Question

1. simplify: \\(\frac{5n}{6nm} - \frac{2n}{5m}\\), teks a2.7(f)

a) \\(\frac{25 - 12n}{30m}\\)
b) \\(\frac{12 - 25n}{30m}\\)
c) \\(\frac{13n}{11nm}\\)
d) \\(\frac{-13n}{11nm}\\)

Explanation:

Step1: Simplify the first fraction

Simplify \(\frac{5n}{6nm}\) by canceling out the common factor \(n\) in the numerator and denominator.
\(\frac{5n}{6nm} = \frac{5}{6m}\)

Step2: Find a common denominator

The denominators are \(6m\) and \(5m\). The least common denominator (LCD) of \(6m\) and \(5m\) is \(30m\).

Step3: Rewrite the fractions with the LCD

Rewrite \(\frac{5}{6m}\) and \(\frac{2n}{5m}\) with the denominator \(30m\).
For \(\frac{5}{6m}\), multiply the numerator and denominator by \(5\): \(\frac{5\times5}{6m\times5}=\frac{25}{30m}\)
For \(\frac{2n}{5m}\), multiply the numerator and denominator by \(6\): \(\frac{2n\times6}{5m\times6}=\frac{12n}{30m}\)

Step4: Subtract the fractions

Now subtract the two fractions: \(\frac{25}{30m}-\frac{12n}{30m}=\frac{25 - 12n}{30m}\)

Answer:

A. \(\frac{25 - 12n}{30m}\)