How does $22/20$ simplify to $11/10$ in this check?

Conditions

• The numerator (22) and denominator (20) share a common factor greater than 1.
• The same nonzero factor (2) divides both the numerator and the denominator.

Reasoning, step by step

1. Identify the numerator (22) and denominator (20) of the fraction $\frac{22}{20}$.
2. Find the greatest common factor (GCF) of 22 and 20, which is 2.
3. Divide the numerator by 2: $22 \div 2 = 11$.
4. Divide the denominator by 2: $20 \div 2 = 10$.
5. Write the reduced fraction as $\frac{11}{10}$.
6. Compare $\frac{11}{10}$ to the right-hand side of the original equation to confirm equality.

Example

After subtracting $\frac{8}{20}$ from $\frac{30}{20}$, the result is $\frac{22}{20}$. The instructor reduces this by canceling the common factor 2, yielding $\frac{11}{10}$, which matches the right-hand side of the equation $\frac{3}{4}x + \frac{1}{5}y = \frac{11}{10}$, confirming the solution is correct.

Common misconceptions

• Dividing only the numerator or only the denominator by the common factor, which would change the value of the fraction.
• Forgetting to reduce the fraction and concluding the check fails because $\frac{22}{20}$ does not look identical to $\frac{11}{10}$ at first glance.

Watch the explanation

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