Division of Algebraic Expressions

Algebraic expressions can also be simplified by division.

Example 2.3.1:

Simplify the following algebraic expressions:

i. \( \scriptsize a \: \div \: b \)

ii. \( \scriptsize 2 \: \div \: 7 \)

iii. \( \scriptsize 2a \: \div \: 4a \)

iv. \( \scriptsize 15y \: \div \: 5 \)

Solution

i. \( \scriptsize a \: \div \: b \\ = \frac{a}{b} \)

ii. \( \scriptsize 2 \: \div \: 7 \\ = \normalsize \frac{2}{7} \)

iii. \( \scriptsize 2a \: \div \: 4a \\ = \normalsize \frac{2a}{4a} \\ = \normalsize \frac{2\not{a}}{4 \not{a}} \\ = \normalsize \frac{2}{4} \\ = \normalsize \frac{1}{2} \)

iv. \( \scriptsize 15y \: \div \: 5 \\ = \normalsize \frac{15y}{5} \\ = \scriptsize 3y \)

Example 2.3.2:

Solve the following:

i. \( \scriptsize 16ab \div 4ab \)

ii. \( \scriptsize 12xyz \div 4y \)

iii. \( \normalsize \frac{1}{4} \scriptsize \; of \; 24pq \)

iv. \( \scriptsize y \div xy \)

Solution

i. \( \scriptsize 16ab \div 4ab \\ = \normalsize \frac{16ab}{4ab}\\ = \normalsize \frac{16\not{a} \not{b}}{4\not{a}\not{b}} \\ = \normalsize \frac{16}{4} \\ = \scriptsize 4\)

ii. \( \scriptsize 12xyz \div 4y \\ = \normalsize \frac{12xyz}{4y} \\ = \normalsize \frac{12x \not{y}z}{4 \not{y}} \\ = \normalsize \frac{12xz}{4} \\ = \scriptsize 3xz \)

iii. \( \normalsize \frac{1}{4} \scriptsize \; of \; 24pq \\ =\normalsize \frac{1}{4}\scriptsize \; \times \; 24pq \\ = \normalsize \frac{24pq \; \times \; 1}{4} \\ = \normalsize \frac{24pq}{4} \\ = \scriptsize 6pq \)

iv. \( \scriptsize y \div xy \\ = \normalsize \frac{y}{xy}\\ = \normalsize \frac{\not{y} }{x \not{y}} \\ = \normalsize \frac{1}{x} \)