Finding the value of algebraic expressions

Finding the value of algebraic expressions

You can find the value of an algebraic expression by substituting the value of a given variable, and then perform the mathematical operations in the algebraic expression.

Example 1

Find the value of $10ab/c$, if $a = 2$, $b = 3$ and $c = 5$.

Solution

$10ab/c = 10 \times a \times b/c$

Substitute the values of $a$, $b$ and $c$ into the algebraic expression:

$10ab/c = 10 \times 2 \times 3/5 = 12$

Therefore, the answer is 12.

Example 2

If $n = 3$, $r = 4$ and $t = -3$, find the value of $(n + r) \times t$.

Solution

Substitute the values of $n$, $r$ and $t$ into the given algebraic expression:

$(n + r) \times t = (3 + 4) \times (-3)$

$= 7 \times (-3)$

$= -21$

Therefore, the answer is $-21$.

Example 3

Find the value of $y^m + ym^b$, given that $y = 4$, $b = 3$ and $m = 2$.

Solution

Substitute the values of $y$, $b$ and $m$ into the given algebraic expression:

$y^m + ym^b = 4^2 + 4 \times 2^3$

$= 16 + 4 \times 8$

$= 16 + 32$

$= 48$

Therefore, the answer is 48.

Word problems on algebra

Example 1

Jawala's present age is $x$ years. If the age of her mother is three times her age, find her mother's age.

Solution

Jawala's age is $x$ years.

Her mother's age is (Jawala's age) × 3

$= x \times 3$

$= 3x$

Therefore, her mother's age is $3x$ years.

Example 2

The sum of three consecutive odd numbers is 57. Find the three numbers.

Solution

Recall that consecutive odd numbers differ by 2. If the first number is $y$, the second number will be $(y + 2)$, and the third number will be $(y + 4)$.

So, the three consecutive numbers are $y$, $(y + 2)$ and $(y + 4)$.

The sum of these numbers is 57.

Formulate an equation as follows:

$y + (y + 2) + (y + 4) = 57$

$3y + 6 = 57$

$3y + 6 - 6 = 57 - 6$

$3y = 51$

Divide both sides by 3:

$3y/3 = 51/3$

$y = 17$

Thus, $y = 17$, $y + 2 = 17 + 2 = 19$, $y + 4 = 17 + 4 = 21$.

Therefore, the first number is 17, the second number is 19 and the third number is 21.