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Decimals, SM-Bank 083

Maureen worked 10 hours last week and was paid $245.80.  Jessica worked 9 hours and received $221.85.

Who was paid the highest hourly rate?  Justify your answer using calculations.  (2 marks)

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\(\text{See worked solutions}\)

\(\text{Jessica by }$0.07\text{ per hour.}\)

Show Worked Solution
 \(\text {Maureen’s hourly rate}\) \(=245.80\ ÷\ 10\)
  \(=$24.58 \text{ per hour}\)

 

 \(\text {Jessica’s hourly rate}\) \(=221.85\ ÷\ 9\)
  \(=$24.65 \text{ per hour}\)

 
\(\therefore \text{ Jessica’s hourly rate of pay is higher by }$0.07\text{ per hour.}\)

Decimals, SM-Bank 077

Brett has three 6-litre cans of paint.

He divides the paint up equally between his 24 art students.

How much paint will each student receive?

Write you answer as a decimal.  (2 marks)

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\(0.75\)

Show Worked Solution
\(\text{Total paint}\) \(= 3\times 6\)
  \(= 18\text{ litres}\)

 

\(\text{Paint per student}\) \(=\dfrac{18}{24}\)
  \(=\dfrac{3}{4}\)
  \(= 0.75\text{ litres}\)

Decimals, SM-Bank 074

Shannon is buying materials to make a bookcase.

She rounds each price in the table below to the nearest dollar to estimate the total cost of the materials.

Materials
Item Cost
hammer $5.65
glue $3.95
wood $11.55
nails $1.60
stain $3.85

How much is Shannon's estimate?  (2 marks)

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\($28\)

Show Worked Solution

\(\text{Rounding each item to the nearest dollar:}\)

\(\text{hammer}\) \(=$6\)
\(\text{glue}\) \(= $4\)
\(\text{wood}\) \(=$12\)
\(\text{nails}\) \(=$2\)
\(\text{stain}\) \(=$4\)

  
\(\text{Shannon’s Estimate}=$6+$4+$12+$2+$4=$28\)

 

Decimals, SM-Bank 073

Gladys is tiling a wall that is 3.6 metres high.

She is using ceramic tiles that are 0.06 metres wide.

There are no gaps between the tiles.

How many ceramic tiles does Gladys need to buy?  (2 marks)

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\(60\)

Show Worked Solution
\(\text{Number of tiles}\) \(=3.6\ ÷\ 0.06\)
  \(=(3.6\times 100)\ ÷\ (0.06\times 100)\)
  \(=360\ ÷\ 6\)
  \(=60\)

  
\(\therefore \text{ Gladys needs to buy 60 ceramic tiles.}\)

 

Decimals, SM-Bank 070

Bert, Gary and Miles are weighing themselves.

Bert weighs 48.65 kilograms.

Gary weighs 0.3 kilograms more than Bert.

Miles weighs 0.75 kilograms less than Bert.

How many kilograms do the three boys weigh altogether?  (2 marks)

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`text(145.5 kg)`

Show Worked Solution

`text(Bert’s weight = 48.65 kg)`

`text(Gary’s weight = 48.65 + 0.3 = 48.95 kg)`

`text(Miles’ weight = 48.65 − 0.75 = 47.9 kg)`
 

`:.\ text(Total weight)` `= 48.65 + 48.95 + 47.9`
  `=48 + 48 + 47 + 0.65 + 0.95 + 0.9`
  `= 143 + 2.5`
  `= 145.5\ text(kg)`

Decimals, SM-Bank 069

Jane has two 4-litre cans of paint.

She divides the paint up equally between her 32 art students.

How much paint, in litres, will each student receive?

Write you answer as a decimal.  (2 marks)

Show Answers Only

`0.25\ text(litres)`

Show Worked Solution
`text(Total paint)` `= 2 xx 4`
  `= 8\ text(litres)`

 

`text(Paint per student)` `= 8/32 = 1/4`
  `= 0.25\ text(litres)`

Decimals, SM-Bank 068

Onions cost $3 per kilogram.

Peter buys 3.35 kilograms of onions.

How much does Peter pay for the onions?  (2 marks)

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`$10.05` 

Show Worked Solution

`text(Strategy 1)`

`text(C)text(ost of 3 kg) = 3 xx $3 = $9`

`text(C)text(ost of 0.1 kg) = 3/10 = text(30 cents)`

`=>\ text(C)text(ost of 0.35 kg)` `= 3.5 × 30\ text(cents)`
  `= 105\ text(cents)`
  `= $1.05`

  

`:.\ text(C)text(ost of 3.35 kg)` `= 9 + 1.05`
  `= $10.05` 

  
`text(Strategy 2)`

`:.\ 3.35 xx $3 = $10.05`

Decimals, SM-Bank 059

The temperature at Mawson in Antarctica was recorded as `-13.6°`C at 11:30 pm on 22/10/2023.

At 4:30 am on 23/10/23 the temperature had fallen to `-15.4°`C.

What was the change in temperature from 11:30 pm to 4:30 am?  (2 marks)

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`-1.8°`C

Show Worked Solution

`text(Change in temperature:)`

`-15.4-(-13.6)` `= -15.4+13.6`
  `=-15.4+13+0.6`
  `= -2.4+0.6`
  `=-1.8`

`:.\ text(The change in temperature was)\ -1.8°text(C)`

Decimals, SM-Bank 054

Verne sells produce at the local market.

By 11:30am on Saturday morning he has sales of $31.25, $15.67 and $28.30.

  1. What was the total of Verne's sales by 11:30am?  (1 mark)

  2. Verne wanted to sell $100 in produce this week. How much more does he have to sell to make this goal?  (1 mark)

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a.    $75.22

b.    $24.78

Show Worked Solution
a.   

`:.\ text(Verne has sales of $75.22.)`

b.   

`:.\ text(Verne needs to sell an additional $24.78 of produce.)`

Decimals, SM-Bank 052

The table below compares the approximate populations of two countries.

Country

Approximate population

(millions)
Cuba 11.475
Benin 11.096

Approximately how many more people live in Cuba than in Benin?   (2 marks)

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`379\ 000`

Show Worked Solution

`text(Extra people living in Cuba)`

`=(11.475-11.096) xx 1\ 000\ 000`

`= 0.379 xx 1\ 000\ 000`

`= 379\ 000`

Decimals, SM-Bank 051 MC

Four groups of backpackers picked blueberries over a two hour period.

The weight of the blueberries collected (in kg) by the groups in each hour is shown in the table below.

  Group 1 Group 2 Group 3 Group 4
1st Hour 2.57 2.89 2.5 2.87
2nd Hour 2.35 2.06 2.92 2.53

Which group picked the greatest mass over the two hours?

  1. Group 1
  2. Group 2
  3. Group 3
  4. Group 4
Show Answers Only

`C`

Show Worked Solution

`text(A possible strategy:)`

`text(A quick estimate of the 1st 2 options shows)`

`text(that both sums will be lower than 5 kg.)`

`=>\ text(Evaluate only the last 2 options:)`

`text(Group 3:)\ \ 2.5 + 2.92 = 5.42\ text(kg)`

`text(Group 4:)\ \ 2.87 + 2.53 = 5.40\ text(kg)`

`=>C`

Decimals, SM_Bank 024

John measured the water depth at the end of his jetty for five days in a row.

The measurements are summarised in the table below.

  Monday Tuesday Wednesday Thursday Friday
Water Level 1.24 m 1.07 m 1.42 m 1.15 m 1.38 m
  1. On which day was the water level the highest?  (1 mark)

  2. On which day was the water level the lowest?  (1 mark)

  3. On which day was the median (middle) water level measurement?  (1 mark)

  4. What is the difference between the highest and lowest water levels?  (2 marks)

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a.    `text(Wednesday)`

b.    `text(Tuesday)`

c.    `text(Monday)`

d.    `0.35\ text(metres)`

Show Worked Solution

`text(Order from lowest to highest water level)`

`=>\ text(Tues , Thurs , Mon , Fri , Wed) `

a.    `text(Highest) = 1.42\ text(m) =>text(Wednesday)`

b.    `text(Lowest) = 1.07\ text(m) =>text(Tuesday)`

c.    `text(Middle) = 1.24\ text(m) =>text(Monday)`

d.    `text(Difference between highest and lowest)`

`=1.42-1.07`

`= 0.35\ text(metres)`

Decimals, SM-Bank 019

Vivian and Curtly throw a cricket ball from the boundary of the cricket oval to the wicket-keeper.

It takes Vivian's throw 3.48 seconds to reach the wicket-keeper.

It takes Curtly's throw 1.84 seconds.

What is the difference in the time taken to reach the wicket-keeper between the two throws?  (2 marks)

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`1.64\ text(seconds)`

Show Worked Solution
`text(Time Difference)` `= 3.48-1.84`
  `= 3.48-2 + 0.16`
  `= 1.48 + 0.16`
  `= 1.64\ text(seconds)`

 
`:.\ text(The difference in the time taken is 1.64 seconds.)`

Decimals, SM_Bank 018

A hot air balloon is 25.2 metres high.

The length of the balloon section is 21.55 metres.
 

  
What is the height of the basket section?  (2 marks)

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`text(3.65 metres)`

Show Worked Solution

`text(Let)\ \ h =\ text(height of basket section)`

`h + 21.55` `= 25.2`
`:. h` `= 25.2-21.55`
  `= 25.2-22 + 0.45`
  `= 3.2 + 0.45`
  `= 3.65`

`:.\ text(The basket section is 3.65 metres high)`

Decimals, SM-Bank 014 MC

Roger had tests to check his health that are summarised in the table below.

Test Normal range Roger's result
Resting heart rate 60 to 95 92
Blood sugar 4.2 to 6.1 4.1
Vitamin C 0.4 to 1.7 0.5

For which tests were Roger's results within the normal range?

  1. Resting heart rate and blood sugar
  2. Blood sugar and vitamin C only
  3. Resting heart rate only
  4. Resting heart rate and vitamin C only
Show Answers Only

`D`

Show Worked Solution

`text(Checking each test:)`

`text(Resting heart rate → 92 is within 60 and 95)`

`text(Blood sugar → 4.1 is not within 4.2 and 6.1 )`

`text(Vitamin C → 0.5 is within 0.4 and 1.7)`

`:.\ text(Resting heart rate and vitamin C only)`

`text(are within the normal range.)`

`=> D`

Decimals, SM-Bank 002 MC

India recorded the results of a 400 metres running race final in the table below.

Ist Place 52.26 seconds
2nd Place 52.62 seconds
3rd Place ?
4th Place 53.19 seconds

The time of the runner who came in 3rd place could be

  1. `text(52.57 seconds.)`
  2. `text(52.71 seconds.)`
  3. `text(53.21 seconds.)`
  4. `text(53.94 seconds.)`
Show Answers Only

`B`

Show Worked Solution

`text{Eliminate A as it lies between 1st and 2nd place.}`

`text{Eliminate C and D as both are larger than 4th place.}`

`text{52.71 is slower than 2nd place (52.62) but faster than 4th place (53.19).}`

`=> B`

Decimals, SM-Bank 004 MC

Kelly measures the length of fish she catches for her research.

A. B. C. D.

  
Which fish has a length closest to 25 cm?

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`A`

Show Worked Solution

`text(Difference of each option:)`

`25.14-25` `= 0.14\ text(cm)`
`25-24.8` `= 0.20\ text(cm)`
`25-24.76` `= 0.24\ text(cm)`
`25.3-25` `= 0.30\ text(cm)`

 
`:. 25.14\ text(cm is closest.)`

`=> A`

Decimals, SM-Bank 006

Richard is a runner.

The length of his last 4 half marathon distances are recorded in the table below.

Half marathon Distance (km)
1 21.1
2 20.35
3 20.295
4 22.095

Which half marathon had the shortest distance?  (1 mark)

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`text(Half marathon 3)`

Show Worked Solution

`20.295\ text(is the shortest distance.)`

`:.\ text(Half marathon 3 was the shortest.)`