From words to expressions

The idea

A relationship is first described in words and then written as an algebraic expression, and any algebraic expression can likewise be read back in ordinary language.

Matchstick Ls

Parthiv makes Ls from matchsticks. Each L has 2 matchsticks. 5 Ls need 5 × 2 sticks, 7 Ls need 7 × 2, 45 Ls need 45 × 2.

For *n* Ls, how would you write the number of matchsticks?

• 2 × n
• n + 2
• n × n

Build the expression

Say the relationship in words first. Then build the expression from tiles. The table tells you what the story needs.

Words, expression, and back

First describe the relationship in words, then write it as an expression. It also works backwards: an expression can be read back in words.

A relationship is first described in words and then written as an algebraic expression. Any algebraic expression can likewise be read back in ordinary language.

• In words | Expression
• Shabnam’s age is 3 more than Aftab’s age | a + 3
• Aftab’s age is 3 less than Shabnam’s age | s − 3
• The sticks are 2 times the number of Ls | 2 × n

Notes

Say the relationship in words, write it as an algebraic expression, and read it back: a + 3 is read as 3 more than *a*.

Check yourself

Which expression means 5 more than *x*?

Read the expression y − 4 back in ordinary language.

Each L needs 2 matchsticks. The expression is 2 × n. How many matchsticks do 45 Ls need?

Answer: 90 sticks

2 × 45 = 90 matchsticks.

A pen costs ₹12. Which expression gives the cost of *p* pens?

• x − 5. That is 5 less than *x*.
• 5 − x. That is *x* taken away from 5.
• x + 5 — correct. Yes! More than means add.
• 4 more than y. More than would be y + 4.
• 4 less than y — correct. Yes! Take 4 away from *y*.
• 4 times y. Times would be a multiplication.
• 12 + p. Adding does not count pens. Each pen costs ₹12.
• 12 × p — correct. Yes! *p* pens cost 12 rupees each.
• p − 12. That takes 12 away from *p*.