Question

3 simplify the following by cancelling.
a \\(\frac{8b}{2}\\)
b \\(-\frac{2a}{6}\\)
d \\(\frac{3mn}{6n}\\)
e \\(-\frac{5xy}{20y}\\)
g \\(\frac{u^2v}{u}\\)
h \\(\frac{5r^2s^2}{8rs}\\)

Explanation:

Identify the common factors in each expression

We need to simplify each algebraic fraction by identifying and cancelling common numerical and variable factors in the numerator and denominator.

Simplify parts a and b

For part a:

$$ \frac{8b}{2} = \frac{2 \times 4b}{2} = 4b $$

For part b:

$$ -\frac{2a}{6} = -\frac{2 \times a}{2 \times 3} = -\frac{a}{3} $$

Simplify parts d and e

For part d:

$$ \frac{3mn}{6n} = \frac{3 \times m \times n}{3 \times 2 \times n} = \frac{m}{2} $$

For part e:

$$ -\frac{5xy}{20y} = -\frac{5 \times x \times y}{5 \times 4 \times y} = -\frac{x}{4} $$

Simplify parts g and h

For part g:

$$ \frac{u^2v}{u} = \frac{u \times u \times v}{u} = uv $$

For part h:

$$ \frac{5r^2s^2}{8rs} = \frac{5 \times r \times r \times s \times s}{8 \times r \times s} = \frac{5rs}{8} $$

Answer:

No.	Problem	Answer
b	\(-\frac{2a}{6}\)	\(-\frac{a}{3}\)
d	\(\frac{3mn}{6n}\)	\(\frac{m}{2}\)
e	\(-\frac{5xy}{20y}\)	\(-\frac{x}{4}\)
g	\(\frac{u^2v}{u}\)	\(uv\)
h	\(\frac{5r^2s^2}{8rs}\)	\(\frac{5rs}{8}\)