10/30/14 Warm up Adding Tax to Cost How much change will you get when buying a sweater for $29.95...
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Transcript of 10/30/14 Warm up Adding Tax to Cost How much change will you get when buying a sweater for $29.95...
![Page 1: 10/30/14 Warm up Adding Tax to Cost How much change will you get when buying a sweater for $29.95 plus 8.5% sales tax and paying with forty dollars?](https://reader035.fdocuments.net/reader035/viewer/2022070407/56649e395503460f94b2ad3c/html5/thumbnails/1.jpg)
10/30/14 Warm up Adding Tax to Cost
How much change willyou get when buying a
sweater for $29.95plus 8.5% sales tax
and paying with fortydollars?
![Page 2: 10/30/14 Warm up Adding Tax to Cost How much change will you get when buying a sweater for $29.95 plus 8.5% sales tax and paying with forty dollars?](https://reader035.fdocuments.net/reader035/viewer/2022070407/56649e395503460f94b2ad3c/html5/thumbnails/2.jpg)
Adding Tax to Cost First I will change the 8.5% sales tax into a decimal.
* Move the decimal 2 places to the left. = .085
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Adding Tax to Cost Next I will use the sales tax as a decimal and multiply it by $29.95 to find out the extra cost for the tax. (I will round the product to the hundredths place)
2 9. 9 5
X .0 8 5
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Adding Tax to Cost Then I will add the tax to $29.95 to get the total cost of the sweater.
$29.95+$2.55
$32.50 Total Cost to buy sweater
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Adding Tax to Cost Last I will subtract the total cost of the sweater by the forty dollars used to pay for the sweater, to find out how much change I would receive.
$40.00 -$32.50
$7.50 Change you will receive
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RATIO: a comparison of _____________________
Equivalent Ratios: Two ratios that name the same product. The __________
of equivalent ratios are equal
You should knowRatio can be
written ____ ways1.________2._______3.________
Examples: 1. Four Black Dogs
out of 15 dogs2. Write
Equivalent ratio for:
10:135 to 7
PROPORTION: an equation which
sets__________________________
CROSS PRODUCT: found by _________ the denominator of each
ratio by the ___________ of the other.
You should know…..When solving
proportions, set up an equation using
______________________________________________
_____
EXAMPLES: 5 = x 8 206 = x9 15Eighteen roses cost $25. What is the cost of 27 roses?
RATE: Compares two quantities measured in
______________.
You should know…..UNIT RATE: the rate for
______ unit of a given quantity
EXAMPLES:Find the unit rate
$205 lbs525 candy bars 15 children324 miles12 gallons
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Answers Ratios and Equivalent Ratios
RATIO: a comparison of two similar quantitiesEquivalent Ratios: Two ratios that name the same
product. The cross product of equivalent ratios are equal
You should know…Ratio can be written 3 ways
1. 1/22. 1 to 2 3. 1 :2
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Examples: 1.Four Black Dogs out
of 15 dogs2.Write Equivalent
ratio for: 10:13 =5 to 7 = =
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• Vocabulary • PROPORTION: an equation which
sets two ratios equal • CROSS PRODUCT: found by
multiplying the denominator of each ratio by the numerator of the other
• You should know….• When solving proportions, set up an
equation using equivalent cross products.
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EXAMPLES: 5 = x 8 206 = x9 15Eighteen roses cost $25. What is the cost of 27 roses?
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• Vocabulary • RATE: Compares two quantities
measured in different labels.
• You should know…
•UNIT RATE: the rate for 1 unit of a given quantity (the second one)
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EXAMPLES:Find the unit rate
$20 5 lbs525 candy bars 15 children324 miles12 gallons
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10/29/14 Warm up UNIT RATES
1/400 and 0.0025
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Unit Rates
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Rates
A rate is a comparison of two different units, such as miles per hour, or two different things measured with the same unit, such as cups of concentrate per cups of water.
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What is a unit rate?
A unit rate tells the price of one item.
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Johnny spend $75 on 15 hamburgers. At this rate, how much does 1 hamburger cost?
Would it make sense for 1 hamburger to cost $75? Why? (*Hint- do not just say $75 is too much for a hamburger. )
+ = $75 = ??
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Johnny spend $75 on 15 hamburgers. At this rate, how much does 1 hamburger
cost?
Why wouldn’t it make sense for 1 hamburger to cost $1?
=$75 = 1?? NOOO!
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Johnny spend $75 on 15 hamburgers. At this rate, how much does 1 hamburger
cost?
Should you add, subtract, multiply, or divide to solve the problem in yellow? WHY?
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Johnny spend $75 on 15 hamburgers. At this rate, how much does 1 hamburger
cost?
1. Solve the problem above. Show your work.
+ = $75 = ?????
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The answer…
$75 ÷ 15 = $5 per every 1 hamburger
That means we took all of our money ($75) and split it evenly. Each hamburger was $5.
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If each hamburger costs $5, how much do 15 hamburgers cost? What are some different ways
you can find out?
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It takes Mary 12 minutes to play 3 songs on her piano. How many
minutes long is 1 song?
2. Solve the problem in yellow. Show your work.
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The answer….
12 ÷ 3 = 4 minutes per every song
That means we took all of the minutes she played (12 minutes) and split it evenly. Each song was 4 minutes.
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So far you have found unit rates.
A Unit Rate is the ratio of two measurements in which the second term is 1.
$5_____ 4 minutes 1 burger 1 song
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This is what we were actually solving….
$75______ = $5___15 burgers 1 burger
How did we get from 15 to 1 on the bottom?What did we divide by?How did we get from $75 to $5 on the top?What did we divide by?
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This is actually what we were solving….
12 minutes = 4 minutes3 songs 1 song
How did we get from 3 to 1 on the bottom?What did we divide by?How did we get from $12 to $4 on the top?What did we divide by?
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But…..sometimes you have to do more than just divide
to find an answer.
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For example…..
Johnny spend $75 on 15 hamburgers. At this rate, how much does 20 hamburgers cost?
- Just dividing will not work. - Let’s find out why…..
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Soooo…..
$75__________ = ___x_________ 15 hamburgers 20 hamburgers
Look at the ratios above. The x means that we do not know what number goes there yet. Remember you have to multiply or divide to find equivalent ratios. So, I cannot add 5 on the bottom and add 5 on the top. I have to multiply or divide.
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We know that if Johnny paid $75 for 15 hamburgers each hamburger costs $5. So how
much would 20 burgers cost?
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$75______ = $100____ 15 burgers 20 burgers
Where did the $100 come from?
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Now, let’s find out how to solve a proportion without pictures.
$75______ = __x_____15 burgers 20 burgers
The x means we are trying to find out what number goes there. We already know that $100 goes there. Let’s solve this proportion without pictures.
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$75__________ = $5 per burger15 hamburgers
If we want to know how much 20 burgers would cost, what should we multiply?
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If we want to know how much 20 burgers would cost, what should we multiply?
We should multiply 20 burgers times $5 per burger which gives us $100 for 20 burgers.$75______ = $100____ 15 burgers 20 burgers
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Cross multiplying is exactly what it sounds like. You multiply the numbers that are across from
each other.$75______ = __x_____15 burgers 20 burgers
$75 times 20 = 1,50015 times x = 15x
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$75 times 20 = 1,50015 times x = 15x1,500 = 15xDivide both sides by the number with the letter beside it.1,500 divided by 15 =15 divided by 15=So, x =
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We still get
$75______ = $100_ 15 burgers 20 burgers
$75____÷ 15 = $5__ 15 burgers ÷15 1 burger
$100____÷20 = $5__20 burgers ÷20 1 burger
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Exit Rate?
•A factory can produce small wheels for the mousetrap cars at a rate of 18,000 wheels in 3 hours. What is the unit rate per hour?
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Rate?
• A factory can produce small wheels for the mousetrap cars at a rate of 18,000 wheels in 3 hours. What is the unit rate per hour?• 18,000 ÷ 3 = 6,000 = 6,000 wheels • 3 ÷ 3 = 1 per hour•