What stays and what changes

The idea

Letter-numbers in an algebraic expression are also called variables; the number multiplying a variable in a term is its coefficient, and a term without a variable is a constant.

Raju's boxes

Raju goes to a shop that sells sealed boxes. Every red box has 4 pens. Every blue box has 5 pencils. The shop also gives him 3 pens free. Raju buys x red boxes and y blue boxes.

Next week Raju buys a different number of boxes. Which numbers in the story change?

• Only the number of boxes
• The 4, the 5 and the 3 as well
• Only the 3 free pens

Go shopping

Use + and − to change how many boxes Raju buys. Watch the total, and see which numbers stay the same.

Three kinds of parts

The letters that stand for numbers are called variables. The number multiplying a variable in a term is its coefficient. A term without a variable is a constant.

In 4x + 5y + 3, the terms are 4x, 5y and 3. The variables x and y change with every purchase. The coefficients 4 and 5 and the constant 3 stay the same.

Notes

Variables are letters that stand for numbers. A coefficient is the number multiplying a variable in a term. A constant is a term without a variable.

Check yourself

In the term 7a, which number is the coefficient of a?

How many variables does 4x + 5y + 3 have?

Answer: 2

The letters are x and y: 2 variables. The 3 is a constant.

Which part of 9p − 4 is the constant?

In 5y³ + y² + 2y − 1, what is the coefficient of y²?

• a. a is the variable. The coefficient is the number that multiplies it.
• 7 — correct. Yes. 7 multiplies the variable a, so it is the coefficient.
• There is none. 7 is written right next to a. It multiplies a.
• 9. 9 multiplies p, so it is the coefficient of p.
• p. p is the variable.
• −4 — correct. Yes. −4 has no variable, so it is the constant term.
• 1 — correct. Yes. y² means 1 × y², so its coefficient is 1.
• 2. 2 is the coefficient of y, not of y².
• 5. 5 is the coefficient of y³.
• It has no coefficient. When no number is written, the coefficient is 1.