Understanding Ratios and Their Applications
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Questions and Answers

What is a ratio?

A ratio is a way of comparing two or more similar quantities.

How are ratios written?

Ratios are written using whole numbers separated by colons, with no units.

What is the ratio of the length of a 1m model boat to a 25m actual boat?

1:25

In order to master the techniques explained in this text, it is vital that you undertake plenty of ______ exercises.

<p>practice</p> Signup and view all the answers

Which of the following can you do after reading this text?

<p>All of the above</p> Signup and view all the answers

If a model boat is 1m long and the real boat is 25m long, what is the ratio of the length of the model to the actual boat?

<p>1:25</p> Signup and view all the answers

What does a colon (:) represent in a ratio?

<p>The colon represents the word &quot;to&quot; in a ratio.</p> Signup and view all the answers

What is mortar for building a brick wall made of, in terms of its ratio?

<p>It's made of 2 parts cement to 7 parts of sand.</p> Signup and view all the answers

What is the ratio of 4 oz flour and 2 oz fat in its simplest form?

<p>2:1</p> Signup and view all the answers

What is the simplest form of the ratio 250:150?

<p>5:3</p> Signup and view all the answers

Ratios are normally expressed using decimal numbers.

<p>False</p> Signup and view all the answers

In a ratio, the units used for the numbers must be the same. If they are not, they should be converted to [blank] units.

<p>the same</p> Signup and view all the answers

A ratio is a way of comparing two or more ______ quantities.

<p>similar</p> Signup and view all the answers

Which of the following is a key point about ratios?

<p>All of the above</p> Signup and view all the answers

The ratio of girls to boys in a class is 15:12. What is the ratio in its simplest form?

<p>5:4</p> Signup and view all the answers

If Anna has 75 pence and Rashid has £1.20, what is the ratio of Rashid's money to Anna's money, in its simplest form?

<p>8:5</p> Signup and view all the answers

What is the total number of parts in the ratio 3:2:1?

<p>6</p> Signup and view all the answers

If a total of 12 m³ of concrete is divided into 6 parts according to a ratio, how much concrete does each part represent?

<p>2 m³</p> Signup and view all the answers

If 1 part in a ratio represents 2 m³, and gravel makes up 3 parts in the ratio, how much gravel is needed?

<p>6 m³</p> Signup and view all the answers

What is the ratio of gravel, sand, and cement in the concrete mixture?

<p>3:2:1</p> Signup and view all the answers

If we have 6 m³ of sand and an unlimited amount of the other ingredients, how much concrete can be made?

<p>18 m³</p> Signup and view all the answers

What is the ratio of garlic, chick peas, olive oil, and tahini paste for a houmous recipe for 6 people?

<p>2:4:4:5</p> Signup and view all the answers

If a houmous recipe for 6 people is scaled down for one person by dividing each number by 6, what is the new ratio for one person?

<p>1/3:2/3:2/3:5/6</p> Signup and view all the answers

If the ratio for one person is scaled up by multiplying each number by 9, what is the new ratio for 9 people?

<p>3:6:6:7.5</p> Signup and view all the answers

What is the value of 1 euro in pence if 1.65 euros is worth £1?

<p>100/1.65 pence</p> Signup and view all the answers

What is the value of 50 euros in pence?

<p>3030 pence</p> Signup and view all the answers

What is the value of 50 euros in pounds, to the nearest penny?

<p>£30.30</p> Signup and view all the answers

What is the actual distance between two points X and Y if the distance on a map is 8.5 cm and the map scale is 1:20,000?

<p>1700 m</p> Signup and view all the answers

What is the length of a living room on a scale drawing if its actual length is 13.7 meters and the scale is 1:100?

<p>13.7 cm</p> Signup and view all the answers

If 300 grams of minced beef are needed for a lasagna serving 5 people, how much minced beef is needed for 9 people?

<p>540 grams</p> Signup and view all the answers

There are 28 boys in a youth club where the ratio of boys to girls is 4:5. How many girls are there in the club?

<p>35</p> Signup and view all the answers

What is the value of 20 pounds in euros if 1 pound is worth 1.65 euros?

<p>33 euros</p> Signup and view all the answers

What is the value of 60 euros in pounds, to the nearest penny, if 1.65 euros is worth 1 pound?

<p>£36.36</p> Signup and view all the answers

If £150 is divided between Betty and Liz in the ratio of their ages, 12 years old and 3 years old, how much does each of them get?

<p>Betty receives £120 and Liz receives £30.</p> Signup and view all the answers

How do you divide 360° into three angles in the ratio 1:2:3?

<p>The angles are 60°, 120°, and 180°.</p> Signup and view all the answers

How much water is there in 5 kg of copper sulphate if it's made of 32 parts copper, 16 parts sulfur, 32 parts oxygen, and 48 parts water by weight?

<p>1875 grams or 1.875 kg.</p> Signup and view all the answers

How much copper sulphate can be made with 96 kg of copper assuming an unlimited supply of the other ingredients, if it's made of 32 parts copper, 16 parts sulfur, 32 parts oxygen, and 48 parts water by weight?

<p>384 kg.</p> Signup and view all the answers

If Robert wants to make 12 rock cakes, how much margarine does he need, if the recipe for 18 rock cakes calls for 6 oz of margarine?

<p>4 oz.</p> Signup and view all the answers

If Jenny has only 9 oz of sugar and plenty of the other ingredients, what is the greatest number of rock cakes she can make if the recipe for 18 rock cakes calls for 6 oz of sugar?

<p>27</p> Signup and view all the answers

Study Notes

Ratios

  • A ratio is a way to compare two or more similar quantities.
  • Ratios are written using whole numbers, separated by colons.
  • Units are not included in ratios.
  • Ratios are used in various applications, including comparing costs, weights, sizes, and other similar quantities.
  • Ratios can be simplified by dividing both numbers by a common factor.
  • Ratios should use the same units. Convert to the same units if necessary.

Simplifying Ratios

  • Simplify ratios by dividing both numbers by their greatest common factor.
  • This results in an equivalent ratio in its simplest form.

Sharing Quantities Using Ratios

  • Ratios can be used to divide quantities proportionally.
  • To find the amount each part receives, divide the total quantity by the sum of the parts in the ratio, then multiply the result by the number of parts for each share.
  • Amounts must be in the same unit before calculation.

Key Points

  • A ratio is a way to compare similar quantities.
  • Use whole numbers in ratios.
  • Use the same units when comparing quantities in a ratio.

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Related Documents

Ratios Explained PDF

Description

This quiz covers the concept of ratios, focusing on how to compare similar quantities using whole numbers. It also includes methods for simplifying ratios and dividing quantities proportionally. Test your knowledge on these fundamental mathematical skills and their practical uses.

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