Download Fractions and Algebra Presentation

Maths Workshop for Parents 2
Fractions and Algebra
What is a fraction?
• A fraction is a part of a whole. There
are two numbers to every fraction:
2
7
Numerator
Denominator
2
7
This is a proper
(or common)
fraction
Improper and mixed fractions
• An improper fraction has a numerator
that is bigger than its denominator,
for example 10/7
• 9/4 is also an improper fraction. It
means nine quarters. If you think of
this as cakes, nine quarters are more
than two whole cakes. It is 2 1/4
cakes.
Changing a mixed number to an
improper fraction
• To change a mixed number to an improper
fraction, multiply the whole number by the
denominator and add the numerator.
• This gives you the new numerator; the
denominator stays the same
e.g.
2¼
9/4
2x4=8
8+1=9
Changing an improper fraction to a
mixed number
• To change an improper fraction into a
mixed number, divide the numerator by
the denominator.
e.g.
9/2 = 9 ÷ 2 = 4 ½
2 goes into 9 four times, with a half left over.
¼
¼
¼
¼
¼
¼
¼
¼
¼
2 1/4 is a mixed fraction because it has
a whole number and a fraction together.
Fractions of quantities
To find a fraction of a quantity:
• Divide the quantity by the denominator
• Multiply the answer you get by the numerator
• To find 2/ 5 of £15, for example:
• Divide 15 by 5 (the denominator):
15 ÷ 5 = 3
• Multiply the answer 3 by 2 (the numerator):
3x2=6
• So 2/ 5 of £15 is £6
Equivalent Fractions
• Equivalent
fractions are
fractions that
look different but
show exactly the
same amount.
1/3, 2/6, 4/12
• You can make equivalent fractions by
multiplying or dividing the numerator
and denominator by the same
number.
• You can simplify fractions by dividing
the numerator and denominator by
the same number. This is called
cancelling.
• Sometimes fractions will cancel more
than once.
Ordering and comparing
fractions
• To compare fractions, you must first change them so
they have the same denominator.
• Compare 2/3 and 3/5 and find out which fraction is
bigger.
• First look at the denominators (the bottom numbers).
• Find a new number that both denominators go into:
– Try 9 - you can divide 9 by 3 but you can't divide 9 by
5.
– Try 10 - you can divide 10 by 5 but not by 3, so that
isn't right either.
– Try 15 - you can divide 15 by 5 (which equals 3) and
you can also divide 15 by 3 (which equals 5), so 15 is
the new denominator.
Ordering and comparing
fractions
• Now you have found a new denominator that is
divisible by both numbers, you need to change
the numerators (the top numbers).
• To change the numerators, simply multiply them
by the number of times the denominator goes
into 15.
– So for 2/3 - 3 goes into 15 five times, so you must
multiply the numerator (2) by 5 which equals 10.
– And for 3/5 - 5 goes into 15 three times, so you must
multiply the numerator (3) by 3 which equals 9.
Common Denominators
• You can compare fractions by writing them
over their lowest common denominator.
This is the lowest number that is a multiple
of both denominators.
Converting fractions to decimals
You can use a calculator to turn a
fraction into a decimal.
• Just divide the numerator by the
denominator.
¾ = 3 ÷ 4 = 0.75
Adding or Subtracting Fractions
• Change any whole or mixed numbers into
improper fractions.
• If the fractions have different denominators
find a common denominator.
• Add or subtract the numerators and cancel
answer down to its simplest form.
1 2/3 + ½ = 5/3 + ½ = 10/6 + 3/6 = 13/6 = 2 1/6
Multiplying Fractions
• Change any whole or mixed numbers into
improper fractions.
• Multiply the numerators then multiply the
denominators.
• Cancel down the answer to its simplest
form.
2 2/3 x ½ = 8/3 x ½ = 8/6 = 1 2/6 = 1 1/3
Dividing Fractions
• Change any whole or mixed numbers into
improper fractions.
• Turn the second fraction upside down and
multiply the fractions together.
• Cancel answer to its simplest form.
2 2/3 ÷ ½ = 8/3 x
2/1
= 16/3 = 5 1/3
Fractions, Decimals and
Percentages
½ = 0.5 = 50%
¼ = 0.25 = 25%
¾ = 0.75 = 75%
1/1 = 1 = 100%
Algebra
• Algebra is about seeing mathematical
patterns, understanding the patterns and
describing them using words and symbols.
• You use algebra every day without even
noticing:
e.g. A box of 4 doughnuts costs £6
4d = £6
2d = £3
d = £1.50
Think of a numberE
•
•
•
•
Double it:
Double it again:
Add the number you first thought of:
Divide by 5, and you get the number you
first thought of:
Word formulae and equations
•
•
•
•
Alice sells candles for 50p each.
So if she sells 2 candles, she earns £1.
3 candles will cost £1.50 and so onE.
She can sell 80 candles for £40 and 120
candles for £60.
• As a word formula, the total cost is the
cost for one item multiplied by how many
items are bought or sold
Equations
• Much the same as word formulae, except
symbols like X and = are used, and
instead of words, letters are used.
• The rule for total cost becomes:
T=nxP
Which is just a short way of writing:
Total cost = number of items X price per item
What’s my number?
•
•
•
•
I’m thinking of a number: n
I subtract 1: n – 1
I multiply it by 3: 3 (n – 1) = 15
The answer is 15. What’s my number?
• You can work backwards and undo the
operations to find out:
Patterns in sequences
• Algebra can help you to find terms in
number sequences.
e.g. here are the first few terms in the
sequence of even numbers. The rule for
finding the nth term is 2n:
1
2
3
4
5
100
n
2
4
6
8
10
?
2n
• Here are the first few terms in the
sequence of odd numbers. The rule for
finding the nth term is 2n – 1
1
2
3
4
5
100
1
3
5
7
9
?
n
2n – 1
Tips for writing algebra
• A number, letter or combination of
numbers and letters multiplied together is
called a term. The terms are separated by
+ and – signs, and each + or – is ‘joined’
to the term that follows it. Any term that
does not have a + or – sign is always
positive:
e.g.
3a + 2ab – 5
Tips for writing algebra
• A collection of terms is called an expression.
So 3a + 2ab – 5 is an expression.
• Write single letters on their own: a not 1a
• Avoid using multiplication signs: ab = a x b
• Write divisions as fractions: a / b
• When you multiply numbers and letters,
always write the number first: 2ab = a x 2 x b
Useful websites:
http://www.woodlandsjunior.kent.sch.uk/maths/
http://www.crickweb.co.uk/Key-Stage-2.html
http://nrich.maths.org
http://uk.ixl.com/math
http://lgfl.skoool.co.uk/primary_maths.aspx
http://www.bbc.co.uk/bitesize/ks2/maths
http://www.taw.org.uk/lic/itp/itps/fractions_1_1.swf