Download Percentages - Cleveden Secondary School

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Elementary mathematics wikipedia, lookup

Addition wikipedia, lookup

Location arithmetic wikipedia, lookup

Mathematics of radio engineering wikipedia, lookup

Rounding wikipedia, lookup

Ratio wikipedia, lookup

Transcript
Percentages
Examples
Percent means “out of one hundred”.
1%=
In a survey of 160 people,
75% said they had a
computer at home. How many
people was this?
1
100
Some percentages can easily be turned
into fractions:
5% =
25% =
1
20
1
4
10% =
331/3% =
1
10
1
3
20% =
50% =
75% =
662/3% =
80% =
3
10
2
3
4
5
40% =
70% =
90% =
2
5
7
10
9
10
60% =
75% =
3
4
of 160 = (160  4) x 3
= 120 people.
1
5
1
2
And we can also say that:
30% =
3
4
3
5
3
4
100% = 1
Jim earns £24000 per year
and gets a 4% pay rise. How
much more money is this?
4% of £24000 = 4  100 x 24000
= £960 more
Write 18 out of 20
as a percentage.
18  20 x 100
= 90%
Fractions
Examples
8
are shaded
12
Fractions are made when objects or
amounts are split up evenly.
Fractions are made up of two parts:
2
the NUMERATOR (how many)
3
the DENOMINATOR (the type)
Fractions which describe the same
amount using different numerators and
denominators are called EQUIVALENT.
To find a fraction of an amount:
1. Divide by the denominator
2. Multiply the answer by the numerator
4
12
8
12
 4
 4
=
2
3
20
50
 10
 10
=
2
5
aren’t shaded
Divide top and bottom
to simplify equivalent
fractions.
Of the 900 people at a concert,
3
4
aged 16 or under. How many is this?
900  4 = 225
225 x 3 = 675
So 675 people are
aged 16 or under.
are
Estimating
Examples
 Height and length
mm, cm, m, km
10 cm
15 mm
 Area – covering of a surface
mm2, cm2, m2, hectares
The area of a football
pitch is 7500 m2
 Volume – measurement of the shape
enclosed by a shape
mm3, cm3, m3 , ml or litres
 Weight
grams and kg
Estimate the volume
of liquid in the flask.
Answer: 100ml
Proportion
Example
If 5 bananas cost 80
If you know the cost of several items, you
pence, then what do 3
can easily find the cost of one item.
bananas cost?
The cost of one item is usually called the
“cost per item”.
 Record appropriate headings with the
unknown on the right.
 Find the value per item first then
multiply to find the required value
 If rounding is required, do not round
until the last stage.
Bananas
5
Cost
80
80  5
1
3
3 x 16
16
48
Divide to find
the cost of one
Multiply to find
the cost of the
required amount
3 bananas cost 48 pence
Bar Graphs
Examples
Bar graphs are used to compare values or
amounts.
 Use correct scales
10
Number of Pupils
 Use a pencil and a ruler
Shoe sizes in class 1S6
8
6
4
2
0
3.5
4
4.5
5
5.5
6
Shoe Size
 Label the axes
Shoe sizes in one class
Shoe sizes in classes 1S6 and 2S6
 Each bar is in the middle of its label
10
Number of Pupils
 Give the graph a title
8
6
1S6
4
2S6
2
0
3.5
4
4.5
5
5.5
6
Shoe Size
Shoe sizes in two classes
Line Graphs
Examples
Line graphs are often used to show trends
(how amounts change over time).
 Use correct scales
25
Temperature (C)
 Use a pencil and a ruler
Temperature over 1 week
20
15
10
5
0
Mon
Tues
Wed
Thurs
Fri
Sat
Sun
Day
 Label the axes
Temperature in July
Temperature over 1 week
 Give the graph a title
 Join each point
Temperature (C)
 Plot each point carefully
25
20
15
July
10
January
5
0
-5
Mon
Tues
Wed
Thurs
Fri
Sat
Sun
Day
Temperatures in January & July
Pie Charts
Examples
Pie charts are circular graphs which are
used to compare information given in
percentages.
Transport to School
Bus
 Use a pencil, ruler, compasses and
protractor
 Measure each slice accurately
 Label the slices
 Give the graph a title
Walk
Car
Bike
If 80 pupils were surveyed:
Bus = 90 = 25%
25% of 80
= 80  4
= 20 pupils
48 walk to school
/80 of 360
= (360  80) x 48
= 216
48
Coordinates
The position of an objector point can be
described by using a coordinate grid
system.
Examples
6
5
A
4
3
 Use a pencil and a ruler
 Use correct scales
 Label the axes
 Plot each point carefully
 Write using brackets and a comma,
e.g. (1,2)
2
1
-6
-5
-4
C
-3
-2
0
-1 -1 0
B
1
2
3
4
5
6
-2
-3
-4
First number is the x-axis (along/back)
Second number is the y-axis (up/down)
A = (2,4)
B = (0,2)
C = (-4,-2)
Subtraction
We can subtract numbers using a number of different methods:
41 – 27 = ?
27
 Counting on
 Breaking up the number being
subtracted
30
40
41
+10
+1
=14
+3
41 – 20 = 21
41 – 27 =
21 – 7 = 14
3
 Decomposition
 Using a number line
-
-4
-3
-2
-1
4
2
1
1
0
1
1
7
4
2
3 – 5 = -2
3
4
5
Equations
Examples
An equation shows you that two things are Solve: a) x + 5 = 9
equal, for example
b) 2y = 10
2+3=5
c) 3z – 2 = 7
5x – 13 = 22
a)
x+5 =9
are both equations.
Change SIDE,
Terms in equations that we don’t know are
given a letter instead of a number (e.g. x). b)
Finding the value of the unknown is called
solving the equation.
c)
x =9–5
x =4
change SIGN!
2y = 10
Y = 10  2
Y =5
Divide by the
number of “y”s!
3z – 2
3z
3z
z
z
=
=
=
=
=
7
7+2
9
9 3
3
Change SIDE,
change SIGN!
Divide by the
number of “z”s!
Using Formulae
Examples
A formula is a set of instructions which
tell you how to carry out a calculation
A bus travels a distance of 250km in 4 hours.
What was the average speed of the journey?
Formulae can be written using words or
shortened to just letters:
 Speed = Distance  Time
 S=DT
Speed = Distance  Time
= 250 4
= 62.5
Average speed = 62.5 km/hour
Convert 100C into F by using the formula
When using formulae:
Temp(F) = (Temp(C) x 1.8) + 32
 always show your working
 be careful to put the correct
Temp(F) = (100 x 1.8) + 32
= 180 + 32
number in the correct place
= 212
 answer the question with a
statement and use the correct units
100C = 212F
Time Calculations
Examples






1 minute = 60 seconds
1 hour = 60 minutes
1 day = 24 hours
1 week = 7 days
1 year = 365 days (366 in a leap year)
1 year = 52 weeks
 a.m. before midday
 p.m. after midday
 1200 = midday, 0000 = midnight
Change 2.37 p.m. to 24 hour time
After midday, so add 12 to the hours
2.37 p.m. = 1437
How many minutes in 4½ hours?
4.5 x 60
= 270 minutes
How long is it from 0755 until 0948?
0755
0800
5 mins
 Change hours to minutes: x by 60
 Change minutes to hours:  by 60
0900
1 hour
0948
48 mins
Total = 1 hour 52 minutes
Ratio
Examples
 Ratios are used to compare the
amounts of different quantities

Ratios can be simplified like
fractions
 We can carry out ratio
calculations by using a table
 Use appropriate headings
Ratio of:
fish : sharks = 2:3
sharks : fish = 3:2
As
6
8
=
3
4
, we can simplify 6:8 to 3:4
In a cat and dog home, the ratio of
cats to dogs is 4:7. If there are
35 dogs, how many cats are there?
Dogs Cats
7
4
 Put the unknown on the right
x5
35
20
Since 35 = 7 x 5,
Cats = 4 x 5
= 20
Rounding
We round numbers when we only need a
rough idea of an amount
Examples
A bag of flour weighs 1483g.
What is this to the nearest
a) 100g b) 10g?
We look at the number to the RIGHT of Answers:
the one we want. To round to:
 100’s, look at 10’s (1874  1900)
 10’s, look at units (1874  1870)
 units, look at 1 d.p. (3.196  3)
 1 d.p., look at 2 d.p. (3.196  3.2)
 2 d.p., look at 3 d.p. (3.196  3.20)
a) 1500g (8 = round UP)
b) 1480g (3 = stays the same)
In the high jump, Jill clears 2.471m.
Round this to a) 1 d.p. b) 2 d.p.
a) Look at the 2nd d.p.
2.471: 7  round UP
Answer: 2.5m
If the number to the right is
0, 1, 2, 3, or 4: we leave our number as it is
5, 6, 7, 8, or 9: we round our number UP by 1
b) Look at the 3rd d.p.
2.471: 1  stays the same
Answer: 2.47m
Symmetry
Examples
Line symmetry
 a line of symmetry through a shape means
one half is an exact mirror image of the
other half
4 lines
Turn (or rotational) symmetry
 if we can spin a shape and it fits back

inside its outline before we do a full turn,
the shape has turn symmetry
/2 - turn
1
Translation (sliding) symmetry
 if we can cover an area with exact copies
of a shape, without leaving any gaps, then
the shape has translation symmetry
2 lines
1 line

/4 - turn
1

/8 - turn
1
Standard Form
Examples
Standard Form is a useful way of writing very Saturn is 884 million
large or very small numbers as :
miles from the Sun.
 a number between 1 and 10
Write this distance
in standard form.
 multiplied by a power of 10
884 million = 884000000
For example,
= 8.84 x 100000000
75000 = 7.5 x 10000 = 7.5 x 104
= 8.84 x 108 miles
0.000021 = 2.1 x 0.00001 = 2.1 x 10-5
A proton has a
diameter of 1.5 x 10-13
The power of 10 (or index) shows how many
cm. Write this number
places the decimal point has moved:
 to the LEFT when positive (BIG numbers)
in the normal way.
 to the RIGHT when negative (SMALL numbers) 1.5 x 10-13 = 0.00000000000015cm
Significant Figures
Examples
Like rounding, significant figures are a way to
give a rough estimate of an amount.
As we increase the significant figures, the
measurement becomes more accurate.
To round whole numbers:
 count in the number of sig figs from the LEFT.
 Round this number up or down
 change the remaining numbers to zero
To round decimals:
 start with the first non-zero number
 count in the number of sig figs from the LEFT.
 round this number up or down
 miss out any numbers left over
There were 36915
people at the 1995
Scottish Cup Final.
This is:
40000 to 1 s.f.
37000 to 2 s.f.
36900 to 3 s.f.
36920 to 4 s.f.
Decimals
63.5 has 3 s.f.
6.35 has 3 s.f.
6.305 has 4 s.f.
6.350 has 4 s.f.
0.592 has 3 s.f.
0.059 has 2 s.f.
0.0590 has 3 s.f. 0.0059 has 2 s.f.