How to subtract with fractions?
Understand the Problem
The question asks for guidance on how to perform subtraction operations involving fractions. This typically involves finding a common denominator and then subtracting the numerators while keeping the denominator the same.
Answer
The result is given by $$ \frac{a \cdot (CD/b) - c \cdot (CD/d)}{CD} $$ after substituting the values.
Answer for screen readers
The final answer will be expressed as:
$$ \frac{a \cdot (CD/b) - c \cdot (CD/d)}{CD} $$
after substituting $a$, $b$, $c$, and $d$ with their specific values.
Steps to Solve
- Identify the fractions and their denominators
First, list the fractions you want to subtract. For example, consider the fractions $\frac{a}{b}$ and $\frac{c}{d}$. Determine their denominators, which are $b$ and $d$.
- Find the common denominator
The common denominator is usually the least common multiple (LCM) of the two denominators. In this case, the LCM of $b$ and $d$ will be your common denominator, which we can denote as $CD$.
- Rewrite the fractions
Convert each fraction to have the common denominator. This is done by multiplying the numerator and the denominator of each fraction by the necessary factor to achieve the common denominator:
$$ \frac{a}{b} = \frac{a \cdot (CD/b)}{b \cdot (CD/b)} $$
$$ \frac{c}{d} = \frac{c \cdot (CD/d)}{d \cdot (CD/d)} $$
- Subtract the fractions
Now that both fractions have the same denominator, you can subtract them. Simply subtract the numerators and keep the common denominator:
$$ \frac{a \cdot (CD/b) - c \cdot (CD/d)}{CD} $$
- Simplify the result
If possible, simplify the resulting fraction by reducing the numerator and denominator by any common factors.
The final answer will be expressed as:
$$ \frac{a \cdot (CD/b) - c \cdot (CD/d)}{CD} $$
after substituting $a$, $b$, $c$, and $d$ with their specific values.
More Information
When subtracting fractions, ensuring that both fractions share a common denominator is crucial. The greatest common divisor (GCD) may help simplify the final result, making it easier to interpret.
Tips
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Forgetting to find the common denominator, which can lead to incorrect subtraction. Always ensure both fractions are expressed with the same denominator before proceeding.
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Not simplifying the final answer. It's important to check if the final fraction can be simplified further.
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