Multiply 7/8 by a Factor of 7: Fraction Scaling Problem

Increasing by a factor of 7 means multiplying the entire fraction by 7. Think of it as making the fraction 7 times bigger while keeping it equivalent to $7 \times \frac{7}{8}$.

When you multiply both numerator and denominator by the same number, you create an equivalent fraction. This is like saying $\frac{7}{8} = \frac{7 \times 7}{8 \times 7}$ - they have the same value!

$\frac{49}{56}$ represents $7 \times \frac{7}{8}$ written as a single fraction. You can verify: $7 \times \frac{7}{8} = \frac{7 \times 7}{8} = \frac{49}{8}$, but we write it with denominator 56 to show the scaling clearly.

Yes! $\frac{49}{56} = \frac{7 \times 7}{7 \times 8} = \frac{7}{8}$. But the question asks for the result after scaling, so $\frac{49}{56}$ shows the multiplication work clearly.

Same process! For factor 3: $\frac{7 \times 3}{8 \times 3} = \frac{21}{24}$. Always multiply both numerator and denominator by the scaling factor.