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Chapter 1: Problem 29

\(\frac{9}{16}-\frac{3}{16}\)

Short Answer

Expert verified
The answer is \(\frac{6}{16}\)

Step by step solution

01

Identifying the Numerators

Identify the numerators of the given fractions, which are 9 and 3 in this case.
02

Subtracting the Numerators

You subtract the numerators because the denominators are the same. 9 - 3 equals 6.
03

Writing the Final Answer

Write the result of the subtraction as the numerator and 16 as the denominator. So, the answer to this problem is \(\frac{6}{16}\).

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Key Concepts

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

Numerators
In the world of fractions, the **numerator** is the number above the fraction line that indicates how many parts of the whole are being considered. Think of it as a simple count of interest.
In the exercise we are looking at, the numerators are 9 and 3 from the fractions \( \frac{9}{16} \) and \( \frac{3}{16} \) respectively.
  • The numerator helps us understand what part of the fraction changes when performing addition or subtraction operations.
  • In subtraction of fractions, where the denominators are already the same, we only need to subtract these numerators to get our new numerator.
Therefore, the task becomes straightforward: take the numerators (9 and 3, in this case), and subtract them to find the new numerator. This is a crucial step before you move on to rewriting your fraction.
Denominators
The **denominator** of a fraction is the number beneath the fraction bar. It lets us know into how many parts the whole is divided.
In our provided exercise, both fractions have the same denominator, which is 16. This is a key factor that makes subtraction of these fractions simple.
  • When denominators are alike, you do not need to change or adjust them during subtraction.
  • You can focus on just the numerators for subtraction, while the denominator remains the constant part of your answer.
Having common denominators is essential for directly subtracting fractions without further complications or conversions. It simplifies the process significantly.
Simplifying Fractions
**Simplifying fractions** is an important step that makes a fraction as simple as possible. A simplified fraction has no common factors between the numerator and the denominator other than 1.
After subtracting the fractions in this exercise, you ended up with \( \frac{6}{16} \).
  • To simplify this, identify the greatest common factor (GCF) of the numerator and the denominator, which is 2 here.
  • Divide both the numerator and the denominator by this GCF to reduce the fraction.
Doing this, you simplify \( \frac{6}{16} \) to \( \frac{3}{8} \), where 3 and 8 have no common factors except 1. Always remember, simplifying fractions not only provides a cleaner answer but also makes it easier to understand and compare the magnitude of different fractions.

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Most popular questions from this chapter

\(\left(\frac{1}{4}\right)^{3}\)

\((10-16) \cdot(20-26)\)

\(-2.54(3.8)(6.55)\)

The product of two nonzero rational numbers is a rational number.

\(\frac{3+[15 \div(-3)]}{16}\)
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