Expressions with letter-numbers
An expression with a letter-number in it is called algebraic.
Ketaki’s shopping
Ketaki makes coconut-jaggery laddus. A coconut costs ₹35 and 1 kg of jaggery costs ₹60. For 10 coconuts and 5 kg of jaggery she pays 10 × 35 + 5 × 60 = ₹650.
Every day she buys different amounts. Can 10 × 35 + 5 × 60 tell her cost on every day?
What this lesson covers
The idea
A mathematical expression that contains letter-numbers is called an algebraic expression.
Ketaki’s shopping
Ketaki makes coconut-jaggery laddus. A coconut costs ₹35 and 1 kg of jaggery costs ₹60. For 10 coconuts and 5 kg of jaggery she pays 10 × 35 + 5 × 60 = ₹650.
Every day she buys different amounts. Can 10 × 35 + 5 × 60 tell her cost on every day?
- Yes, it works for any amounts.
- No, it works only for 10 coconuts and 5 kg.
- Yes, but only if the prices change.
Turn numbers into letters
The prices stay the same, but the amounts change. Swap the changing numbers for letters.
Numbers only, or letters too
The first expression has numbers only and gives one answer. The second has letter-numbers, so its value changes with *c* and *j*.
A mathematical expression that contains letter-numbers is called an algebraic expression.
- Expression | Letter-numbers in it | Kind
- 10 × 35 + 5 × 60 | none | arithmetic expression
- c × 35 + j × 60 | c and j | algebraic expression
Notes
A mathematical expression that contains letter-numbers is an algebraic expression: c × 35 + j × 60 works for any number of coconuts and any weight of jaggery.
Check yourself
Which of these is an algebraic expression?
How many letter-numbers are in c × 35 + j × 60?
Priya writes 4 × m for the number of wheels on *m* cars. Is 4 × m an algebraic expression?
Ketaki buys 2 coconuts and 1 kg of jaggery. What is the value of c × 35 + j × 60 when *c* = 2 and *j* = 1?
Answer: 130 ₹
2 × 35 + 1 × 60 = 70 + 60 = 130.
- 23 + 3. It has numbers only, so it is an arithmetic expression.
- 50 − 15. It has numbers only, so it is an arithmetic expression.
- a + 3 — correct. Yes! It contains a letter-number, *a*.
- Four: c, 35, j and 60. 35 and 60 are numbers. Only *c* and *j* are letter-numbers.
- Two: c and j — correct. Yes! 35 and 60 are numbers.
- One. There are two letters here: *c* and *j*.
- No. It has a × sign in it.. Arithmetic expressions use × too. What makes it algebraic is the letter *m*.
- No. It has the number 4 in it.. Algebraic expressions can have numbers too. The letter *m* is what makes it algebraic.
- Yes. *m* is a letter-number in it. — correct. Yes! Any expression with a letter-number is algebraic.