Understanding Ratios and Percentages

What is the ratio of 3 red marbles to 9 blue marbles?

• 1:2

• 1:3

• 3:1

• 3:9

Answer explanation

The ratio of red marbles to blue marbles is 3:9. To simplify, divide both numbers by 3, resulting in 1:3. Therefore, the correct answer is 1:3.

If a shirt costs $50 and is on sale for 20% off, what is the sale price?

• $10

• $30

• $40

• $45

Answer explanation

To find the sale price, calculate 20% of $50, which is $10. Subtract this discount from the original price: $50 - $10 = $40. Therefore, the sale price is $40.

What is 25% of 200?

• 25

• 50

• 75

• 100

Answer explanation

To find 25% of 200, multiply 200 by 0.25. This gives 200 * 0.25 = 50. Therefore, the correct answer is 50.

A recipe requires 2 cups of sugar for every 5 cups of flour. What is the ratio of sugar to flour?

• 2:5

• 5:2

• 1:2

• 2:1

Answer explanation

The recipe states that for every 5 cups of flour, 2 cups of sugar are used. This establishes a ratio of sugar to flour as 2:5, making the correct answer 2:5.

• 25%

• 50%

• 75%

• 100%

Answer explanation

To convert the fraction \(\frac{3}{4}\) to a percentage, multiply by 100. \(\frac{3}{4} \times 100 = 75\%\). Therefore, the correct answer is 75\%.

If a car travels 150 kilometres in 3 hours, what is its average speed in kilometres per hour?

• 30 km/h

• 50 km/h

• 60 km/h

• 75 km/h

Answer explanation

To find the average speed, divide the distance by the time. Here, 150 km ÷ 3 hours = 50 km/h. Therefore, the average speed of the car is 50 km/h.

What is the percentage increase from 40 to 50?

• 10%

• 20%

• 25%

• 50%

Answer explanation

To find the percentage increase from 40 to 50, use the formula: ((new value - old value) / old value) * 100. Here, ((50 - 40) / 40) * 100 = (10 / 40) * 100 = 25%. Thus, the correct answer is 25%.

If 60% of a number is 24, what is the number?

• 36

• 40

• 50

• 60

Answer explanation

To find the number, set up the equation: 0.6x = 24. Dividing both sides by 0.6 gives x = 24 / 0.6 = 40. Thus, the number is 40.

A school has 120 students, and 30 of them are in Grade 6. What percentage of the students are in Grade 6?

• 15%

• 20%

• 25%

• 30%

Answer explanation

To find the percentage of students in Grade 6, divide the number of Grade 6 students (30) by the total number of students (120) and multiply by 100. (30/120) * 100 = 25%. Thus, 25% of the students are in Grade 6.

What is the ratio of 8 to 12 in simplest form?

• 2:3

• 3:2

• 4:3

• 3:4

Answer explanation

To simplify the ratio of 8 to 12, divide both numbers by their greatest common divisor, which is 4. Thus, 8 ÷ 4 = 2 and 12 ÷ 4 = 3, giving the simplest form of the ratio as 2:3.