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Chapter 4: Problem 47

Rewrite each fraction with the indicated denominators. $$\frac{11}{9}=\frac{ }{99}$$

Short Answer

Expert verified
\frac{11}{9} = \frac{121}{99}

Step by step solution

01

Identify the relationship between the denominators

The given fraction is \(\frac{11}{9}\). The new fraction鈥檚 denominator is 99. To determine the equivalent fraction, find how to convert 9 to 99. Note that \(\frac{99}{9} = 11\), so we need to multiply the denominator by 11.
02

Multiply the numerator by the same factor

To keep the fraction equivalent, also multiply the numerator (11) by the same factor (11) that you used for the denominator. \(\frac{11 \times 11}{9 \times 11} = \frac{121}{99}\).
03

Write the final fraction

Thus, \(\frac{11}{9} = \frac{121}{99}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fractions
Fractions represent parts of a whole. When you see a fraction, you are looking at two numbers separated by a line. The number on top is called the numerator, and the number on the bottom is called the denominator.
Fractions like \(\frac{11}{9}\) show how many parts we have out of a total number of parts. In our example, the total parts are 9, and we have 11 of those parts.
Converting a fraction to an equivalent fraction means that the fraction will have the same overall value, even if the numerator and denominator are different.
Denominators
The denominator is the number below the fraction line. It tells us into how many equal parts the whole is divided.
For instance, in the fraction \(\frac{11}{9}\), the denominator is 9, which means the whole is divided into 9 parts.
When changing the denominator to find an equivalent fraction, you must determine the relationship between the old and the new denominators.
In our problem, we need to change the denominator from 9 to 99. We can see that by multiplying 9 by 11, we get 99: \[9 \times 11 = 99\]
This tells us how to adjust the numerator to keep the fraction equivalent.
Numerators
The numerator is the top number in a fraction. It shows how many parts we have. In the fraction \(\frac{11}{9}\), the numerator is 11.
When you change the denominator to find an equivalent fraction, you must multiply the numerator by the same number you used for the denominator.
This maintains the fraction's value. In our case, since we multiplied the denominator by 11, we must also multiply the numerator by 11:
\[11 \times 11 = 121\]
This changes our fraction to \(\frac{121}{99}\), which is equivalent to the original fraction because both fractions represent the same value.
Multiplication
Multiplication helps us create equivalent fractions. You multiply both the numerator and the denominator by the same number to keep the value of the fraction the same.
In our example, to change \(\frac{11}{9}\) to a fraction with a denominator of 99, we multiply both parts of the fraction by 11:
The denominator: \[9 \times 11 = 99 \]
The numerator: \[11 \times 11 = 121\]
This gives us the equivalent fraction \(\frac{121}{99}\).
Remember, whatever you do to the bottom of the fraction, you must also do to the top to keep the fraction's value unchanged.

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