A reliable method
Keep a common denominator for addition; use exponent laws for products. A matrix product entry is a row-by-column dot product.
The common trap
Multiplying matrices is not the same as multiplying matching entries. Also remember that i² equals −1, not 1.
Make the connection
Test a small example before applying a rule. Track signs through complex multiplication and estimate the size of a fractional answer.
Worked example: choose the requested quantity
What is 3/6 − 1/4? Use denominator 12: 6/12 − 3/12. Subtract the numerators and reduce the fraction. The requested value is 1/4.
Contrast and diagnose an error
What is the value of (3²)³ / 3⁴? Multiply exponents for a power of a power: 2×3=6. Divide equal bases by subtracting exponents: 6−4=2. The requested value is 9. A tempting answer is 3: Add the power exponents before subtracting the denominator exponent.
Transfer practice and check
If i² = −1, what is the real part of (3 + 2i)(4 − 3i)? Try it before reading on. Check: 18. Multiply all four pairs of terms. The real contributions are the constant product and −6i²; the terms with one i are imaginary.
What is 3/6 − 1/4?
- Use denominator 12: 6/12 − 3/12.
- Subtract the numerators and reduce the fraction.
- The requested value is 1/4.
Compare the other answer choices
Add numerators and denominators instead of subtracting fractions.
Keep denominator six while subtracting numerators without converting.
Add the fractions rather than subtract.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
ACT Mathematics content