magnitudes

RATIO ANDPROPORTIONS

What is ratio?ratio is a way of comparing amounts of something. it shows how much bigger one thing is than another. For example: Use 1 measure screen wash to 10 measures water Use 1 shovel of cement to 3 shovels of sand Use 3 parts blue paint to 1 part white ratio is the number of parts to a mix. the paint mix is 4 parts, with 3 parts blue and 1 part white.the order in which a ratio is stated is important. For example, the ratio of screenwash to water is 1:10. this means for every 1 measure of screenwash there are 10 measures of water. Mixing paint in the ratio 3:1 (3 parts blue paint to 1 part white paint) means 3 + 1 = 4 parts in all.

3 parts blue paint to 1 part white paint = is blue paint to white paint.if the mix is in the right proportions, we can say that it is in the correct ratio.

ProPortionsa proportion is a name we give to a statement that two ratios are equal. it can be written in two ways:

two equal fractions, or,

using a colon, a:b = c:d

When two ratios are equal, then the cross products of the ratios are equal.

that is, for the proportion, a:b = c:d , a x d = b x c

ab

cd

=

UsuarioTypewritten Text1

direct ProPortiontwo quantities are in direct proportion when they increase or decrease in the same ratio. For example you could increase something by doubling it or decrease it by halving.if we look at the example of mixing paint the ratio is 3 pots blue to 1 pot white, or 3:1.

But this amount of paint will only decorate two walls of a room. What if you wanted to decorate the whole room, four walls? You have to double the amount of paint and increase it in the same ratio.if we double the amount of blue paint we need 6 pots.if we double the amount of white paint we need 2 pots.

the amount of blue and white paint we need increase in direct proportion to each other. Look at the table to see how as you use more blue paint you need more white paint:

Pots of blue paint 3 6 9 12Pots of white paint 1 2 3 4

have a look at this graph:

two quantities which are in direct proportion will always produce a graph where all the points can be joined to form a straight line.

ProPortion Word ProblemsProportion problems are word problems where the items in the question are proportional to each other.Example : Jane ran 100 meters in 15 seconds. how long did she take to run 1 meter?

step 1: think of the word problem as:

if 100 then 15. if 1 then how many?

step 2: Write the proportional relationship:

answer: she took 0.15 seconds

1001

15=x

x x= =15 1100

0 15.


PercentAGes this rectangle has been divided into 100 squares.

21 of the squares are yellow. of the rectangle is yellow.

a fraction out of 100 is called a percentage.

21 per cent of the rectangle is yellow. this in writing is 21%.the whole rectangle is 100% .100 21 = 79 , so 79% of the rectangle is green.

PercentAGes oF An AmoUntto work out a percentage of something, multiply it by the number of per cent and divide it by 100. For example: Find 40% of 30 pupils of pupils pupils

FrActions, decimAls And PercentAGesany percentage is just a fraction in hundredths.

For example 21% =

Anyfractionhasapercentagethatisequivalenttoit.Toworkitout,findanequivalentfraction. this needs to have a denominator of 100.

For example: Find the percentage equivalent to

to make 5 into 100, multiply by 20. You have to multiply 2 by the same number.

to convert a decimal to an equivalent percentage, simply write it as a number of hun-dredths. this is the equivalent percentage.For example :

40100

30 40100

x 30 40 100 1200 100 12x = =

25

25 100= *

25

40100

40= = %

0 42 42100

42. %= =


REMEMBERratio is a way of comparing amounts of something. a proportion is a name we give to a statement that two ratios are equal.two quantities are in direct proportion when they increase or decrease in thesame ratio. a percentage is a fraction in hundredths.Percentages match decimals: 24% = 0.24to find a percentage of something, multiply by the number of percent and divide by 100.

USEFUL WEBSITEShttp://www.ngfl-cymru.org.uk/vtc/ngfl/maths/caerphilly/percentageshttp://www.mathsisfun.com/quiz/percenttest.html

here is a table of commonly occuring values shown in Percent, Decimal and Fraction form:

PErCENt DECiMaL FraCtioN

1% 0.01 1/100

5% 0.05 1/20

10% 0.1 1/10

12 1/2% 0.125 1/8

20% 0.2 1/5

25% 0.25 1/4

50% 0.5 1/2

75% 0.75 3/4

80% 0.8 4/5

90% 0.9 9/10

99% 0.99 99/100

100% 1

125% 1.25 5/4

150% 1.5 3/2

200% 2


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SThere are 30 questions here and you will find some of the answers on the Bingo card atthebottomofthepage.Whenyoufindtheanswertooneofthequestions,drawalinethrough itWhen you have completed a line of answers, call binGo and when you have found all the answers call FUll HoUse.Well all start together.are you ready?

1) 10% of 450 = ________ 2) reduce 50 by 20% ________

3) 0.1 = _______% 4) 1/8 = __________ %

5) Find 25% of 2.80 _______ 6) 3/4 = _________ %

7) 65 c + 20% iVa =________ 8) 25 + 10 % = ______________

9) 2/5 = _________ % 10) increase 120 by 10%________

11) 3/8 = ________ % 12) 40 % of 170 = _____________

13) 90 + 20% iVa = _______ 14) Find 20% of 360___________

15) increase 360 by 10%_________ 16) 20% of 360 _______________

17) 0.85 = _________ % 18) 20 + 10% = ______________

19) 1/20 = _________ % 20) reduce 75 by 20%_________

21) reduce 60 by 25%___________ 22) 0.4 = _________ %

23) 5/8 = ________ % 24) 1/8 = 0.____

25) 8.50 + 20% iVa =__________ 26) Find 60% of 135=__________

27) Decrease 540 by 30% =_______ 28) 16 + 20% =_____________

29) 30% of 350 __________ 30) 0.09 = __________ % (also draw a line through the question that has its answer below )

BINGO!! BINGO!!


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SAcross

1. 2/5 = _____%2. Find 30% of 703. 65% = 0.____4. What % of 50 is 30?______5. Find 40% of 360._______6. 10% of 7.50 is_______ c.7. 0.85 = _____ %8. 40% of 2 Km = _____ m.9.

What % is coloured?_______11. 95% is 0._____

doWn

1. 0.45 = ____ %2. 1/5 =______%3. Find 60% of 1 Kg4. What % of 100 is 65?5.

What % is coloured?____6. 0.7 = _____%7 Jean had 20 .she spent 16. What % did she spend?______8. 25% of 320 = ________9. 10% of 2 metres is _____cm10. 25% of 1.40 = ____c.

CROSSWORD


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