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**Solve Exercises Lesson 24 Algebraic expressions (Chapter 7 Math 7 Connect)**

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### Solve lesson 7.1, page 24, Math 7 textbook Connecting knowledge, volume 2 – KNTT

Write an algebraic expression that represents:

a) Half the sum of x and y.

b) The sum of x and y times the product of x and y.

## Detailed instructions for solving problem 7.1

**Solution method**

Write an expression with 2 variables x, y

**Detailed explanation**

a) (x+y) : 2

b) (x+y). xy

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### Solve problem 7.2, page 24, Math 7 textbook Connecting knowledge volume 2 – KNTT

Write an algebraic expression representing the area of a trapezoid with bases a and b and height h (a, b and h have the same units).

## Detailed instructions for solving Problem 7.2

**Solution method**

Area of trapezoid = (large base + small base) . Height: 2

**Detailed explanation**

The algebraic expression for the area of a trapezoid is:

S = (a+b). h : 2

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### Solve lesson 7.3, page 24, Math 7 Textbook Connecting knowledge, volume 2 – KNTT

Calculate the value of the expression:

a) 4x + 3 at x = 5.8.

b) y^{2} – 2y +1 at y = 2

c) (2m+n).(mn) at m = 5.4 and n = 3.2

## Detailed instructions for solving Problem 7.3

**Solution method**

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Substitute the values of the variables into the expression and calculate the value of the expression

**Detailed explanation**

a) Substituting x = 5.8 into the expression, we get:

4x + 3 = 4. 5.8 + 3 = 26.2

b) Substituting y = 2 into the expression, we get:

y^{2} – 2y +1 = 2^{2} – 2.2 + 1 = 1

c) Substituting m = 5.4 and n = 3.2 into the expression, we get:

(2m+n).(mn) = (2.5,4 + 3.2) . (5.4 – 3.2) = 30.8

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### Solve problem 7.4 page 24 Math 7 textbook Connecting knowledge volume 2 – KNTT

A farmer uses two pumps to water his garden. The first pump can pump 5 m per hour^{3} water. The second pump pumps 3.5 m . per hour^{3} water.

a) Write an algebraic expression expressing the amount of water pumped by the two machines, if the first pump runs for x hours and the second pump runs for y hours.

b) Using the result of question a, calculate the amount of water pumped by both machines when x = 2 (hours), y = 3 (hours).

## Detailed instructions for solving Problem 7.4

**Solution method**

a) Write the expression: Amount of pumpable water = amount of tap water 1 pump + amount of tap water 2 pumps

b) Replace the values of x = 2 and y = 3 into the expression in sentence a

**Detailed explanation**

a) The algebraic expression expressing the pumpable water volume of the two machines is:

N = 5.x + 3.5.y

b) Substituting x = 2 and y = 3 into the expression, we get:

N = 5.2 + 3.5 . 3 = 20.5 (m^{3} )

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