smc-4461-40-Add/Subtract decimals

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 082

Use the order of operations to evaluate:

$2.389 + 4.12\times 20-5.604$ (2 marks)

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$79.185$

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$2.389 + 4.12\times 20-5.604$	$=2.389 + 4.12\times 10\times 2-5.604$
	$=2.389 + 41.2\times 2-5.604$
	$=2.389 + 82.4-5.604$
	$=84.789-5.604$
	$=79.185$

Decimals, SM-Bank 076

Manou was cooking a defrosted chicken in his oven and checking its temperature every 7 minutes.

The first temperature taken was $-8.2^{\circ}\text{C}$.

The second temperature was $4.2^{\circ}\text{C}$.

The third measurement showed that the temperature had increased one and a half times the previous increase.

What was the third temperature? (2 marks)

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$22.8^{\circ}\text{C}$

Show Worked Solution

$\text{1st increase}$	$= 4.2- (-8.2)$
	$= 4.2 + 8.2$
	$= 12.4$

$\text{2nd increase}$	$= 1.5\times 12.4$
	$= 12.4 + 6.2$
	$= 18.6$

$\therefore \text{ Third temp}$	$= 4.2 + 18.6$
	$=22.8^{\circ}\text{C}$

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 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 060

What number will make this number sentence true? (2 marks)

`2.48 + 3.72 =`

`+ 2.50`

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`3.7`

Show Worked Solution

`(2.48 + 3.72)-2.50`	`= 2.48 + 3-2 + 0.72-0.50`
	`=3.48 + 0.22`
	`= 3.7`

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

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`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 058

Evaluate `28.24-15.8`. (1 mark)

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`12.44`

Show Worked Solution

`28.24-15.8`	`= 28.24-15-0.8`
	`= 13.24-0.80`
	`= 12.44`

Decimals, SM-Bank 057

Evaluate `123.9-80.05`. (1 mark)

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`43.85`

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`123.9-80.05`	`= 123.9-80-0.05`
	`= 43.90-0.05`
	`= 43.85`

Decimals, SM-Bank 056

Evaluate `25.1-18.5`. (1 mark)

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`6.6`

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`25.1-18.5`	`= 25.1-18-0.5`
	`= 7.1-0.5`
	`= 6.6`

Decimals, SM-Bank 055

What is the difference between 14.253 and 9.121? (1 mark)

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`5.132`

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`text(Difference:)`

`14.253-9.121`	`= 14.253-9-0.121`
	`= 5.253-0.121 `
	`= 5.132`

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.

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

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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

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

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

Decimals, SM-Bank 053 MC

`135.6 + 23.7 =`

`111.9`
`159.3`
`168.1`
`169.3`

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`B`

Show Worked Solution

`:.\ 135.6 + 23.7 = 159.3`

`=>B`

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`

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`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?

Group 1
Group 2
Group 3
Group 4

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`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 050

Evaluate `3.2 + 14.85 + 0.126`. (2 marks)

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`18.176`

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`text(First line up points and add place holder 0’s)`

`:.\ 3.2 + 14.85 + 0.126`

`= 18.176`

Decimals, SM-Bank 049

Evaluate `7.14 + 3.52`. (1 mark)

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`10.66`

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`text(Add after first lining up points)`

`:.\ 7.14 + 3.52`

`= 10.66`

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

On which day was the water level the highest? (1 mark)

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

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

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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 017

The weather bureau published the weekday maximum temperatures in the table below.

Weekday	MON	TUE	WED	THU	FRI
Max Temp	22.7°	21.8°	20.3°	26.4°	28.7°

How much warmer was it on Thursday than on Monday? (2 marks)

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`3.7^@`

Show Worked Solution

`text(Degrees warmer)`	`= 26.4-22.7`
	`= 3.7^@`

\(2.389 + 4.12\times 20-5.604\)	\(=2.389 + 4.12\times 10\times 2-5.604\)
	\(=2.389 + 41.2\times 2-5.604\)
	\(=2.389 + 82.4-5.604\)
	\(=84.789-5.604\)
	\(=79.185\)

\(\text{1st increase}\)	\(= 4.2- (-8.2)\)
	\(= 4.2 + 8.2\)
	\(= 12.4\)

\(\text{2nd increase}\)	\(= 1.5\times 12.4\)
	\(= 12.4 + 6.2\)
	\(= 18.6\)

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

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

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