Math 7 Unit 4 Review

The price of grapes, g, is $3.14 per pound. The price of bananas, b, is $0.79 per pound. The price of pears, p, is $2.49 per pound.​ Part A: Drag and drop the coefficients below to make a correct expression for this situation. ​ ​ ​ (a)   p + ​ (b)   g +​ (c)   b

Part B: What is the total cost of 3 pounds of grapes, 4 pounds of bananas, and 2 pounds of pears?

​ (d)  

• 79

• 249

• 314

• 2.49
• 3.14
• 0.79
• 17.56
• 12.97
• 15.78

Answer explanation

The correct expression for the situation is 2.49p + 3.14g + 0.79b. The coefficients 2.49, 3.14, and 0.79 represent the prices per pound of pears, grapes, and bananas respectively.

On Monday, John drove 5y - 7 miles. On Tuesday, he drove 4y - 12 miles. What is the difference in miles driven?

• 9y - 19

• y + 5

• y - 5

• y + 19

Answer explanation

The difference in miles driven is given by subtracting the expressions.

(5y - 7) - (4y - 12)

(5y - 7) + (-4y +12)

(5y + -4y) + (-7 + 12)

y + 5.

Therefore, the correct choice is y + 5.

• -12 + 24e - 6f

• 12 - 18e + 6f

• -3f + 8e - 6

• 6 - 18e + 3f

• 2(6 - 9e +3f)

Answer explanation

The expression is equivalent to 12 - 18e + 6f. This choice simplifies the expression correctly. The expression could also be factored as 2(6 - 9e +3f)

Simplify the expression 3(5) + 3(y − 2).

• 3y + 13

• y + 11

• 3y + 11

• 3y + 9

Answer explanation

To simplify the expression, distribute 3 to both terms inside the parentheses. This gives us 15 + 3(y - 2). Combine like terms by multiplying 3 with y and -2, resulting in 3y - 6. Finally, add 15 and -6 to get 3y + 9. Therefore, the correct choice is 3y + 9.

A shop provides a discount of 20% on all its products. If y is the original cost of a product, choose all the expressions that depict the final cost after the discount.

• 1.2y

• 0.8y

• y

• y - 0.2y

• y(1-0.2)

Answer explanation

The final cost after a 20% discount can be calculated using the expressions: 0.8y, y - 0.2y, and y(1-0.2). These expressions represent the correct choices.

On Friday, 5x + 10 pizzas were ordered. On Saturday, 4x - 6 were ordered. What is the total number of pizzas ordered?

• 9x + 16

• 9x + 4

• x+4

• x+16

Answer explanation

The correct choice is 9x + 4.

(5x + 10) + (4x - 6)

(5x +4x) + (10 + -6)

9x + 4

There are 15 ounces of coffee in a jar. Additional coffee is poured into the jar at a rate of 4 ounces per second. How many ounces are in the jar after 3 seconds?

Answer explanation

The expression 15 + 4(3) represents this situation. Therefore, the correct answer is 27. There are 27 ounces of coffee in the jar.

Select all correct ways of factoring -4x + 12.

• 4(x+3)

• -4(x + 3)

• -4(x - 3)

• 4(x − 3)

• 4(-x + 3)

Answer explanation

The correct ways of factoring -4x + 12 are:

-4(x - 3) = -4x +12

4(-x + 3) = -4x+12

The other choices are incorrect:

4(x+3) = 4x +12

-4(x + 3) = -4x - 12

4(x − 3) = 4x - 12

Consider the expression -4b + 8c + 12.

Part A: Factor the expression using the GCF by dragging and dropping the numbers to the correct locations.

​ (a)   (​ (b)   b + ​ (c)   c + ​ (d)   )

Part B: What is the value of the expression when b = 2 and c =1?

​ (e)  

• 4

• -1

• 2

• 3

• 12

• -4

• 20

• -3

Answer explanation

The expression -4b + 8c + 12 can be factored as 4(-b + 2c + 3). When b = 2 and c = 1, the expression evaluates to 4(-2 + 2 + 3) = 4(3) = 12. Therefore, the correct answer is 12.

Consider the expression 12a - 7b + 9 - 4a + 3b - 3.

Part A : Simplify the expression by combining the like terms.

​ (a)   ​ a ​ (b)   b + ​ 6

Part B: Factor the simplified expression using the GCF.

​ (c)   ( ​ (d)   a - 2b + 3 )

Part C: What is the value of the expression when a = -2 and b = -3?

​ (e)  

• 8
• - 4
• 2

• 4
• 5

• 6

• 2

Answer explanation

The expression can be simplified to 8a - 4b + 6. Factoring the expression gives 2(4a - 2b + 3). When a = -2 and b = -3, the expression evaluates to 8.