Subtract 4/7 - 2/3 and write your answer in simplest form.
Understand the Problem
The question is asking us to subtract two fractions, specifically 4/7 and 2/3, and present the answer in its simplest form.
Answer
The answer is $\frac{-2}{21}$.
Answer for screen readers
The final answer is $\frac{-2}{21}$.
Steps to Solve
- Find a common denominator
To subtract the fractions $\frac{4}{7}$ and $\frac{2}{3}$, we need a common denominator. The least common multiple (LCM) of 7 and 3 is 21.
- Convert the fractions
We will convert both fractions to have the common denominator of 21:
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For $\frac{4}{7}$: $$ \frac{4}{7} \times \frac{3}{3} = \frac{12}{21} $$
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For $\frac{2}{3}$: $$ \frac{2}{3} \times \frac{7}{7} = \frac{14}{21} $$
- Subtract the fractions
Now that both fractions have the same denominator, subtract them:
$$ \frac{12}{21} - \frac{14}{21} = \frac{12 - 14}{21} = \frac{-2}{21} $$
- Simplify the result
The fraction $\frac{-2}{21}$ is already in its simplest form since there are no common factors between -2 and 21.
The final answer is $\frac{-2}{21}$.
More Information
The result of subtracting $\frac{2}{3}$ from $\frac{4}{7}$ is negative, indicating that $\frac{2}{3}$ is larger than $\frac{4}{7}$. The simplest form of the fraction is essential for clarity in mathematical communication.
Tips
- One common mistake is forgetting to find a common denominator when subtracting fractions. Always ensure denominators are the same before proceeding.
- Another mistake is not simplifying the result appropriately. Always check if the final fraction can be reduced.
