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Chapter 4: Problem 627

In the following exercises, subtract. $$\frac{11}{12}-\frac{5}{12}$$

Short Answer

Expert verified
\frac{1}{2}

Step by step solution

01

- Identify the Denominators

First, look at the denominators of the two fractions. In this case, both fractions have the same denominator, which is 12.
02

- Subtract the Numerators

Since the denominators are the same, simply subtract the numerator of the second fraction from the numerator of the first fraction: \[ 11 - 5 \]
03

- Write the Result as a Fraction

Now, put the result of the numerator subtraction over the common denominator: \[ \frac{11 - 5}{12} = \frac{6}{12} \]
04

- Simplify the Fraction

Simplify the fraction by finding the greatest common divisor (GCD) of 6 and 12, which is 6. \[ \frac{6}{12} = \frac{6 eq 6}{12 eq 6} = \frac{1}{2} \]

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Key Concepts

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

Subtracting Fractions
When you need to subtract fractions, the first thing you should check is if the denominators (the numbers at the bottom) are the same.
In our given problem, we have \(\frac{11}{12} - \frac{5}{12}\).
Luckily, both denominators are the same (12), making our job easier!
All you need to do is subtract the numerators (the numbers on top): \ 11 - 5 \.
Putting it together, we get \(\frac{6}{12}\).

In cases where the denominators are different, the process involves finding a common denominator before performing the subtraction.
This might sound tricky, but it gets easier with practice!
Simplifying Fractions
Once you've performed the subtraction, the next step is to simplify the fraction if possible.
Simplifying a fraction means making the fraction as simple as it can be,
which usually means making the numerator and denominator as small as possible while keeping the fraction equivalent.

For example, our fraction after subtraction was \(\frac{6}{12}\).
To simplify this, we need to find a number that can evenly divide both 6 and 12.
This number is called the Greatest Common Divisor (GCD).

By dividing both the numerator and the denominator by their GCD (in this case, 6), we get \(\frac{1}{2}\).

This is the simplest form of \(\frac{6}{12}\)!
Greatest Common Divisor (GCD)
The Greatest Common Divisor (GCD) of two numbers is the largest number that evenly divides both of them.
Finding the GCD is crucial when simplifying fractions because it's the key to reducing fractions to their simplest forms.

In our example, to simplify \(\frac{6}{12}\), we needed to find the GCD of 6 and 12.
First, identify the factors of each number.
The factors of 6 are 1, 2, 3, and 6.
The factors of 12 are 1, 2, 3, 4, 6, and 12.
The largest common factor is 6.
So, the GCD of 6 and 12 is 6.

By dividing both the numerator and the denominator by their GCD, the fraction \(\frac{6}{12}\) simplifies to \(\frac{1}{2}\).
This way, the fraction is as simple as possible!

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Most popular questions from this chapter

In the following exercises, simplify. $$ -\frac{5}{6} \div \frac{5}{12} $$

Convert the mixed number to an improper fraction. $$ 3 \frac{2}{7} $$

In the following exercises, solve the equation. $$ -\frac{2}{3} c=18 $$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x+\frac{1}{2}\) when (a) \(x=-\frac{1}{8} \quad\) ( b) \(x=-\frac{1}{2}\)

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(\frac{r-s}{r+s}\) when \(r=10, s=-5\)
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