

Meaning and Models  Key Ideas
 Addition  Subtraction
 Multiplication  Division

Meaning
and models quiz answers
1. 
Five
out of nine means five ninths. The five is the numerator and the nine
is the denominator, 
2. 
There
are 5 equal parts, so we shade 2 parts

3. 
To
shade
of the following shape, cut the shape into 8 equal pieces and shade
one piece

4. 
She
is not correct because although she divided the rectangle into seven
pieces, the pieces are not equal.

5. 
There
are 11 marbles altogether. Seven of them are blue, so the fraction
of blue =

6. 
To
shade
of this
shape, we must shade 3 out of every 5 squares. There are 15 squares
altogether, i.e. 3 lots of 5 squares, so we must shade 3 lots of 3
squares, i.e. 9 squares must be shaded.

7. 
For
every group of six apples, five apples were eaten. First, put the
24 apples into groups of six.
There
are 4 groups of apples. If 5 apples from each group are eaten, there
will be one apple from each of the four groups left. This means
there will be 4 apples left.

8. 
I
want two out of every three smiley faces stickers. First, put the
eighteen smiley faces stickers into groups of three.
I
receive two from each of these six groups of three. I
receive 12 smiley faces stickers.

9. 
For
, the rectangle is divided into 6 equal parts and one part is shaded.
For
the
rectangle is divided into 4 equal parts and three parts are shaded.
From
the above diagram it can be seen that there is more green than orange.
Hence,
is bigger than

10. 
Each
hexagon is divided into 6 equal pieces. This gives 12 equal pieces
altogether.
is one piece out of 6 or 2 pieces out of 12. Since we have 12 pieces
here, we must shade 2 pieces in order to shade

11(a) 
There
are twelve hexagons altogether, eight of which are coloured yellow.
Therefore the fraction coloured yellow = 
11(b) 
means 8 yellow for every 12, or 4 yellow for every 6, or 2 yellow
for every 3
= =
.
In simplest form the fraction is
8
out of 12 hexagons are coloured yellow 
4
out of 6 hexagons are coloured yellow 
2
out of 3 hexagons are coloured yellow 







12. 
There
are nine ninths in one whole. The shape is divided into 9 equal pieces
and all 9 pieces are required to give the whole. 
13. 
Any
integer can be written as a fraction by putting the integer over a
denominator of one. 8 = 
14. 
A.
2 B.
C.  2 D. E.
2
and  2 are integers and so can be written as fractions.
is written as a fraction already. =
2 which can be written as a fraction.
cannot be written as a fraction. Answer B

15. 
We
can answer this question without referring to the number of eggs
because we are told that the eggs are partioned into 3 parts and
that Sophie receives 1 of these parts. Therefore Sophie receives
one third, ,
of the eggs.
An
alternative explanation follows:
Twentyseven
eggs are partitioned in 3 parts , means there are 9 eggs to each
part.
Sophie
gets one part, therefore Sophie gets 9 eggs. 9 eggs out of 27 eggs
is .
This is the same as getting 1 egg for every three eggs, i.e. .

16. 
Five
fifths in one whole plus another fifth = six fifths =

Key
Ideas quiz answers
1. 
1.To
find fractions that are equivalent to another fraction, just multiply
the numerator and the denominator by the same number or divide the
numerator and the denominator by the same number.
is equivalent to all of the following fractions and more ...

2. 
is equivalent to all of the following fractions and more ...

3. 
a)
The
fractions in the boxes are
The
sequence goes as follows,


b)
The
fractions in the boxes are
The
sequence goes as follows,

4. 
a)


b)


c)

5. 
a)
Multiples
of the denominator 5 are:
5,
10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60…
Multiples
of the denominator 6 are:
6,
12, 18, 24, 30, 36, 42, 48, 54, 60, 66…
Multiples
of the denominator 12 are:
12,
24, 36, 48, 60, 72, 84…
Multiples
of the denominator 4 are:
4,
8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60…
The
smallest number common to all these denominators is 60, so make
equivalent fractions of the given fractions with denominator 60
Ordering
these fractions from smallest to largest gives
That
is,


b)
Multiples
of the denominator 8 are:
8,
16, 24, 32, 40, 48, 56, 64, 72…
Multiples
of the denominator 6 are:
6,
12, 18, 24, 30, 36, 42, 48, 54, 60, 66…
Multiples
of the denominator 3 are:
3,
6, 9, 12, 15, 18, 21, 24, 27, 30…
Multiples
of the denominator 4 are:
4,
8, 12, 16, 20, 24, 28, 32, 36, 40…
The
smallest number common to all these denominators is 24, so make
equivalent fractions of the given fractions with denominator 24
Ordering
these fractions from smallest to largest gives
That
is,


c) Multiples
of the denominator 9 are:
9,
18, 27, 36, 45, 54, 63, 72…
Multiples
of the denominator 4 are:
4,
8, 12, 16, 20, 24, 28, 32, 36, 40…
Multiples
of the denominator 3 are:
3,
6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36…
Multiples
of the denominator 12 are:
12,
24, 36, 48, 60, 72, 84…
The
smallest number common to all these denominators is 36, so make
equivalent fractions of the given fractions with denominator 36
Ordering
these fractions from smallest to largest gives
That
is,

Addition
quiz answers
Subtraction
quiz
answers
Multiplication
quiz
answers
1. 
The
yellow shading (Y) represents and
the blue shading (B) represents .
The rectangles with the double shading of purple (Y,B) represent
of .
There
are 10 out of 24 rectangles with double shading, so
x =
Y,B

Y,B

B

Y,B

Y,B

B

Y,B

Y,B

B

Y,B

Y,B

B

Y,B

Y,B

B

Y

Y


Y

Y


Y

Y



2. 

a) 

b) 

c) 
First
we change the mixed number to an improper fraction.
The
number 2 has 10 fifths and another fifth gives us 11 fifths. We
can also work this out by multiplying 2 x 5, which gives us 10 and
adding 1  so we have 11 fifths, 11 over 5.
Then
we do the multiplication,

d)


e) 

f)

6
goes into 66 11 times and 6 goes into 30 5 times, so we can reduce
the improper fraction by a factor of 6 to give the answer of 11
fifths.

3. 

a) 

b) 

c) 

d) 

e) 

f) 

Division
quiz
answers
1. 

(a) 

(b) 

(c) 

2. 

(a) 

(b) 

(c) 

