Algebraic Expressions
2.0 Algebra · 2.1 Algebraic Expressions
Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 2.0 Algebra | Sub-Strand 2.1 Algebraic Expressions (5 lessons)
Lesson objectives
By the end of this topic, you will be able to:
- Form algebraic expressions from real-life situations
- Form algebraic expressions from simple algebraic statements
- Simplify algebraic expressions
- Appreciate the use of algebraic expressions in real life
Algebraic Expressions
When a quantity is unknown, we give it a letter. An algebraic expression is a combination of letters and numbers, with no equals sign.
a) Turning words into algebra
Read carefully. "Two less than t" is t − 2, not 2 − t. The order matters for subtraction and division.
A letter with a number in front means multiply. So 3m means 3 × m.
Say what the letter stands for before you use it. "Let n be the number of goats" makes the whole expression readable.
b) From real situations
A pen costs x shillings. Three pens cost 3x.
A boy is y years old. In five years he will be y + 5.
A rectangle is L long and W wide. Its perimeter is 2L + 2W.
The pattern is always the same. Name the unknown, then describe the situation with it.
c) The parts of an expression
A term is a single part, separated from others by + or −. In 3a + 5b there are two terms.
The coefficient is the number in front of a letter. In 3a the coefficient is 3.
A constant is a term with no letter, such as the 7 in 3a + 7.
d) Like terms
Like terms have exactly the same letter or letters. So 3a and 2a are like terms; 3a and 3b are not.
Only like terms can be combined.
Add or subtract the coefficients and keep the letter unchanged. 3a + 2a is 5a, not 5a².
Terms with different letters simply stay as they are. 5a + 4b cannot be shortened.
e) Watch the signs
The sign in front of a term belongs to it. In 5b − b, the second term is negative one b, so the result is 4b.
A term with no visible number has a coefficient of 1. So b means 1b.
f) Where this is used
A formula is an expression. Pay from hours worked is one. So is a bill from a number of items. Both are written this way before any numbers arrive.
Words to know
- Algebraic expression — a mathematical phrase using letters (variables) to represent unknown or changeable numbers.
- Variable — a letter standing in for a number that is unknown or can change.
- Like terms — terms with exactly the same variable(s) raised to the same power.
- Simplify — to combine like terms so an expression is written in its shortest form.
:::checkpoint Check yourself
- Write "seven more than twice k" in algebra.
- Simplify 4x + 3y + 2x + y.
- Simplify 8m − 3m + 2n.
- Why can 5a and 4b not be combined? :::
Bridge to practice
Try the exercises below — on forming and simplifying algebraic expressions.