7th Math: Ratios & Proportional Reasoning

John eats a bowl of cereal for 3 of his 4 meals each day. He finishes two gallons of milk in eight days. How much milk does John use for one bowl of cereal? (Assume he only uses the milk for his cereal.)

Answer explanation

John eats cereal 3 times a day for 8 days, totaling 24 bowls. He uses 2 gallons of milk, which is 256 ounces. Dividing 256 ounces by 24 bowls gives approximately 10.67 ounces of milk per bowl of cereal.

Mary uses one third of a gallon of gasoline driving back and forth to work every day. How much gasoline does she use in 30 days?

Answer explanation

Mary uses 1/3 gallon per day. In 30 days, she uses 30 * (1/3) = 10 gallons of gasoline.

A recipe to make a cake calls for three-fourths of a cup of milk. Mary used this cake as the first layer of a wedding cake. The second layer was half the size of the first layer, and the third layer was half the size of the second layer. How much milk would be used for the entire wedding cake?

Answer explanation

The first layer uses 3/4 cup of milk. The second layer is half, so 3/8 cup. The third layer is half of the second, so 3/16 cup. Total milk = 3/4 + 3/8 + 3/16 = 12/16 + 6/16 + 3/16 = 21/16 cups.

One third of a quart of paint covers one fourth of a basketball court. How much paint does it take to paint the entire basketball court?

Answer explanation

If one third of a quart covers one fourth of a court, then to cover the whole court, you need 3 times that amount of paint. Thus, it takes 3 times one third of a quart, which equals 1 quart to paint the entire basketball court.

If a vehicle is traveling at a constant rate, and it takes 1.5 hours to travel 97.5 miles, how long does it take to travel 130 miles?

Answer explanation

The vehicle's speed is 65 mph (97.5 miles / 1.5 hours). To find the time for 130 miles, use time = distance/speed. Thus, time = 130 miles / 65 mph = 2 hours.

The following table shows two variables in a proportional relationship: x y 2 6 3 9 4 12 What is the constant of proportionality?

Answer explanation

To find the constant of proportionality, divide y by x for any pair. For example, for x=2 and y=6, 6/2=3. This is consistent for all pairs (3,9) and (4,12), confirming the constant of proportionality is 3.

Does the graph show a proportional relationship?

Answer explanation

A proportional relationship is characterized by a constant ratio between two variables. If the graph is a straight line passing through the origin, it indicates a proportional relationship. Check if this is the case.

The following table shows two variables in a proportional relationship: x y 4 8 5 10 6 12 What is the constant of proportionality?

Answer explanation

To find the constant of proportionality, divide y by x for any pair. For example, 8/4 = 2, 10/5 = 2, and 12/6 = 2. Thus, the constant of proportionality is 2.

If the ratio of the length of a rectangle to its width is 3 to 2, what is the length of a rectangle whose width is 4 inches?

Answer explanation

The ratio of length to width is 3:2. If the width is 4 inches, we can set up the equation: length = (3/2) * width = (3/2) * 4 = 6 inches. Thus, the length of the rectangle is 6 inches.

Does the graph show a proportional relationship?

Answer explanation

A proportional relationship is shown by a straight line through the origin. If the graph is linear and passes through (0,0), it indicates a proportional relationship. Check if the line meets these criteria.