Shopping: Tax
Situation: You are purchasing four items and want to calculate the tax. The items
cost $2.50, $8.75, $3.00, and $10.25. The tax rate is 6%. How much is the tax?
Calculation With Distribution
(Show all steps.)
Calculation Without Distribution
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I think is easier: to distribute. to not distribute.
Why I Think it is Easier
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Mental Math
Situation: You exercised 24 hours each month for a year. How many hours did you
exercise by the end of the year? You may be able to do the math mentally thanks
to expanded notation and the Distributive Property.
Calculation With Distribution
(Show all steps.)
Calculation Without Distribution
(Show all steps.)
I think is easier: to distribute. to not distribute.
Why I Think it is Easier
© 2015 Connections Education LLC. All rights reserved. 5
Multiplying by a Negative Number
Situation: Find the value of this integer expression: 2( 3 4 8 7) −+ − − + +++ .
Calculation With Distribution
(Show all steps.)
Calculation Without Distribution
(Show all steps.)
I think is easier: to distribute. to not distribute.
Why I Think it is Easier
© 2015 Connections Education LLC. All rights reserved. 6
Multiplying and Adding Fractions
Situation: Find the value of this fraction computation:
123 6
234
+ +
.
Calculation With Distribution
(Show all steps.)
Calculation Without Distribution
(Show all steps.)
I think is easier: to distribute. to not distribute.
Why I Think it is Easier
© 2015 Connections Education LLC. All rights reserved. 7
Geometry formulas
Situation: Find the perimeter of a rectangular area with a length of 13 inches and
a width of 7 inches.
Calculation With Distribution
(Show all steps.)
Calculation Without Distribution
(Show all steps.)
I think is easier: to distribute. to not distribute.
Why I Think it is Easier
© 2015 Connections Education LLC. All rights reserved. 8
Original Example
Give an original example of a situation in which the Distributive Property could be
used.
Situation
Calculation With Distribution
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Calculation Without Distribution
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9
I think is easier: to distribute. to not distribute.
Why I Think it is Easier
here are the answers:.06(2.50 + 8.75 + 3.00 + 10.25)
= .06(2.50) + .06(8.75) + .06(3.00) + .06(10.25)
= 24.50 then subtract 25.97-24.50=1.47
1.47 is what you saved! The first one was distribute the next is not distribute
2.50+8.75+3.00+10.25=24.50
24.50*1.06=25.97
25.97-24.50=1.47
Then you saved 1.47
Sorry guys looks like I'm a few years behind lol! If you every need me again remember all you have to say #lost I will be here waiting :)
I meant few years late lol
try just posting a problem without copying all the surrounding text, eh?
Don't make us figure out the question as well as the answer. Clean it up and post it again. Maybe just one question. Learn from its solution and try more on your own.
Im doing this right now and need help :(
#lost I need your help with this one Multiplying and Adding Fractions
Situation: Find the value of this fraction computation:
123 6
234
+ +
.
Calculation With Distribution
(Show all steps.)
Calculation Without Distribution
(Show all steps.)
Please help
To calculate the tax on the four items, you can either distribute the tax rate to each item individually or not distribute the tax rate and calculate it at the end.
Calculation with Distribution:
1. Multiply each item's cost by the tax rate (6%) to get the tax amount for each item.
- Item 1: $2.50 x 0.06 = $0.15
- Item 2: $8.75 x 0.06 = $0.525
- Item 3: $3.00 x 0.06 = $0.18
- Item 4: $10.25 x 0.06 = $0.615
2. Add all the tax amounts together to get the total tax.
- Total Tax = $0.15 + $0.525 + $0.18 + $0.615 = $1.47
Calculation without Distribution:
1. Add up all the item costs to get the total cost.
- Total Cost = $2.50 + $8.75 + $3.00 + $10.25 = $24.50
2. Multiply the total cost by the tax rate (6%) to get the total tax.
- Total Tax = $24.50 x 0.06 = $1.47
In this case, it is easier to distribute the tax rate because you can calculate the tax amount for each item separately and then add them together to get the total tax. This method can be more accurate if you need to keep track of the tax amount for each item.
For mental math, the choice of distributing or not depends on the specific numbers and how easy they are to work with mentally. You can choose the method based on whether it simplifies the calculation or makes it easier to mentally manage the numbers.
Similarly, for the other examples mentioned (multiplying by a negative number, multiplying and adding fractions, and finding the perimeter of a rectangular area), whether to distribute or not distribute depends on the specific situation and the numbers involved.
For the original example of a situation where the Distributive Property could be used, let's consider finding the cost of purchasing multiple items with different prices and quantities. For example, suppose you bought 3 pens at $1.50 each and 5 notebooks at $2.00 each. You can use the Distributive Property to calculate the total cost as follows:
Calculation with Distribution:
1. Multiply the cost of each item by its quantity.
- Pens: 3 x $1.50 = $4.50
- Notebooks: 5 x $2.00 = $10.00
2. Add the costs of all the items together to get the total cost.
- Total Cost = $4.50 + $10.00 = $14.50
Calculation without Distribution would involve adding the costs of each item separately without using the Distributive Property.
In this specific example, distributing the quantities to the prices allows for a more organized and systematic calculation of the total cost. Therefore, using the Distributive Property is easier in this case.