Framing Algebraic Expressions (Including Evaluation)

The rule is n2, so the sum is 7 × 7 = 49.

ICSE Class 6 · Mathematics · Chapter 21

What this chapter covers

An algebraic expression is a group of numbers and letters joined by operation signs, such as x + 7 or 4y - 3.

Framing an algebraic expression is the process of turning a word statement into an expression made of numbers, letters and operation signs.

Evaluating an expression is finding its numerical value by putting a given number in place of each letter in it.

A variable is a letter in an expression that can take different number values, such as n in 3n + 1.

An algebraic expression is made of numbers and letters joined by operation signs.
Words such as "more than", "less than", "times" and "divided by" tell you which sign to use.
"5 less than x" is x - 5, while "x subtracted from 5" is 5 - x.
Brackets show which part of an expression must be worked out first, as in 2(x + 4).
The nth even number is 2n and the nth odd number is 2n - 1.
The sum of the first n odd numbers is n².
To find the rule of a pattern, see how much it grows at each step, then match the first step.
To evaluate an expression, replace each letter with its value and follow the order of operations.
Always check that the answer makes sense.

Frame an expression for "8 less than k".

k - 8.

Frame an expression for "k subtracted from 8".

8 - k.

Frame an expression for "thrice the sum of p and 2". Which sign shows that the sum is found first?

3(p + 2). The brackets show that the sum is found first.

A packet holds m biscuits. How many biscuits are there in 7 packets?

7m biscuits.

Write the nth odd number as an expression, and use it to find the 20th odd number.

2n - 1. For n = 20, 2 × 20 - 1 = 39.

A row of n squares needs 3n + 1 matchsticks. How many sticks are needed for 12 squares?

3 × 12 + 1 = 37 sticks.

Evaluate 5x + 2y when x = 3 and y = 4.

5 × 3 + 2 × 4 = 15 + 8 = 23.

Find the sum of the first 7 odd numbers using a rule.

The rule is n², so the sum is 7 × 7 = 49.