250 word response to each question - JustAnswer



250 word response to each question.

Question 1.

Describe a simple process for using rates and unit prices that might help someone who is having difficulty understanding these concepts. Include an example to explain the solution process.

A rate is used to compare two measurements of different quantities. It is the same as a fraction or a ratio, but instead of just having a numerator divided by a denominator, you also include the units and say “per”. Common examples of rates in everyday life are miles per gallon (fuel efficiency), dollars per gallon (gas prices), and miles per hour (speed). To calculate a rate, you use the first unit (before the per) as the numerator, and the second unit (after the per) as the denominator. So if you can drive from one city to another in 5 hours, and you know that the two cities are 300 miles apart, then to get miles per hour you divide the miles by the hours. 300 miles / 5 hours = 60 miles per hour, which is the average speed you drove.

Unit prices work the same way, but you use the money as the numerator and the unit as the denominator. That tells you how much you pay for each unit, like a pound or a single item. If you can buy corn on the cob for $3.00 for 10 ears, then how much does each ear cost? You divide the money ($3.00) by the units (10 ears). It can be easier to convert the dollars into cents first. $3.00/10 ears = 300 cents / 10 ears = 30 cents/ear, which is what the corn costs. That lets you compare different deals.

Question 2.

Describe an application for the use of ratios or proportions that is not mentioned in the text, or describe how an application problem in the text could be useful in your daily life.

I can use proportions for dividing up the check when I go out with my friends. Sometimes I eat out with a group, and everyone doesn’t have the same thing. It doesn’t seem fair that we should all split the tip equally. If we had a calculator, we could figure out the proportion of the bill that each person spent. Then we could use the same proportion for the tip. If I am with 4 friends but all I have is a Coke, then my part of the bill might be $2.00 out of a $50 bill. The proportion is $2/$50 = 1/25. If we leave a $10 tip, then we shouldn’t have divide it up 5 ways. Instead, we can use the proportion to find 1/25 of $10, which is 1000 cents/25 = 40 cents. If we figure out everyone’s proportion of the bill and get them to pay the right amount of the tip, then it should all add up to $10 and is more fair. I can use the same technique for figuring out how much of the utility bills I should pay to my housemates. We all pay different rents because the rooms are different sizes and we all moved in at different times. Our rent is $700 but I only pay $150, which is 150/700 or 3/14. I should be paying 3/14 of the electric bill and the local phone bill, too.

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