Ratios and Unit Conversion

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Questions and Answers

Explain the process of converting ounces to kilograms, and then kilograms to grams. Why is it important to understand both conversions?

To convert ounces to kilograms, divide the number of ounces by 35 (since 1 kilogram is approximately 35 ounces). To convert kilograms to grams, multiply the number of kilograms by 1000. Understanding both conversions is essential for working with different units of measurement in various contexts.

If Mai and Priya continue traveling at their respective speeds, how much farther will Mai travel than Priya after 30 seconds?

Mai travels 2.5 meters per second, and Priya travels 2.2 meters per second. After 30 seconds, Mai will have traveled 75 meters, while Priya will have traveled 66 meters. Therefore, Mai will have traveled 9 meters farther than Priya.

A vendor decides to sell 5 pints of raspberries for $18.00. How does this price per pint compare to the farm's price, and what is the percentage difference?

The farm's price is $4.00 per pint. The vendor's price is $3.60 per pint. The percentage difference is 10% ($0.40/$4.00).

If the kangaroo maintains the same hopping rate, how long would it take to travel 8 kilometers? Show your reasoning.

Since the kangaroo travels 2 kilometers in 3 minutes, its speed is 2/3 kilometers per minute. To travel 8 kilometers, it would take 8 / (2/3) = 12 minutes. Signup and view all the answers

If Han increases his pace to 10 minutes per mile, how much time will he save in running 5 miles?

Currently, Han runs at 12 minutes per mile, so it takes him 60 minutes to run 5 miles. If he runs at 10 minutes per mile, it would take him 50 minutes. Thus, he would save 10 minutes. Signup and view all the answers

By converting all the weight measurements to pounds, explain how you can accurately order the items from heaviest to lightest.

First, convert all weights to pounds: School bus (18,000 lbs), Horse (1,100 lbs), Elephant (12,100 lbs), Grand Piano (990 lbs). Then, arrange them from heaviest to lightest based on these pound values: school bus, elephant, horse, grand piano. Signup and view all the answers

If Mai attempted 50 free throws instead of 40, and her success rate remained at 25%, how many successful free throws would she make?

If Mai attempts 50 free throws, and her success rate is 25%, she would make 50 * 0.25 = 12.5 free throws. Since she can't make half a free throw, we would expect her to make approximately 12 or 13. Signup and view all the answers

If Priya wanted to make 20 free throws today, what percentage more than yesterday’s 12 free throws would she need to make?

Priya would need to make 8 more free throws. This would require $8/12 = .6666 = 66.66%$ more free throws. Signup and view all the answers

If the school band also includes 10% fifth graders and 5% teachers, what percentage of the band members are not sixth, seventh, or eighth graders?

If 10% are fifth graders and 5% are teachers, then 10% + 5% = 15% of the band members are not sixth, seventh, or eighth graders. Signup and view all the answers

If the number 160 represents the total students at a school, and the number 40 represents students with a certain attribute, explain how one might determine what percentage of the school has this attribute. In your answer, explain the components of a percentage.

To determine the percentage of the school, you can use $\frac{part}{whole}=\frac{40}{160}=.25=25%$. A percentage is the proportion of of a certain attribute to the whole, multiplied by 100. Signup and view all the answers

If Han increased his piano practice time by 25% compared to the weekend, how many minutes did he practice additionally?

Han practiced for 75 minutes. A 25% increase is 75 * 0.25 = 18.75 minutes additionally. Signup and view all the answers

If the roller coaster height requirement was changed to 'You must be 45 inches tall to ride,' what percentage of the original 40-inch height is this new requirement?

This new requirement is 45 ÷ 40 = 1.125 = 112.5% of the original height. Signup and view all the answers

Explain how proportional reasoning can be applied to solve problems involving unit conversions, like converting ounces to kilograms.

Proportional reasoning sets up a relationship between two units, like 1 kilogram is to 35 ounces. You can then create equal ratios such as $1 \text{ kg} / 35 \text{ oz} = x \text{ kg} / y \text{ oz}$ and solve for the unknown to convert any number of ounces to kilograms. Signup and view all the answers

If a store increases the price of raspberries by 15% from the farm's rate, and then offers a 5% discount on bulk purchases (10 pints or more), how much would 12 pints cost?

The new price is $4.60 per pint because $41.15=4.6$. Then, since they are buying in bulk, the discounted rate is $4.37 per pint since $4.6.95=4.37$. Then, 12 pints would cost $52.44 since $12*4.37=52.44 Signup and view all the answers

If Han and Tyler start at the same point and run in the same direction, how far apart will they be after 45 minutes? Show your reasoning.

After 45 minutes, Han would have traveled 3.75 miles and Tyler would have traveled 3 miles. Therefore, they would be 0.75 miles apart. Signup and view all the answers

Suppose a heavier grand piano (20,000 ounces) replaces the original. How does this change affect the order from heaviest to lightest?

The grand piano becomes 1250 lbs (20000/16). With this new weight, the order changes to: grand piano, school bus, elephant, horse. Signup and view all the answers

If the band decides to increase its membership by 20%, and the percentages of sixth, seventh, and eighth graders remain the same, how many new sixth graders will there be?

With 70 members, the band wants to increase by 14 members. Then, out of that increase $0.4*14 = 5.6$. So, about 6 new sixth graders would then be in the band. Signup and view all the answers

In a different school, 200 students were surveyed. If 20% preferred one sport, 30% another, and the rest preferred a third sport, how many students preferred the third sport?

20% + 30% = 50% preferred one of the first two sports, so 50% preferred the third. This is 100 students total. Signup and view all the answers

If Tyler practices the clarinet 100% as much as Han practiced on the piano, how did his minutes change?

Then he practiced the same amount of time as Han, so 75 minutes long. Signup and view all the answers

If a child is 50 inches tall, what percentage over the height restriction of 40 inches is the child?

The child is 10 inches above the restriction, and the child is then %25 above the restriction because 10/40 = .25. Signup and view all the answers

Flashcards

Ounces to Kilograms Conversion

To change ounces to kilograms, divide by 35. 28 ounces is about 0.8 kilograms.

Calculating Speed

Speed is calculated by dividing the distance traveled by the time it took to travel that distance.

Cost Per Pint

To find the cost per pint, divide the total cost by the number of pints. Total cost / number of pints.

Pints Per Dollar

To find how many pints you can get per dollar, divide the total pints by the total cost. Total pints / total cost