Challenge your understanding of ratios and proportions with these straightforward questions designed to reinforce essential math skills, featuring real-life examples for practical learning and exam preparation.
If there are 8 apples and 12 oranges in a basket, what is the simplest form of the ratio of apples to oranges?
Explanation: The ratio of 8 apples to 12 oranges simplifies by dividing both numbers by their greatest common factor, which is 4, resulting in 2:3. The option 3:2 reverses the quantities, which is incorrect. Option 4:5 is incorrect as it does not represent the simplified ratio. Option 8:12 is the original, unsimplified ratio.
A car travels 120 kilometers in 2 hours. What is the ratio of distance to time in its simplest form?
Explanation: Dividing 120 km by 2 hours gives 60 km per 1 hour, so the simplest ratio is 60:1. Option 60:2 does not simplify the ratio, while 120:2 is just the original numbers. Option 2:120 reverses the order and is not correct for distance to time.
If 3 candies cost $6, how much would 5 candies cost at the same rate?
Explanation: The cost per candy is $6 divided by 3, which is $2; multiplying by 5 candies, the cost is $10. Option $9 is not correct, as it would suggest an incorrect rate. $11 and $8 are close but do not match the calculated amount.
Which of the following ratios is equivalent to 4:6?
Explanation: Simplifying 4:6 by dividing both by 2 gives 2:3, making it equivalent. Option 3:2 reverses the numbers, changing the relationship. Option 8:10 is not a correct simplification or multiple, and 6:4 reverses the terms.
A recipe calls for 2 cups of flour for every 5 cups of water. If you use 10 cups of water, how many cups of flour do you need?
Explanation: The ratio is 2:5, so for every 10 cups of water (which is twice the original), double the flour, resulting in 4 cups. Option 5 incorrectly matches water with flour. Option 2 uses the original flour amount, and 6 is unrelated to the proportion.
Which of these ratios is not equivalent to 3:9?
Explanation: 3:9 simplifies to 1:3. Options 2:6 and 6:18 both simplify to 1:3, making them equivalent. Option 9:6 simplifies to 3:2, which is different. Thus, 9:6 is not equivalent to 3:9.
If 6 pencils cost $12, what is the cost of 1 pencil?
Explanation: Dividing $12 by 6 gives $2 per pencil. Option $6 is the total for six pencils. Option $3 would be correct only if 4 pencils cost $12 instead. Option $1 is too low for this scenario.
The ratio of red to blue marbles is 1:4. If there are 8 red marbles, how many blue marbles are there?
Explanation: If 1 red corresponds to 4 blue, then 8 red marbles correspond to 8 times 4, which is 32 blue marbles. Option 16 is half the number needed, 4 matches the original single unit, and 12 does not match the ratio.
Sarah mixes a drink that requires the ratio of juice to water to be 3:7. If she uses 21 cups of water, how many cups of juice does she need?
Explanation: For every 7 cups of water, there are 3 cups of juice; so 21 water divided by 7 equals 3, then 3 times 3 equals 9 cups of juice. Option 30 is too high, 7 would only match the water's original unit, and 3 does not scale with the problem.
A mixture is made by combining rice and beans in a ratio of 5:2. If the total mixture weighs 35 kilograms, how many kilograms of beans are there?
Explanation: There are 5 parts rice and 2 parts beans, so 7 total parts. Each part is 35 divided by 7, which is 5 kilograms. Therefore, beans are 2 parts, or 2 times 5, giving 10 kg. Option 25 is the rice only, 14 is for reverse proportions, and 5 is just one part.