Ratio

Last Updated: 11 December 2023, Monday

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Ratio
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Ratio

Ratios are fundamental mathematical expressions used to compare and relate quantities in various contexts. They are used to establish proportional relationships, make comparisons, and analyze the relative sizes of different quantities. Ratios are expressed as a fraction, often written as “a:b” or “a to b,” where “a” and “b” represent two different quantities or values. These values could be numbers, measurements, or any data points that can be quantified.

Here are some key aspects of ratios:

  1. Comparing Quantities: Ratios are primarily used to compare the size or magnitude of one quantity in relation to another. For example, if you want to compare the number of boys to girls in a classroom, you might express the ratio as “5:3,” meaning there are 5 boys for every 3 girls.
  2. Simplification: Ratios can be simplified by dividing both terms by their greatest common factor. For example, if you have a ratio of 6:8, you can simplify it to 3:4 by dividing both numbers by 2.
  3. Proportions: Ratios can be used to create proportions. A proportion is an equation that states two ratios are equal. For example, if you have the ratios 2:3 and 4:6, you can set up the proportion (2/3) = (4/6).
  4. Scaling: Ratios can be used to scale up or down quantities. If you have a recipe that serves 4 people but you want to serve 8, you can use the ratio of 4:8 to adjust the quantities of ingredients.
  5. Percentages: Ratios are often used to express percentages. For example, a ratio of 3:5 can be converted to a percentage by dividing the first number (3) by the sum of both numbers (3 + 5), which equals 0.375 or 37.5%.
  6. Financial Analysis: In finance, ratios are essential for evaluating a company’s financial health and performance. Common financial ratios include the debt-to-equity ratio, price-to-earnings ratio, and current ratio, among others.
  7. Questions

Questions

Ratios Questions

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Question: The ratio of sugar to flour in a cake recipe is 1:2 . If 300 grams of flour is used , how much sugar is required?

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Question: A school’s student to teacher ratio is 20:1 . If there are 400 students, how many teachers are there?

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Question: A mixture has oil and vinegar in the ratio 3:1 . How much vinegar is there in 400 ml of mixture?

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Question: The sides of a rectangle are in the ratio 3:2 . If the longer side is 18cm , what is the length of shorter side?

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Question: A car’s fuel efficiency is 15 Km per litre. How many litres of fuel are needed for a 225 Km journey?

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Question: In a bag of red , blue and green marbles , the ratio of red to blue to green marbles is 2:3:5 . If there are 40 green marbles , how many blue marbles are there?

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Question: If the ratio of apples to oranges in a basket is 3:2 and there are 15 apples , how many oranges are there?

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Question: A recipe requires flour and sugar in the ratio 4:1 . If 200 grams of flour are used , hoe much sugar is needed?

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Question: In a class , the ratio of boys to girls is 5:4 . If there are 20 girls how many boys are there?

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Question: A map scale is 1:100000 . What distance on the map represents a real distance of 5 kilometres?

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Question: If a recipe requires a ratio of 3 parts water to 2 parts milk , which of these combinations would maintain the correct ratio?

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Question: A school’s teacher to student ratio is 1:30 . If there are 180 students , how many teachers should there be?

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Question: If the ratio of boys to girls in a class is 3:2 , which of the following can be the total number of students in the class?

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Question: A map scale shows a ratio of 1:100,000 . What does this mean?

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Question: The ratio of water to cement in a mixture is 2:3 . Which of the following are possible quantities for the mixture?

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Question: In a ratio 7:5 , if the sum of both terms is 48 , what are the values of the two terms?

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Question: The ratio of red balls to blue balls in a bag is 5:4 . If there are 45 balls in total , how many red and blue balls could there be?

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Question: If the ratio of the lengths of the sides of a rectangle is 2:1 , which of these could be the dimensions of the rectangle?

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Question: In a fruit salad , the ratio of apples to oranges to bananas is 3:2:5 . If there are 40 fruits in total , how many apples and oranges are there?

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Question: The ratio of sugar to flour in a recipe is 1:4 . Which of these amounts could be used in the recipe?

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