frac{26}{3}\)[/tex]:
[tex]\[
x = \frac{\frac{16}{3}}{\frac{26}{3}}
\][/tex]
4. Simplify the Division of Fractions:
- Dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
x = \frac{16}{3} \times \frac{3}{26}
\][/tex]
5. Multiply the Fractions:
- Multiply the numerators together and the denominators together:
[tex]\[
x = \frac{16 \times 3}{3 \times 26}
\][/tex]
6. Cancel the Common Factors:
- Simplify the fraction:
[tex]\[
x = \frac{48}{78}
\][/tex]
- Notice that both 48 and 78 can be divided by their greatest common divisor, which is 6:
[tex]\[
x = \frac{48 \div 6}{78 \div 6} = \frac{8}{13}
\][/tex]
Therefore, the other number is [tex]\(\frac{8}{13}\)[/tex].
So, the step-by-step solution gives us the other number as approximately [tex]\(0.6153846153846154\)[/tex] when expressed as a decimal.
