Convert 6 4/7 to an improper fraction.
Understand the Problem
The question is asking how to convert the mixed number 6 4/7 into an improper fraction. To solve it, we will multiply the whole number by the denominator and add the numerator to find the new numerator, while keeping the same denominator.
Answer
The improper fraction is \(\frac{46}{7}\).
Answer for screen readers
The improper fraction of the mixed number (6 \frac{4}{7}) is (\frac{46}{7}).
Steps to Solve
- Identify the whole number and the fraction parts
In the mixed number (6 \frac{4}{7}), the whole number is 6, and the fraction is (\frac{4}{7}).
- Multiply the whole number by the denominator
We need to multiply the whole number (6) by the denominator (7) of the fraction.
$$ 6 \times 7 = 42 $$
- Add the numerator to the result
Next, we add the numerator (4) to the result from the previous step (42).
$$ 42 + 4 = 46 $$
- Write the new improper fraction
Now that we have a new numerator (46) and we keep the same denominator (7), we can write the improper fraction as:
$$ \frac{46}{7} $$
The improper fraction of the mixed number (6 \frac{4}{7}) is (\frac{46}{7}).
More Information
Converting a mixed number into an improper fraction is useful in various mathematical operations, such as addition and subtraction of fractions, where improper fractions can make calculations easier.
Tips
- Forgetting to multiply the whole number by the denominator before adding the numerator can lead to incorrect results. Always perform the multiplication step first.
- Misplacing the numerator and denominator when writing the final improper fraction. Remember that the improper fraction format is always (\frac{\text{new numerator}}{\text{denominator}}).
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