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Chapter 5: Problem 6

Add or subtract. $$\frac{9}{11}-\frac{1}{11}$$

Short Answer

Expert verified
Answer: The result is \(\frac{8}{11}\).

Step by step solution

01

Identify the numerators and denominators of both fractions.

We are given the following fractions to subtract: $$\frac{9}{11}-\frac{1}{11}$$ Here, the numerators are 9 and 1, and the common denominator is 11.
02

Subtract the numerators.

We will keep the same denominator, which is 11, and subtract the numerators 9 and 1: New numerator: $$9 - 1 = 8$$
03

Write the result as a fraction.

The result of the subtraction will have a numerator of 8 and the common denominator of 11: $$\frac{8}{11}$$ The final result is \(\frac{8}{11}\).

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Key Concepts

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

Numerators
In fraction subtraction, the numerator plays a crucial role. The numerator is the top number of a fraction. It indicates how many parts out of a whole are considered. In the problem \( \frac{9}{11} - \frac{1}{11} \), the numerators are 9 and 1 respectively.
  • In \( \frac{9}{11} \), the numerator 9 means we have 9 parts out of 11 total parts.
  • Similarly, in \( \frac{1}{11} \), the numerator 1 means we have 1 part out of 11 total parts.
To subtract fractions with the same denominator, we simply find the difference between the numerators. In this exercise, we performed the subtraction \( 9 - 1 = 8 \). This new numerator 8 represents the remaining parts after the subtraction. Keeping track of numerators helps you understand how parts are combined or removed in fraction operations.
Denominators
The denominator is the bottom number of a fraction, indicating into how many equal parts the whole is divided. In the example \( \frac{9}{11} - \frac{1}{11} \), both fractions have the same denominator, which is 11. This consistency in denominators is essential for straightforward subtraction:
  • The denominator tells us that the whole is divided into 11 equal parts.
  • All fractions in this operation are parts out of the same whole.
When subtracting fractions, maintaining the same denominator ensures that the parts being subtracted are of uniform size or quantity. Thus, only the numerators are manipulated, while the denominator remains unchanged. This simplification makes subtraction straightforward without any adjustment necessary for the denominators.
Common Denominator
In fraction subtraction, having a common denominator is vital. It allows us to directly subtract the numerators. A common denominator refers to fractions having the same denominator, showing parts out of an equal whole. In our example \( \frac{9}{11} - \frac{1}{11} \), 11 is the common denominator.

  • Fractions must have a common denominator to be directly subtracted or added.
  • This ensures the parts being considered are of the same size.
With a common denominator in place, subtraction becomes simple:
  • You only focus on subtracting the numerators.
  • The common denominator makes sure no extra adjustments are needed.
Understanding and finding a common denominator is essential when dealing with more complex fractions where denominators might initially differ. This ensures accurate calculations.

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Most popular questions from this chapter

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