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Number and Algebra, NAP-B1-18

4 groups of 6 plums is the same number of plums as 3 groups of

`8` `6` `4` `3`
 
 
 
 
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`8`

Show Worked Solution
`text(Number of plums)` `= 4 xx 6`
  `= 24`

`text(If 3 groups,)`

`text(Number in each group)`

`= 24 ÷ 3`

`= 8`

Number and Algebra, NAP-D1-30

In 5 years time, Megan will be 16.

Brian will then be half Megan's age.

How old is Brian now?

`3` `6` `8` `11`
 
 
 
 
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`3`

Show Worked Solution

`text(In 5 years time:)`

`text{Megan will be 16 (given)}`

`=>\ text(Brian will be 8.)`

`:.\ text(Brian’s age now)` `= 8-5`
  `= 3`

Number and Algebra, NAP-G1-34 SA

Archer has blocks with two square faces.

He builds the model below.
 

What is the height of the model in centimetres?

  centimetres
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`12\ text(cm)`

Show Worked Solution

`text(2 × length of block = 18 cm)`

`text(Length of 1 block = 9 cm)`

`text(Side length of the square face)`

`= 9 ÷ 3`

`= 3\ text(cm)`
 

`:.\ text(Height)` `= 3 xx 4`
  `= 12\ text(cm)`

Number and Algebra, NAP-D1-23 SA

Kelly is buying tennis balls from the sporting goods shop.

It costs $12 to buy 4 balls.

If each ball costs the same, how many tennis balls can Kelly buy for $60?
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`20`

Show Worked Solution
`text(C)text(ost of 1 ball)` `= 12 ÷ 4`
  `=$3`

 

`:.\ text(Number of balls she can buy)`

`= 60 ÷ 3`

`= 20`

Number and Algebra, NAP-D1-11

Melinda placed some shells in rows of 8.

She then put the same number of shells into bags of 6 and had some left over.

How many shells were left over?

`4` `3` `2` `1`
 
 
 
 
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`2`

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`text(Total number of shells)`

`=8 xx 4`

`= 32`
 

`32 ÷ 6 = 5\ text(remainder 2)`

`:. 2\ text(shells were left over.)`

Number and Algebra, NAP-E1-35 SA

Katrina puts some Rubik's cubes and identical bolts end to end.

3 Rubik's cubes are the same length as 4 bolts.

Each Rubik's cube is 8 cm long.
 


 

How many centimetres long is each bolt?

  centimetres
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`text(6 cm)`

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`text(Total length of 3 Rubik’s cubes)`

`= 3 xx 8`

`= 24\ text(cm)`
 

`:.\ text(Length of one bolt)`

`= 24 ÷ 4`

`= 6\ text(cm)`

Number and Algebra, NAP-E1-34

5 of plastic cups cost 30 cents.

How many cents does one cup cost?

 
   cents

What is the greatest number of cups that can be bought with exactly $6?

 
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`6\ text(cents), 100\ text(cups)`

Show Worked Solution
`text(C)text(ost of 1 cup)` `= 30 ÷ 5`
  `= 6\ ¢`

 

`=>\ text(Greatest number of cups)`

`= $6.00 ÷ 6\ ¢`

`= 600\ ¢ ÷ 6\ ¢`

`= 100\ text(cups)`

Number and Algebra, NAP-E1-32 SA

Mr. Lantry asked his students to follow the steps below.

  • Step 1: Think of an even number between 1 and 10.
  • Step 2: Halve it.
  • Step 3: Add twice the number you started with.
  • Step 4: Multiply by 2.
  • Step 5: Divide by the number you started with.

What answer should everyone get?
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`5`

Show Worked Solution

`text{Step 1:  Choose 8 (say)}`

`text(Step 2:  8 ÷ 2 = 4)`

`text{Step 3:  4 + (2 × 8) = 20}`

`text(Step 4:  20 × 2 = 40)`

`text(Step 5:  40 ÷ 8 = 5)`

`=>\ text(All numbers should result in an answer of 5.)`

Number and Algebra, NAP-G1-29 SA

A shop sells eggs in small and large cartons.

A small carton holds 6 eggs.

A large carton holds 12 eggs.

Alice buys a total of 60 eggs.

She buys 3 large cartons and some small cartons.

How many small cartons does she buy?
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`4`

Show Worked Solution

`text(Eggs in 3 large cartons)`

`= 3 xx 12`

`= 36`
 

`text(Eggs needed in small cartons)`

`= 60 – 36`

`= 24`
 

`:.\ text(Small cartons needed)`

`= 24 ÷ 6`

`= 4`

Number and Algebra, NAP-F1-27

Eliza took half the chocolates that were in a bowl.

Without any other chocolates being taken, Eliza took two more.

Eight chocolates were left in the bowl.

How many chocolates were in the bowl at the start?

`6` `10` `18` `20`
 
 
 
 
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`20`

Show Worked Solution

`text(If we add the last 2 chocolates to the 8 left in)`

`text(the bowl, there are 10 in the bowl.)`

`=>\ text(10 is half the chocolates at the start.)`

`:.\ text(20 chocolates were in the bowl.)`

Number and Algebra, NAP-F1-14

Five people collected a total of 70 aluminium cans to recycle.

Three of the people collected 20 cans each.

The other two, Randy and Thor, collected the rest of the cans equally.

How many cans did Thor collect?

`5` `10` `35` `50`
 
 
 
 
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`5`

Show Worked Solution

`text(3 people collected 20 cans each.)`

`=> 60\ text(cans were collected, 10 left.)`

`:.\ text(Cans collected by Thor)`

`= 10 ÷ 2`

`= 5`

Number and Algebra, NAP-H1-33 SA

Three children were playing a card game.

There were 52 cards. Each child was given 11 cards.

How many cards were left over?
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`19\ text(cards)`

Show Worked Solution
`text(Cards used)` `= 3 xx 11`
  `= 33`

 

`:.\ text(Cards left over)` `= 52 – 33`
  `= 19`

Number and Algebra, NAP-H1-30

Andrew kept 3 bird cages.

Each bird cage had 8 birds in it.

He then bought one more bird cage and spread the birds out evenly between the 4 cages.

How many birds were then in each cage?

`5` `6` `8` `9`
 
 
 
 
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`6`

Show Worked Solution
`text(Total birds)` `= 3 xx 8`
  `= 24`

 

`:.\ text(Birds in each of 4 cages)`

`= 24 ÷ 4`

`= 6`