- Identify the objective: find the missing numerator \(x\) such that \(\frac{11}{12} = \frac{x}{132}\).
- Determine the scaling factor: divide 132 by 12, which gives \(132 \div 12 = 11\).
- Calculate the new numerator: multiply the original numerator 11 by the scaling factor 11, resulting in \(11 \times 11 = 121\).
- Final fraction: \(\frac{121}{132}\). The missing numerator is \(\boxed{121}\).
Explanation
- Understanding the Problem
The problem asks for an equivalent fraction to \(\frac{11}{12}\) with a denominator of 132. Two equivalent fractions are already given: \(\frac{11}{12} = \frac{55}{60}\) and \(\frac{11}{12} = \frac{33}{36}\). To find the third, we set up the equation \(\frac{11}{12} = \frac{x}{132}\), where \(x\) is the unknown numerator.
- Finding the Scaling Factor
To maintain the equivalence of the fraction, the numerator and the denominator of the original fraction \(\frac{11}{12}\) must be multiplied by the same non-zero constant \(k\). That is: \(\frac{11 \times k}{12 \times k} = \frac{x}{132}\). We need to find \(k\) such that \(12 \times k = 132\). Dividing 132 by 12 gives \(k = 132 \div 12 = 11\).
- Calculating the Missing Numerator
Now that we have determined the scaling factor \(k = 11\), we apply it to the numerator of the original fraction \(\frac{11}{12}\) to find \(x\). We calculate \(x = 11 \times k = 11 \times 11 = 121\). Therefore, the equivalent fraction is \(\frac{121}{132}\).
Examples
Equivalent fractions are used frequently in real life when measuring ingredients for recipes or dividing resources. For example, if a recipe calls for \(\frac{11}{12}\) of a cup of flour, but you only have a measuring cup that is marked in units of 132nd of a cup, you would need to calculate \(\frac{121}{132}\) to measure the exact amount required. Understanding how to scale fractions helps ensure that proportions remain consistent regardless of the unit of measure.