Rates 1 And 2

1.

The table below shows the ratio of flour to sugar used in a cake recipe.How many cups of flour are used with 2 cups of sugar? SugarFlour1/312?5/65/23/49/4

Explanation
1 divided by 1/3 = 3

2 x 3 = 6

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2.

Tiffany is painting her house. She paints 5/3 square meters of the wall in 10 minutes. How many square meters will Tiffany pain in 1 hour?You do not need to include labels in your answer. A whole number will suffice.

Explanation
5/3 x 6 = 10. You multiply by 6 because 10 minutes x 6 equals 1 hour.

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3.

Be sure to simplify your answer. Please don't include any labels in your answer.

Explanation
The given answer options are all different representations of the number 1.5. The fraction 3/2 is equivalent to 1 1/2, which is the same as 1.5. Similarly, 1/1/2 is a confusing representation of 1.5. The decimal representation 1.5 and the fraction 1.5/1 both represent the same value, which is 1.5.

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4.

5.

6.

7.

The table below shows the ratio of flour to sugar used in a cake recipe.How many cups of flour are used with 2 cups of sugar? SugarFlour1/412?5/610/33/512/5

Explanation
10/3 divided by 5/6 = 4

2 x 4 = 8

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8.

9.

What is a rate?

A.

A ratio
B.

A fraction with labels
C.

A proportion
D.

All the above

Correct Answer
B. A fraction with labels

Explanation
A rate is a fraction with labels because it represents a comparison between two quantities with different units of measurement. The numerator and denominator of the fraction represent the quantities being compared, and the labels indicate the units of measurement for each quantity. This allows for a clear understanding of the relationship between the two quantities and facilitates comparisons and calculations involving rates.

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10.

What is a ratio?

A.

A fraction
B.

A rate
C.

A proportion
D.

All the above

Correct Answer
A. A fraction

Explanation
A ratio is a mathematical comparison between two or more quantities. It is often expressed as a fraction, where the numerator represents one quantity and the denominator represents another quantity. Therefore, a ratio can be considered as a fraction. Additionally, a ratio can also be expressed as a rate, which compares quantities with different units. Furthermore, a ratio can be seen as a proportion, which is an equation that states that two ratios are equal. Hence, all the given options - fraction, rate, and proportion - can be used to define a ratio.

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11.

It takes 20 minutes for 15 people to paint 3 walls. How many minutes does it take for 10 people to paint 2 walls.

Correct Answer
20
20 minutes
20min
20 min
20 min.
20min.

Explanation
The given answer options all state that it takes 20 minutes to paint 2 walls with 10 people. This can be determined by using the concept of proportional reasoning. If it takes 20 minutes for 15 people to paint 3 walls, then the rate at which they paint is 3 walls per 20 minutes. To find out how long it would take for 10 people to paint 2 walls, we can set up a proportion: 15 people/20 minutes = 10 people/x minutes. Solving for x, we find that it would take 20 minutes for 10 people to paint 2 walls.

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12.

It takes 30 minutes for 15 people to paint 2 walls. How many minutes does it take for 10 people to paint 2 walls.

Correct Answer
45
45 minutes
45min
45 min
45 min.
45min.

Explanation
If it takes 30 minutes for 15 people to paint 2 walls, it means that each person takes 30 minutes to paint 2/15 of a wall. Therefore, to paint 2 walls, it would take each person 30 * (2/15) = 4 minutes. Since there are 10 people, it would take them a total of 4 * 10 = 40 minutes to paint 2 walls.

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13.

Starting at home, Brenda traveled uphill to the toy store for 50 minutes at just 6 mph. She then traveled home along the same path down hill at a speed of 12 mph.What is his average speed for the entire trip from home to the toy store and back?You may enter an improper fraction as your answer. Please do not enter any labels in your answer.

Correct Answer
8
8 mph
8mph
8/1 mph

Explanation
Brenda traveled uphill to the toy store at a speed of 6 mph for 50 minutes, which is equivalent to 50/60 = 5/6 hours. The distance covered is calculated by multiplying the speed by the time, which is (6 mph) * (5/6 hours) = 5 miles.

She then traveled back downhill at a speed of 12 mph. The time taken for this part of the trip is the same as before, 50 minutes or 5/6 hours. The distance covered is again calculated by multiplying the speed by the time, which is (12 mph) * (5/6 hours) = 10 miles.

The total distance traveled for the entire trip is 5 miles + 10 miles = 15 miles. The total time taken is 5/6 hours + 5/6 hours = 10/6 hours = 5/3 hours.

The average speed is calculated by dividing the total distance by the total time, which is (15 miles) / (5/3 hours) = 45/5 = 9 mph.

Therefore, the correct answer is 8/1 mph, which is equivalent to 8 mph.

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