Using Letters to Represent Numbers

In Mathematics, we use letters of the alphabet to stand for numbers instead of boxes.

We write \( \scriptsize 10 \: + \: x \) instead of \( \scriptsize 10 \: + \: \boxed{?}\).

We can use any letter e.g. a, b, c, t, y, z etc.

Example 1.2.1:

Each sentence is true. Find the number that each letter stands for.

i. \( \scriptsize x = 2 + 7 \\ \rightarrow \scriptsize x = 9 \)

ii. \( \scriptsize y = 14\: – \: 4 \\ \rightarrow \scriptsize y = 10 \)

iii. \( \scriptsize 12 + 8 = P \\ \rightarrow \scriptsize P = 20 \)

iv. \( \scriptsize 2 + m = 5 \\ \rightarrow \scriptsize m = 5 \: – \: 2 \\ \rightarrow \scriptsize m = 3 \)

v. \( \scriptsize C + 11 = 30 \\ \rightarrow \scriptsize C = 30 \: – \: 11 \\ \rightarrow \scriptsize C = 19 \)

vi. \( \scriptsize P \: \times \: 3 = 18 \\ \rightarrow \scriptsize P = \normalsize \frac{18}{3} \\ \rightarrow \scriptsize P = 6 \)

vii. \( \scriptsize 8 \: \times\: x = 24 \\ \rightarrow \scriptsize x = \normalsize \frac{24}{8} \\ \rightarrow \scriptsize x = 3 \)

viii. \( \scriptsize x \: \div \: 7 = 2 \\ \rightarrow \scriptsize 14 \: \div \: 7 = 2 \\ \scriptsize \therefore x = 14 \)

or

\( \scriptsize x \: \div \: 7 = 2 \\ \rightarrow \frac{x}{7} \scriptsize = 2\\ \scriptsize x = 2 \: \times \: 7 \\ \scriptsize \therefore x = 14 \)

ix. \( \scriptsize 10 \: \div \: f = 2 \\ \rightarrow \scriptsize 10 \: \div \: 5 = 2 \\ \rightarrow \scriptsize f = 5 \)

or

\( \scriptsize 10 \: \div \: f = 2 \\ \rightarrow \frac{10}{f} = 2\\ \rightarrow \scriptsize 10 = 2 \: \times \: f \\ \rightarrow \scriptsize f = \normalsize \frac{10}{2} \\ \rightarrow \scriptsize f = 5 \)

x. \( \scriptsize 36 = x + x + x \\ \rightarrow \scriptsize 36 = 3x \\ \rightarrow \scriptsize x = \normalsize \frac{36}{3} \\ \rightarrow \scriptsize x = 12 \)