Bethany thinks of a number. 6/13 of her number is 48. What is 1/13 of her number?
Understand the Problem
The question is asking to find what one-thirteenth of a number is, given that six-thirteenths of that number equals 48. We will first determine what the number is and then calculate one-thirteenth of it.
Answer
The value of one-thirteenth of her number is $8$.
Answer for screen readers
The value of one-thirteenth of her number is $8$.
Steps to Solve
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Identify the variable Let the number Bethany thinks of be represented by $x$.
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Set up the equation We know that six-thirteenths of $x$ is equal to 48. We can express this as: $$ \frac{6}{13}x = 48 $$
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Solve for $x$ To find $x$, we first multiply both sides by $\frac{13}{6}$ to isolate $x$: $$ x = 48 \times \frac{13}{6} $$ Now calculate: $$ x = 48 \times \frac{13}{6} = 48 \div 6 \times 13 = 8 \times 13 = 104 $$
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Find one-thirteenth of $x$ Now that we have found $x = 104$, we need to calculate one-thirteenth of this number: $$ \frac{1}{13}x = \frac{1}{13} \times 104 $$ Calculating that gives: $$ \frac{104}{13} = 8 $$
The value of one-thirteenth of her number is $8$.
More Information
Bethany's number was determined to be 104, and finding one-thirteenth of it led to the conclusion that it is 8. This shows how fractions can represent parts of a whole in numerical problems.
Tips
- A common mistake is forgetting to simplify or correctly multiply fractions. Always double-check your calculations when working with fractions.
- Another mistake could be misinterpreting the fractions. Ensure you understand how the fractions relate to the total number.
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