Substitution into Algebraic Expressions

In algebraAlgebra is a branch of mathematics that substitutes letters for numbers. Algebra is about finding the unknown or putting real-life variables into equations and then solving them. More, substitution means replacing letters with numbers. The operation sign is important when carrying out the substitution.

Example 3.3.1:

If a = 2, b = -5, c = 10, d = 3

Evaluate:

i. \( \scriptsize a \: + \: b \: + \: c \)
ii. \( \scriptsize c \: \div \: b \)
iii. \( \scriptsize a \: \times\: d \)
iv. \( \frac{d \: \times \: c}{a} \)
v. \( \frac{2b \: \times \: c}{10} \)

Solution

i. \( \scriptsize a \: + \: b \: + \: c \)

From the question the values given are a = 2, b = -5, c = 10

Substituting the values for a, b and c into the equation we get

= \( \scriptsize 2 \: + \: (-5) \: + \: 10 \)

Note:

\( \scriptsize +(-) \; = \; – \)

or

\(\scriptsize \; + \; \times \; \; – \; = \; – \)

= \( \scriptsize 2 \; – \: 5 \: + \: 10 \)

Using Bodmas rule, Addition comes before subtraction

Add 2 + 10 before subtracting 5

\( \scriptsize 2\: + \: 10 \; – \: 5 \)

= \( \scriptsize 12 \; – \: 5 \)

= \( \scriptsize 7\)

ii. \( \scriptsize c \: \div \: b \)

From the question, the values given are c = 10, b = -5

Substituting the values for c and b into the equation we get

\( \scriptsize 10 \: \div \: (-5) \)

= \( \frac {10}{-5}\)

= \( \scriptsize \: -2 \)

iii. \( \scriptsize a \: \times\: d \)

From the question, the values given are a = 2, d = 3

Substituting the values for a and d into the equation we get

\( \scriptsize 2 \: \times\: 3 = 6 \)

iv. \( \frac{d \: \times \: c}{a} \)

From the question, the values given are a = 2, c = 10, d = 3

Substituting the values for a, c and d into the equation we get

\( \frac{3 \: \times \: 10}{2} \\ \frac{30}{2} \\ = \scriptsize 15\)

v. \( \frac{2b \: \times \: c}{10} \)

From the question, the values given are b = -5, c = 10

Substituting the values for b and c into the equation we get

\( \frac{2(-5) \: \times \: 10}{10} \\ = \frac{-10 \: \times \: 10}{10} \\ = \frac{-100}{10} \\ = \scriptsize -10 \)

Note: When you divide a negative number by a positive number then the quotient is negative. When you divide a positive number by a negative number then the quotient is also negative. When you divide two negative numbers then the quotient is positive. The same principle rules hold for multiplication.