Y8 – Autumn– Block 3 – ANS1 – Represent multiplication of fractions

Question Answer

1

a) !" × 5

b) !# × 5

c) !$× 5

d) #$ × 3

2

3

Various answers e.g.a)

b)

c)

4

a)

b)

c)

d)

Y8 – Autumn– Block 3 – ANS1 – Represent multiplication of fractions

Question Answer

5

a)

b)

c)

d)

6 Whitney is looking at the shaded parts and Alex is looking at the unshaded parts.

7

a)

b)

Y8 – Autumn– Block 3 – ANS2 – Multiply a fraction by an integer

Question Answer

1

a) 15b) 15𝑎c) 15𝑥𝑦d) !"#

2

3

a)

b)

4

a) 2 !$b) 2 %&c) 3 %"d) 5

5 Eva has multiplied the denominator by the integer when she shouldn’t have. 4 × 35 =

125

6

a) 3 !$ f) 6 %&b) 5 !% g) !$!#c) 1 #' h) 6 $%d) 2 !$ i) 10e) 5 j) 6

7a) 4 &" m

b) 3 %& hoursc) 4kg

8

a) 3b) 5c) %!! , 1 #!!d) "' , $"'e) %& , 18

9

8 × &" =

'×&" = &×)

" = 4 × '"

8 × &" = 2 × 4 × '

!* = 2 × 0.8 × 4

8 × &" = 8 × $×$

" = 8 × 2 × $" = 16 × $

" =$" × 16

Students should compare their method with a partner.

Y8 – Autumn– Block 3 – ANS3 – Find the product of a pair of unit fractions

Question Answer

1

a) The square is split into 2 equal rows, 1 of these is indicated with an arrow showing 12The square is split into 3 equal columns, 1 of which is indicated with an arrow showing 13These bits are shaded and 1 out of 6 equal parts is shaded.

b)

2

a) !!"b) !

#× !#= !

!$c) !% ×

!" =

!&"

3

4

a) !' f) !" ×!" =

!("

b) !(! g) !!) ×!!) =

!!))

c) !#) h) !"d) !#( i) !(e) !!$ j) !#

5

E.g. a) !$ ×

!# =

!(#

b) !& ×!!( =

!&$

c) !" ×!' =

!#)

There are multiple ways to complete each. b) has the most options as 36 has the most factors out of 24, 36 and 40.

6Yes he is correct because the numerators are both 1 and so it is their product.E.g. !* ×

!+ =

!*+

7

a) !$b) !'c) !"

8

a) !"b) !("c) !#

!(

!(

Y8 – Autumn– Block 3 – ANS4 – Find the product of a pair of any fractions

Question Answer

1

a) The square is split into 3 equal rows, 2 of these are indicated with an arrow showing 23The square is split into 5 equal columns, 3 of which are indicated with an arrow showing 35These bits are shaded and 8 out of 15 equal parts are shaded.

b)

2

a) !"# (or $#)

b) %& ×%& =

'"!

c) &# ×#( =

$)%# (or &()

3

4

a) %* f) &# ×&# =

"!$#

b) *$" g) %") ×%") =

'"))

c) ")$& (or #"$) h) &#d) #

"*i) "(

e) '"! j) ('

5

E.g.a) "$ ×

#'

b) $%× &#

c) "$ ×"#

There are multiple ways to complete the calculations.

6Yes Whitney is correct because when you multiply by a number less than one, the answer is smaller.

57

57

Y8 – Autumn– Block 3 – ANS4 – Find the product of a pair of any fractions

Question Answer

7

a) "!% e) %")

b) "' f) %#c) $'

g) "*

d) $' h) &"#

Students should discuss their method with a partner.

Y8 – Autumn– Block 3 – ANS5 – Divide an integer by a fraction

Question Answer

1

a) There are 5 fifths in one whole. So 1 ÷ !" = 5

b) There are 3 thirds in one whole. So 1 ÷ !# = 3 and 2 ÷ !

# = 6 c) 10

1520

2

3

a) 6 f) 24b) 9 g) 60c) 12 h) 90d) 12 i) 120e) 18 j) 4𝑥

4a) There are 3 thirds in 1 whole and 12 thirds in 4 wholes.b) There are 6 lots of two-thirds in 4.Students should compare their reasoning with a partner.

5

a) 8b) 30 ÷ 2 = 15c) 8 ÷ 5 = 16d) 5 ÷ 3 = 15

6

Group 1: The answer is 28 × !

$16 × !

%8 ÷ 416 ÷8

Group 2: The answer is 328 ÷ !

$8 ×416 × 216 ÷ !

&4 ÷ !

%

7

a) 2 , 8b) 1 , 16c) &

# , 24

8

a) 24b) 48c) 16d) 20

Y8 – Autumn– Block 3 – ANS6 – Divide a fraction by a unit fraction

Question Answer

1a) 3 , 3b) 2 , 2c) 6 , 6

2

a) 2b) 6c) 4d) 12e) 30f) 3g) 6

3a) 4b) 8c) 9

4

5

<><>

6

a) !" ÷#" = 6 ÷ 1 = 6

b) $#%÷ ##%= 9 ÷ 1 = 9

c) #&%' ÷#%' = 15 ÷ 1 = 15

7

a) 𝑎 = 5b) 𝑏 = 5c) 𝑐 = 18d) 𝑑 = 10

Y8 – Autumn– Block 3 – ANS7 – Understand and use the reciprocal

Question Answer

1

2 No because !" <!#

3

a) 5 , 5b) 10 , 10c) 15 , 15d) 20 , 20

Dividing by a fraction is the same as multiplying by its reciprocal.

4

a) 30b) 35c) 20d) 32

5

a) 4 = 12 e) 8b) 4 ÷ 3 = 4 f) 13!#c) 8 = 24 g) 5d) 8 ÷ 3 = 8 h) 2!

#

Tommy has found how many lots of 13 there are in 4 which is 12. He has then used the fact

that there are two lots of 13 in 23 which means there are half as many lots of 23 in 4 than there

are 13 so he has divided 12 by 2 to give that there are 6 lots of two thirds in 4.

62!#Students should discuss their answer with a partner.

7

a) 9b) 4!#c) 1!#d) "

$e) 9f) 4!#You could knowledge of fraction and decimal equivalents. 0.5 is equivalent to 12 and 0.125 is

equivalent to 18 so 0.5 ÷ 0.125 is equivalent to 12÷18 which is 4.

Y8 – Autumn– Block 3 – ANS8 – Divide any pair of fractions

Question Answer

1 a) 18b) 24

2

a) 4 e) !"b) #! f) "! (= 1#! )

c) "$% (= 16&% ) g) ###&d) %"$ h) #&## (= 1 ### )

3

a) 4 e) !"b) #! f) "! (= 1#! )

c) "$% (= 16&% ) g) ###&d) %

"$h) #&

##(= 1 #

##)

4 Students should discuss their preferred method with a partner.

5 a) 15b) 15

6

a) %!÷ #!= 3

b) #& ÷#' = 4

c) %" ÷#! =

#&" (= 2&" )

d) (#$ ÷#! =

#'" (= 3%" )

7

a)

b)

c)

8

a) %'b) &%c) %"d) #"#)e) %#$f) #"%&

Y8 – Autumn– Block 3 – ANS9 – Multiply and divide improper and mixed fractions

Question Answer

1 The answers are the same because when 𝑥 = 7 the calculations are equivalent.

2

a) !" d) 16#$

b) 6#% e) 8#&

c) 6#$ f) 9%'

3

4 × 1 = 44 × #

$ = 2

4 + 2 + #& = 6#&

4

a) 6$"

b) 9 (#$

c) 2%(&)

5

a) There are 4 #$ circles shaded. There are 9 lots of #$ so 4 #$ ÷#$ = 9.

b) There are 4 #$ circles shaded. There are 3 lots 1 #$ so 4#$ ÷ 1#$ = 3.

c) 5 , 4

6

a) (&= 1%

&

b) (' = 1$'

c) #&" = 1'"d) 2

7

a) 5#(

b) 4#(%$

cm²

c) 3'(*'cm

Y8 – Autumn– Block 3 – ANS10 – Multiply and divide algebraic fractions

Question Answer

1

a) !"

b) #"

c) !"d) Students should discuss their preferred method with a partner.

2

3

a) 1$" , 1$"

b) 2$%

, 2$%

c) 7$" , 7$"Teddy is correct. This can be seen by the fact that the two answers are equal in each part. 34 𝑥 and 3#4 are equivalent.

4

a) #&

d) #'

b) %() e) "($)

c) &*) f) '*)

5

a)

b)

6

a) +$%

b) &"+

c) &+!

d) $$,

7

a) -.$)

d) -.$)

b) &-). e) -./c) &-). f) -".