Lesson1- Percents


INTRODUCTION

 

In this diagram, 39 out of 100 squares have been shaded. So 39 % has been shaded

 

 

 

What percentage has been shaded? …..................................................


 

Percent means 'per 100'. If 70 percent of students own a pet, this means that 70 out of every hundred students own a pet. The symbol % means percent.A percent is 1 part out of 100

 

1% is equal to 1/100 or 0.01

 

 How do you write 0.3 as a percentage?     0.3 = 0.3 x 100% = 30 %

 

How do you write 44% as a decimal?     44/100 = 22/50 = 11/25   or   0.44

 

 

Percentage of a quantity

 

It's often useful to be able to find a percentage of a quantity.

For example, you might be told that bus fares are going up by 5% and you need to know how much more you will need each week.

Bus ticket price – 4 zł

5% x 4 = 0.05 x 4 = 0,20 zł = 20 gr

 

In a class of 25 pupils, 64% live at home. How many pupils live at home ?

….......................................................................................................................

 

Last year Marek earned 40,000 zł. This year his pay has increased by 8%.

 

By how much money has Marek's pay increased?..............................................

 

What is his new salary? …..................................................................................

 

 

GLOSSARY

price - cena

fare - opłata za przejazd

go up - wzrosnąć

earn - zarabiać (pieniądze)

salary - pensja, płaca, wynagrodzenie

invest - inwestować

interest - interes, korzyść

podwyżka - increase (in prices) rise in salary/wages

obniżka - decrease, reduction, drop, cut, fall (in prices, in salary)

READ ME

Only a small percentage of pupils were prepared today.

(Tylko mały procent uczniów był dzisiaj przygotowany)

 

We've observed a twenty percent increase in sales. (Zaobserwowaliśmy dwudziestoprocentowy wzrost w sprzedaży)


USEFUL EXPRESSIONS

FALSE FRIENDS

Percent (Per cent ) - procent (jedna setna czegoś)

 

Percentage - procent (część czegoś wyrażona w procentach)


CHOOSE THE PROPER WORD

LABEL TRUE OR FALSE

If the population of some city grew from 25,000 to 28,000 in 2 years, the percent of the increase for this period was 10%. ( T/F)

 

A possible method of finding a given per cent of a number is to find 1% of this number first and then multiply that amount by the given per cent. (T/F)

 

SELECT THE PHRASE that best completes the sentence

FILL IN THE GAPS (one word per gap)- additional task

  

....... is 8% of 75, ....... % of 40 is 6 and 140 is 35% of .......

 

The percent of ....... from 5 to 7 is ........

 

When water freezes, its volume becomes approximately 9% ......., so ......... litres of water are necessary to produce 100 litres of ...........

 

The percent of increase from 6,000 to 8,000 is .......

 

 

TIME FOR PROBLEMS

Percents- word problems

 

  1. Jacek  ordered a set of green and blue pins. He received 90 pins in all. 27 of the pins were green. What percentage of the pins were green?

  2. Yesterday, there were 36 problems assigned for math homework. Ewa did 25% of them correctly. How many problems did Ewa get right?

  3.  90% of the tickets sold at a school carnival were early-admission tickets. If the school sold 50 tickets in all, how many early-admission tickets did it sell?
  4. 5 out of the 50 teachers in a school staff meeting were male teachers. What percentage of the teachers in the meeting were male teachers?
  5. A particular truck in a transportation fleet was driven 100,000 km last year. In comparison, it was driven 30% less this year. How much was the truck driven this year?
  6. Of the 427 people responding to a public opinion poll, 224 answered YES to a certain question and 154 answered NO. What per cent of the responding people  were undecided?

 

 Additional problems

 

  1. Tomek is 153 cm tall and he is 15% shorter than Jakub. Standing on a chair he is 15% taller than Mathew. How High is the chair?
  2.  One side of a rectangle was diminished and the second was prolonged by the same prime number of per cent. As a result the area of the rectangle was reduced by 2%. What was the per cent of increase of the side length?