Subtract 4/7 - 2/3. Write your answer in simplest form.

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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

  1. 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.

  1. 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} ):

$$ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} $$

  1. Subtract the fractions

Now that both fractions have the same denominator, we can subtract them:

$$ \frac{12}{21} - \frac{14}{21} = \frac{12 - 14}{21} = \frac{-2}{21} $$

  1. 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.

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