الأسبوع 4 · العبارات والمعادلات والمجاهيل؛ العوامل الأولى · 3 دروس
1
Expressions, equations and letters
Discover Mathematics P5: Term 1, Unit 2, Lessons 1–5
GoalTell an expression from an equation, and use a letter for an unknown number.
New words
expression · numbers, letters and signs put together, with no equals sign, such as n + 6equation · a statement with an equals sign, such as n + 6 = 15variable · a letter that stands for a number that can change or is not known yetsolution · the number that makes an equation true
Explanation
An expression is a number phrase: 8 × 5 or n + 6. It has a value but it does not say that two things are equal, so it has no equals sign. An equation is a full sentence with an equals sign: n + 6 = 15. It can be true or false. We use a letter, called a variable, when a number is unknown or can change. In n + 6 the letter n stands for a number. If n = 9, the expression n + 6 has the value 15. If we are told n + 6 = 15, only one number makes the sentence true, n = 9. We call it the solution. Multiplication next to a letter can be written without the sign, so 4 × n can be written 4n, but in this lesson we keep the × sign to be clear.
Expressions
Equations
8 × 5
8 × 5 = 40
n + 6
n + 6 = 15
n − 3.5
n − 3.5 = 2
Worked examples
Marwan has n pencils and buys 6 more. The expression for the pencils he has now is n + 6. If he had 9 pencils at first, then n = 9 and n + 6 = 15. If he had 20, then n + 6 = 26. The value of the expression changes when the letter changes.
A box holds 12 sweets. For b boxes the number of sweets is 12 × b. For 4 boxes: 12 × 4 = 48 sweets. For 2.5 boxes (two full boxes and half a box): 12 × 2.5 = 30 sweets.
★Remember
An expression has no equals sign. An equation has one and can be true or false.
Is m = 5 a solution of m + 4.5 = 10? Replace m by 5: 5 + 4.5 = 9.5, and 9.5 is not 10, so the sentence is false and 5 is not a solution. Try m = 5.5: 5.5 + 4.5 = 10, true. So m = 5.5 is the solution.
Class activity
Letter cards. Write three expressions on cards, such as n + 4, 3 × n and n − 1.5, and the numbers 2, 5 and 10 on other cards. Pick one expression and one number, replace the letter by the number and say the value. Then write an equation with the answer and ask whether the number is its solution.
Practice
1
Which are expressions and which are equations? 7 + 2; x + 2 = 9; 3 × y; 15 − 6 = 9.
Expressions: 7 + 2 and 3 × y. Equations: x + 2 = 9 and 15 − 6 = 9.
2
Write an expression: (a) a number c increased by 8; (b) 5 times a number d; (c) a number k divided by 4.
(a) c + 8; (b) 5 × d; (c) k ÷ 4.
3
Find the value of 3 × n + 2 when n = 6.
3 × 6 + 2 = 18 + 2 = 20.
4
Is n = 4 a solution of 2.5 + n = 7? If not, find the number that is.
2.5 + 4 = 6.5, not 7, so no. n = 4.5 works because 2.5 + 4.5 = 7.
5
Find the value of the expression x + 3 when x = 0.5 and when x = 12.
