Question

simplify. \\(\dfrac{40xy}{56wxy}\\)

Explanation:

Step1: Cancel common factors in numerator and denominator

First, identify the common factors in the numerator \(40xy\) and the denominator \(56wxy\). The common factors are \(x\), \(y\), and the greatest common divisor (GCD) of 40 and 56.

The GCD of 40 and 56:

• Factors of 40: \(1, 2, 4, 5, 8, 10, 20, 40\)
• Factors of 56: \(1, 2, 4, 7, 8, 14, 28, 56\)
• GCD is 8.

So, we can divide both the numerator and the denominator by \(8xy\) (since \(x\) and \(y\) are common in both numerator and denominator).

Step2: Simplify the fraction

Dividing the numerator \(40xy\) by \(8xy\): \(\frac{40xy}{8xy} = 5\)

Dividing the denominator \(56wxy\) by \(8xy\): \(\frac{56wxy}{8xy} = 7w\)

So, the simplified form of \(\frac{40xy}{56wxy}\) is \(\frac{5}{7w}\) (after canceling out \(x\) and \(y\) which are non - zero, as they are in the original expression, so we can cancel them).

Answer:

\(\frac{5}{7w}\)