الرياضيات (بالإنجليزية) الصف السادس الابتدائي، الأسبوع 6: Evaluating an expression by substituting a value

Writing and evaluating expressions

الأسبوع 6 · كتابة المقادير الجبرية وتبسيطها وإيجاد قيمتها · 3 دروس

Evaluating an expression by substituting a value

Discover Mathematics P6: Term 1, Unit 3, Lessons 3–5

GoalReplace the letter by a number and work out the value of an expression, including real-life formulas.

New words

substitute · replace a letter by a numberevaluate · work out the value of an expressionformula · an expression that gives a quantity, like the cost of n tickets

Explanation

To evaluate an expression, substitute the number for the letter, then follow the order of operations. Write the number in brackets at first, so that the multiplication is not lost: for 3x + 5 with x = 4, write 3(4) + 5 = 12 + 5 = 17. The same expression gives different values for different numbers. Expressions are also formulas for real things: the cost of n tickets at 25 LE with a fixed booking fee of 10 LE is 25n + 10. For n = 3 the cost is 25 × 3 + 10 = 85 LE.

★Remember

Write the number in place of the letter, then use the order of operations.

Worked examples

x	2	4	10
3x + 5	11	17	35

Evaluate 3x + 5 for three values of x. When x = 2: 3 × 2 + 5 = 11. When x = 4: 3 × 4 + 5 = 17. When x = 10: 3 × 10 + 5 = 35.

Expression	Value of the letter	Result
n² − 1	n = 6	35
2(a + 3)	a = 5	16

With exponents and brackets. n² − 1 with n = 6: 6² − 1 = 36 − 1 = 35. And 2(a + 3) with a = 5: 2 × (5 + 3) = 2 × 8 = 16.

n	1	2	3	4
25n + 10 (LE)	35	60	85	110

A formula from real life. A cinema ticket costs 25 LE and the booking fee is 10 LE for the whole order. For n tickets the cost is 25n + 10 LE. 1 ticket costs 35 LE, 2 cost 60 LE, 3 cost 85 LE, 4 cost 110 LE.

Class activity

Value machine. Choose an expression, such as 5n − 2, and write it on a card. A grown-up says a number for n and you say the value. Make the machine harder by using a decimal like 2.5 or a bigger number like 20. Keep a table of the inputs and outputs.

Practice

Find 4a when a = 7.

Find y + 2.5 when y = 3.5.

Find 5n − 8 when n = 6.

Find m² + 3 when m = 5.

The perimeter of a square with side s is 4s. Find it when s = 12.5 cm.