refer equivalent
2. Do you know the meaning of all the words? Discuss in pairs.
Find the words you do not know in the text on the next page and try to guess their meaning.
3. Discuss in pairs or groups.
• In how many ways can a percentage be expressed?
• How can we compare ratios?
• Can you explain what the golden ratio is?
• Can you express the golden ratio algebraically?
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PERCENTAGE, RATIO AND PROPORTION
We have already learned two ways of writing fractional parts: common fractions and decimal fractions. Another method is by using percentage.
Percentage is a particular kind of a decimal fraction, the denominator of which is always 100. Instead of writing the denominator we use the term "percent"* to indicate that the denominator is 100. The word "percent" and the sign % actually refer to the denominator of a fraction expressed as hundredths*. When we speak of "6 percent", we mean
100
6 or 0.06. These all mean the same thing, namely, 6 parts out of 100. In working with problems involving percentage we must be able to change a percent to a decimal and a decimal to a percent.
We can change a percent to a decimal by dropping the percent sign and moving the decimal point two places to the left. We can change a percent to a common fraction with a given number as the numerator 100 as a denominator.
One hundred percent of quantity is the entire quantity. To find a percent of a number, change the percent to the equivalent decimal fraction or common fraction and multiply the number by the fraction. To find the percent of one number from a second number, form a fraction in which the first is the numerator and the second number is the denominator. Divide the numerator into the denominator and change the decimal fraction to a percent. To find a number when a percent of it is known, change the percent to an equivalent decimal fraction or common fraction, divide the given number by this fraction.
If a student scores 81% in one test and 87% in the next, his average (or mean) percentage is 84%.
If, in a given classroom, there are fourteen boys and seven girls, we say that the ratio of girls to boys is 1:2 (one to two).
When we build a model ship, we make it to the scale. For example, if a model is built to a scale of 1:30 (one to thirty), this means that 10 centimetres on the model re-presents 300 centimetres on the ship itself. The scale of a map shows the ratio of the distance on the map to the distance on the area covered by the map.
3:6 (three to six) and 5:10 (five to ten) are two equal ratios, in other words 3 and 6,
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one hour to do a job, and 10 men half an hour to do the same job, we can say that the number of men and the time are in inverse proportion, or that these quantities are inversely proportional.
When an architect makes a plan of a house, his drawing is much smaller than the actual house. The plan is reduced in size to fit the paper he is using. This process of reducing in size is called drawing to scale. The reduced drawing is known as a scale drawing.
NOTES TO THE TEXT
In British English, percent is sometimes written as two words (per cent, although percentage and percentile are written as one word). In American English, percent is the most common variant, but per mille (1 part in 1,000) is written as two words. In EU context the word is always spelled out in one word percent.
expressed as hundredths - sajalistena väljendatuna
Vocabulary and Language Focus
1. Translate into English . Use some of the expressions in sentences of your own.
1. murdu moodustama, 2. kümnendmurru eriliik, 3. veel üks meetod, 4. täishulk, 5.
nimetaja kirjutamise asemel, 6, märki kasutama, 7. tegelikult, 8. millelegi viitama, 9.
murruna väljendatuna, 10. sedasama tähendama, 11. protsenti kümnendmurruks muutma, 12. protsendimärki ära jätma, 13. kümnendpunkti kahe koha võrra vasakule nihutama, 14.
mõõtkava järgi joonestama , 15. tähistama, 16. tüdrukute ja poiste arvuline suhe klassis, 17. võrdelises sõltuvuses olema, 18. pöördvõrdelises sõltuvuses olema, 19. suuruselt vähendatud olema, 20. tegelik arv, 21. osutama, näitama, 22. keskmine protsent.
2. Fill in the blanks.
1. In a certain country, rainy days and dry days are in the __________ 1:7. 2. If three metres of a material cost 225 units of money and eight metres cost six hundred units
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is drawn to a __________ of 1:65, one centimetre of the plan __________ sixty-five centimetres on the building. 4. To convert a _________ to a fraction, divide __________
100. 5. If we wish to __________ a vulgar fraction as a __________ , we must __________ by one hundred. 6. We can change a percent to a decimal by __________
the percent sign.
7. __________ __________ writing out the words "percent" we more often use a special __________ after the number. 8. The fraction
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8 __________ as a percentage is 20%.
9. One __________ percent of quantity is the entire quantity. 10. The process of __________ in size is called drawing to __________ .
Pair Work
1. Ask and answer the following questions.
1. What percentage is four fifths? 2. What is thirty percent of fifty? 3. Express fifty-six as a percentage of seventy. 4. What is four and a half percent of eight hundred people? 5. What fraction is seventy-five percent? 6. What decimal fraction is sixty-three point nine percent? 7. What is the ratio of men to women if sixty percent are men? 8.
In a class of twenty-five students, twenty come to school by bus and five on foot. What is the ratio of those who come on foot to those who come by bus, and what percentage of the class does each group represent? 9. The numerator of a fraction is 6. This numerator is equal to thirty-three point three recurring percent of the denominator. What is the fraction? 10. Which fraction with a denominator of sixteen is in proportion to one over four? 11. If a plan is drawn to a scale of 1:50, what is the actual measurement which is shown on the plan as four centimetres? 12. Divide one hundred and forty sheep into two groups in the ratio of 3:4. 13. Divide thirty-six pounds into three parts in the ratio 6:5:1.
14. Five families have a total of 100 sheep. How many sheep will six families have if the numbers are in proportion? 15. A concrete mix of cement, sand and gravel (betoonisegu tsemendist, liivast ja kruusast) is made in the ratio
of 2:5:8. What is the weight of each part in thirty tons of concrete? 16. In a class of
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passed the examination, how many failed? 17. If ten litres of oil weighs eight kilograms, and a litre of water weighs one kilogram, what is the ratio of the relative density (suhteline tihedus) of oil and water?
2. Ask and answer the following questions.
1. What is percentage? 2. What methods are there for writing fractional parts? 3. What does the term "percent" indicate? 4. Where do we put the percent sign? 5. How do we change a percent to a decimal fraction? 6. How much is the entire quantity expressed as a percentage? 7. How do we change a vulgar fraction to a percentage? 8. What must an architect do when he wants to build a house? 9. What is the ratio of girls to young men in your group? What percentage of the group do they represent? 10. What kinds of
"proportion" are there?
Group Work
Solve the puzzle.
A father, I know, is 4 times his son's age. And in 30 years the son will be half as old as his father. How old are the father and son each now?
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