Rodney planted 227 small tress on his property.
Some of the small trees died so there was only 203 trees left.
How many of the small trees died?
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Rodney planted 227 small tress on his property.
Some of the small trees died so there was only 203 trees left.
How many of the small trees died?
`24`
`text(Trees that died)` | `= 227 – 203` |
`= 24` |
Kylie planted 175 lemon trees in her orchard.
23 lemon trees died in the first month.
How many lemon trees survived past the first month?
`152`
`text(Lemon trees left)` | `= 175 – 23` |
`= 152` |
Peter grew 137 tomatoes in his vegetable garden.
Lady beetles got into his garden and ruined some tomatoes, so there was only 105 tomatoes left.
How many tomatoes did the lady beetles ruin?
`32`
`text(Tomatoes ruined)` | `= 137 – 105` |
`= 32` |
Candice buys art supplies for her art studio.
She rounds each price to the nearest dollar to estimate the total cost of the supplies.
How much is Candice's estimate?
$ |
`$33`
`text(Rounding each item to the nearest dollar:)`
`text(paint = $7)`
`text(pencil = $2)`
`text(canvas = $13)`
`text(chalk = $7)`
`text(glue = $4)`
`text(Candice’s Estimate)` | `= 7 + 2 + 13 + 7 + 4` |
`= $33` |
`18\ text(°C)`
`text(Each mark is worth 2°C)`
`text(Temperature in Sydney is 36°C)`
`text(Temperature in Melbourne is 18°C)`
`:.\ text(Difference)` | `= 36 – 18` |
`= 18\ text(°C)` |
The picture graph shows how many tonnes of concrete are needed for 4 jobs.
How many more tonnes of concrete does Job 1 need than Job 3?
tonnes |
`2\ text(tonnes)`
`text(Job 1 needs 9 tonnes)`
`text(Job 2 needs 7 tonnes)`
`:.\ text(Extra tonnes)` | `= 9 – 7` |
`= 2\ text(tonnes)` |
The picture graph shows how many tonnes of fertiliser are needed for 4 gardens.
How many more tonnes of fertiliser does Garden 4 need than Garden 3?
tonnes |
`7\ text(tonnes)`
`text(Garden 4 needs 12 tonnes)`
`text(Garden 3 needs 5 tonnes)`
`:.\ text(Extra tonnes)` | `= 12 – 5` |
`= 7\ text(tonnes)` |
The picture graph shows how many tonnes of fertiliser are needed for 4 gardens.
How many more tonnes of fertiliser does Garden 2 need than Garden 3?
tonnes |
`5\ text(tonnes)`
`text(Garden 2 needs 10 tonnes)`
`text(Garden 3 needs 5 tonnes)`
`:.\ text(Extra tonnes)` | `= 10 – 5` |
`= 5\ text(tonnes)` |
Calvin had 72 coloured pencils.
He lined them up so there are 8 pencils in each row.
How many rows are there?
`9`
`text(Number of rows)` | `= 72 ÷ 8` |
`= 9` |
Soda cans are sold in three different ways at the supermarket.
What is the cheapest price that someone can buy 14 cans for?
`$15.80`
`text(Two six packs and two cans:)`
`= (2 xx 7.00) + (2 xx 1.20)`
`= 14 + 2.40`
`= $16.80`
`text(One ten pack and 4 single cans:)`
`= 11 + (4 xx 1.20)`
`= 11 + 4.80`
`= $15.80`
`:.\ text(Cheapest price = $15.80)`
William spent $15.30 on pencils for the new school year.
Each pencil cost 30 cents.
How many pencils did he buy?
`51`
`text(Strategy 1)`
`=> 10\ text(pencils cost $3.00)`
`=> 50\ text(pencils cost $15.00)`
`:. 51\ text(pencils cost $15.30)`
`text(Strategy 2)`
`$15.30 = 1530\ text(cents)`
`text(Using long division:)`
`1530-:30 = 51`
Bonnie and Clyde ate 57 cashew nuts.
Bonnie ate 13 less cashew nuts than Clyde.
How many cashew nuts did Bonnie eat?
`22`
`text(Strategy 1)`
`text(Consider the possible splits -)`
`28 – 29:` | `text(Bonnie eats 1 less)` |
`27 – 30:` | `text(Bonnie eats 3 less)` |
`vdots` | |
`22 – 35:` | `text(Bonnie eats 13 less)` |
`:.\ text(Bonnie eats 22 cashew nuts)`
`text{Strategy 2 (Algebra)}`
`text(Let)\ c =\ text(number of cashews Bonnie eats)`
`c + c + 13` | `= 57` |
`2c` | `= 44` |
`c` | `= 44 ÷ 2` |
`= 22` |
Usain and Merv are the first two runners in a cross country relay team.
Usain runs 1 lap of the course and passes a baton to Merv for the second lap.
Their results are in the table below.
How long after Usain started, in seconds, did Merv finish his lap?
seconds |
`text(350 seconds)`
`text(Total time)` | `= 2:17 + 3:33` |
`= 5\ text(minutes and 50 seconds)` | |
`= (5 xx 60) + 50` | |
`= 300 + 50` | |
`= 350\ \ text(seconds)` |
Penny runs a chicken shop.
At the start of one day, she has 402 chickens for sale.
At the end of the same day, she has 32 chickens not sold.
How may chickens did Penny sell on that day?
`370`
`text(Chickens sold)`
`= 402 – 32`
`= 400 – 30`
`= 370`
George runs a large restaurant.
At the start of one day, George has 506 eggs in his kitchen.
At the end of the day, George has 46 eggs left.
How may eggs, in total, were used on that day?
`460`
`text(Eggs used in day)`
`= 506 – 46`
`= 500 – 40`
`= 460`
At a fun run, Con supplied 307 oranges for the runners.
At the end of the fun run, there were 87 oranges left.
How many oranges, in total, had been used in the fun run?
`220`
`text(Oranges used)`
`= 307 – 87`
`= 300 – 80`
`= 220`
Andrew collected football cards. He had collected 64 cards.
At school, Andrew and his friends put all their football cards together.
There was a total of 404 cards.
How many football cards, in total, had Andrew's friends collected?
`340`
`text(Cards collected by Andrew’s friends)`
`= 404 – 64`
`= 400 – 60`
`= 340`
Vivian had 54 cricket balls.
His club had 6 cricket teams.
He gave the same number of balls to each team.
How many balls did each team receive?
`9`
`text(Number of rows)` | `= 54 ÷ 6` |
`= 9` |
Pablo caught 56 blowfish.
He lined them up in rows so there were 7 blowfish in each row.
How many rows are there?
`8`
`text(Number of rows)` | `= 56 ÷ 7` |
`= 8` |
There are 54 students at an assembly.
Mrs Gibbs lines the students up so there are 9 students in each row.
How many rows are there?
`6`
`text(Number of rows)` | `= 54 ÷ 9` |
`= 6` |
Write a number in the box to make this number sentence true.
`9 + 7 = 11 +` |
`5`
`9 + 7` | `= 11 +` |
|
`16` | `= 11 +` |
|
|
`= 5` |
Write a number in the box to make this number sentence true.
`7 + 6 = 10 +` |
`3`
`7 + 6` | `= 10 +` |
|
`13` | `= 10 +` |
|
|
`= 3` |
Write a number in the box to make this number sentence true.
`4 + 9 = 10 +` |
`3`
`4 + 9` | `= 10 +` |
|
`13` | `= 10 +` |
|
|
`= 3` |
In a bowls competition, a player won 12 games and lost the other 9 games.
Finish the subtraction sentence below to show the number of games he played.
`\ - 12 = 9` |
`21`
|
`\ – 12` | `= 9` |
|
`= 9 + 12` | |
`= 21` |
In a squash competition Michelle won 9 games and lost the other 7 games.
Finish the subtraction sentence below to show the number of games Michelle played.
`\ - 9 = 7` |
`16`
|
`\ – 9` | `= 7` |
|
`= 7 + 9` | |
`= 16` |
The goals scored by 4 players in a season of soccer were recorded in the graph below.
Simon scored 6 goals in the season.
Gigi scored 3 goals.
How many more goals did Henry score than Fiona?
`5`
The goals scored by 4 players in a season of soccer were recorded in the graph below.
Fiona scored 8 goals in the season.
Simon scored 5 goals.
How many more goals did Henry score than Gigi?
`5`
There are 56 students in year 7 at a school.
Every student is either right-handed or left-handed.
There are 6 times more right-handers than left-handers.
How many left handers are there in Year 7?
`8`
`text(S) text(ince there are 6 times more right-handers,)`
`=>\ text(1 out of 7 are left-handers.)`
`:.\ text(Number of left-handers)`
`= 1/7 xx 56`
`= 8`
A group of 8 friends are planning a trip to Leyland Brothers World.
Lunch will cost $7 per person.
Entry will cost $13 per person.
Hiring a bus for transport will cost $180 for the whole group.
What is the expected total cost of the trip for the whole group?
$ |
`$340`
`text(Lunch cost)` | `= 8 xx 7 = $56` |
`text(Entry cost)` | `= 8 xx 13=$104` |
`text(Bus hire)` | ` = $180` |
`:.\ text(Total cost)` | `= 56 + 104 + 180` |
`= $340` |
`17 +` | `+ 9 = 64` |
`38`
`text(Deduct 17 and 9 from both sides:)`
|
`=64 – 17 – 9` |
|
`=64 – 26` |
||
`=38` |
`6 +` | `+ 19 = 52` |
`27`
`text(Deduct 6 and 19 from both sides:)`
|
`=52 – 6 – 19` |
|
`=52 – 25` |
||
`=27` |
`12 +` | `+ 5 = 48` |
`21`
`text(Deduct 12 and 15 from both sides:)`
|
`=48 – 12 – 15` |
|
`=48 – 27` |
||
`=21` |
`16 +` | `+ 9 = 44` |
`19`
`text(Deduct 16 and 9 from both sides:)`
|
`=44 – 16 – 9` |
|
`=19` |
`(1.38 + 6.21)/1.38 =` |
`5.5`
`(1.38 + 6.21)/1.38` | `= 7.59/1.38` |
`= 5.5` |
The pictures show the front, side and top views of an object made of cubes.
How many cubes are needed to make the object?
`11`
A square has an area of 196 square centimetres.
What is the perimeter?
centimetres |
`56`
`text(Let)\ \ x = text(length of 1 side)`
`x^2` | `= 196` |
`x` | `= sqrt196` |
`= 14` |
`:.\ text(Perimeter)` | `= 4 xx 14` |
`= 56\ text(cm)` |
Shinji used 8 litres of paint to paint a wall.
The wall was a square with sides 4 metres long.
How many litres of paint would he need to paint a rectangular wall which is 3 metres high and 10 metres wide?
litres |
`15`
`text(Area of smaller wall)`
`= 4 xx 4`
`= 16\ text(m²)`
`text(Area of larger wall)`
`= 3 xx 10`
`= 30\ text(m²)`
`:.\ text(Paint needed for larger wall)`
`= 30/16 xx 8`
`= 15\ text(litres)`
A farmers market sells potatoes in four different sizes.
What is the lowest price a customer can pay for 8 kg of potatoes?
$ |
`$12.20`
`text(Calculate the cost per kg for each size:)`
`text(1 kg: $3.40 per kg)`
`text(2 kg: $6.10 ÷ 2 = $3.05 per kg)`
`text(3 kg: $9.35 ÷ 3 ≈ $3.12 per kg)`
`text(5 kg: $15.75 ÷ 5 = $3.15 per kg)`
`:.\ text(Cheapest price to buy 8 kg)`
`= 4 xx 3.05`
`= $12.20`
Bill buys a new computer.
The disk in its hard drive makes 110 full turns every second.
How many minutes will it take for the disk to make 363 000 full turns?
minutes |
`55\ text(minutes)`
`text(Turns in 1 minute)`
`= 60 xx 110`
`= 6600`
`:.\ text(Minutes needed)`
`= 363\ 000 -: 6600`
`= 55\ text(minutes)`
The mass of a 50-cent coin is about 13.3 grams.
The mass of a 10-cent coin is about 5.65 grams.
Tom has 226.1 grams of 50-cent coins.
Jerry has 129.95 grams of 10-cent coins.
How much more are Tom's coins worth than Jerry's coins, in cents?
cents |
`620\ text(cents)`
`text(Value of Tom’s coins)`
`= 226.1/13.3 xx 0.50`
`= 17 xx 0.50`
`= $8.50`
`text(Value of Jerry’s coins)`
`= 129.95/5.65 xx 0.10`
`= 23 xx 0.10`
`= $2.30`
`:.\ text(Extra worth of Tom’s coins)`
`= 850 – 230`
`= 620\ text(cents)`
A piece of wood is leaning against four stacks of bricks.
There are 31 bricks in total.
How many bricks are in the tallest stack?
`10\ text(bricks)`
`text(15 bricks can be seen above the wood.)`
`=>\ text(16 bricks cannot be seen)`
`=>\ text(4 stacks of 4 bricks cannot be seen)`
`:.\ text(Height of tallest stack)`
`= 6 + 4`
`= 10`
The fraction `5/8` equals 0.625 as a decimal.
What does `5/16` equal as a decimal?
`0.3125`
`5/16` | `= 5/8 xx 1/2` |
`= 0.625 ÷ 2` | |
`= 0.3125` |
The length of this rectangle is one and a half times its height.
The perimeter of the rectangle is 50 centimetres.
What is the area of the rectangle?
square centimetres |
`150\ text(cm²)`
`text(Let)\ x` | `=\ text(height)` |
`3/2 x` | `=\ text(length)` |
`2 xx (x + 3/2 x)` | `= 50` |
`5x` | `= 50` |
`x` | `= 10` |
`:.\ text(Area)` | `= 10 xx 15` |
`= 150\ text(cm²)` |
Grace and Angie are dog breeders.
The total number of dogs they currently own is 23.
Grace owns 9 more dogs than Angie.
How many dogs does Grace own?
`16`
`text{Solution 1 (Trial and error)}`
`text(If Grace owns 14)`
`=>\ text{Angie owns 9 (5 difference)}`
`text(If Grace owns 16)`
`=>\ text{Angie owns 7 (9 difference)}`
`:.\ text(Grace owns 16 dogs.)`
`text{Solution 2 (Algebra)}`
`text(Let)\ n = text(number of dogs Angie owns)`
`=>\ n + 9 = text(Grace’s dogs)`
`n + n + 9` | `= 23` |
`2n` | `= 14` |
`n` | `= 7` |
`n + 9` | `= 16` |
Health insurance for his family costs Rex $90 per week.
How much does it cost him over 52 weeks?
$ |
`$4680`
`text{One strategy (mental arithmetic)}`
`52 xx 90` | `= 52 xx 100 – 52 xx 10` |
`= 5200 – 520` | |
`= $4680` |
Yuna used 300 grams of sugar to make 15 cookies.
How many grams of sugar will she need to make 25 cookies?
grams |
`text(500 grams)`
`text(Sugar to make 1 cookie) = 300/15 = 20\ text(grams)`
`:.\ text(Sugar to make 25 cookies)`
`= 25 xx 20`
`= 500\ text(grams)`
One litre of cordial contains 25 grams of sugar.
How many millilitres of cordial contain 0.5 grams of sugar?
millilitres |
`20\ text(mL)`
`text(1 litre = 1000 mL)`
`text(1000 mL contains 25 grams)`
`:.\ text(Volume that contains 0.5 grams)`
`= 0.5/25 xx 1000`
`= 20\ text(mL)`