Equivalent Expressions

Equivalent Expressions

EXAMPLE 1:

Jenny bought a TV for 15% off the original price. Write an expression to represent the sale price of the TV.

If Jenny bought the TV without the discount, she would have paid 100% of the cost; however, she got 15% taken off. This means she paid 85% of the original cost. We can represent this with the equation:

100% - 15% = 85%

We can use different parts of this equation to help us write 3 expressions to represent the sale price!

Expression 1

100% - 15% = 85%

 

For Expression 1, convert the right side of the equation to a decimal and multiply it with the variable of your choice!

 

85% = 0.85. The expression to represent the sale price is 0.85p.

Expression 2

100% - 15% = 85%

 

For Expression 2, convert the left side of the equation to decimals and place it inside parentheses. Put the variable of your choice outside the parentheses to show multiplication.

 

100% - 15% is 1 – 0.15 when converted to decimals. The expression to represent the sale price is p(1 - 0.15).

Expression 3

100% - 15% = 85%

 

Expression 3 is simply Expression 2 but simplified. Using the distributive property, we can go from p(1 - 0.15) to 1p – 0.15p. Many times we do not write the 1, so you may see it written as p – 0.15p.

 

PRACTICE

For each situation, write 3 expressions to represent the sale price or final amount.

Open Ended

Amir read 35% of his book. Write an expression to represent the number of pages he has left to read.

Expression 1:

Expression 2:

Expression 3:

Open Ended

Olivia bought art supplies with a coupon for a 10% discount. Write an expression to represent the sale price of the supplies.

Expression 1:

Expression 2:

Expression 3:

Open Ended

Dre bought a pair of Jordans that had been marked down 23%. Write an expression to represent the sale price.

Expession 1:

Expression 2:

Expression 3:

Open Ended

A sign at Walmart reads, “Shirt prices reduced 55%!” Write an expression to represent the sale price of a shirt.

Expression 1:

Expression 2:

Expression 3:

Open Ended

Mariah donated 30% of her allowance to charity. Write an expression to represent the amount of allowance she still has.

Expression 1:

Expression 2:

Expression 3:

Open Ended

CONCLUSION:

What are some clues that you’ll have to SUBTRACT the percentage?

EXAMPLE 2:

Ashtin bought a TV and paid 6% sales tax. Write an expression to represent the sale price.

The problem does not indicate any type of discount, so we can conclude Ashtin bought the TV at 100% of the cost; however, he had to pay sales tax, an additional amount. This means he paid 100% of the original cost plus an extra 6%. We can represent this with a simple equation:

100% + 6% = 106%

We can use different parts of this equation to help us write 3 expressions to represent the sale price!

Expression 1

100% + 6% = 106%

 

For Expression 1, convert the right side of the equation to a decimal and multiply it with the variable of your choice!

 

106% = 1.06. The expression to represent the sale price is 1.06p.

Expression 2

100% + 6% = 106%

 

For Expression 2, convert the left side of the equation to decimals and place it inside parentheses. Put the variable of your choice outside the parentheses to show multiplication.

 

100% + 6% is 1 + 0.06 when converted to decimals. The expression to represent the sale price is p(1 + 0.06).

Expression 3

100% + 6% = 106%

 

Expression 3 is simply Expression 2 but simplified. Using the distributive property, we can go from p(1 + 0.06) to 1p + 0.06p. Many times we do not write the 1, so you may see it written as

p + 0.06p.

PRACTICE. For each situation, write 3 expressions to represent the sale price or final amount.

Open Ended

Caleb left 20% tip on his meal. Write an expression to represent the total amount he spent.

EXPRESSION 1:

EXPRESSION 2:

EXPRESSION 3:

Open Ended

Kyla bought a backpack that was marked up 12%. Write an expression to represent the sale price of the backpack.

EXPRESSION 1:

EXPRESSION 2:

EXPRESSION 3:

Open Ended

When Demetrius bought groceries, he had to pay 7% sales tax. Write an expression to represent the sale price of the groceries.

EXPRESSION 1:

EXPRESSION 2:

EXPRESSION 3:

Open Ended

Shane bought a couch and sold it for 45% more than he paid. Write an expression to represent the sale price of the couch.

EXPRESSION 1:

EXPRESSION 2:

EXPRESSION 3:

Open Ended

Morgan noticed the cost of apples has increased by 60%. Write an expression to represent the current apple price.

EXPRESSION 1:

EXPRESSION 2:

EXPRESSION 3:

Open Ended

CONCLUSION

What are some clues that you’ll have to ADD the percentage?