Subtract 4/7 - 2/3. Write your answer in simplest form.
Understand the Problem
The question is asking to subtract two fractions, 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 first need to find a common denominator. The denominators are 7 and 3. The least common multiple (LCM) of 7 and 3 is 21.
- Convert fractions to the common denominator
Next, we convert each fraction to have the common denominator of 21.
For ( \frac{4}{7} ):
$$ \frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21} $$
For ( \frac{2}{3} ):
$$ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} $$
- Subtract the fractions
Now that both fractions have the same denominator, we can subtract them:
$$ \frac{12}{21} - \frac{14}{21} = \frac{12 - 14}{21} = \frac{-2}{21} $$
- Write in simplest form
The fraction ( \frac{-2}{21} ) is already in its simplest form because -2 and 21 have no common factors other than 1.
The final answer is ( \frac{-2}{21} ).
More Information
Subtracting fractions involves finding a common denominator. In this case, ( \frac{4}{7} - \frac{2}{3} = \frac{-2}{21} ). This is a straightforward process once the common denominator is determined.
Tips
- Not finding a common denominator: Ensure that both fractions are expressed with the same denominator before subtracting.
- Incorrect subtraction of numerators: Be careful with the subtraction of numbers; double-check your calculations to avoid mistakes.
