smc-4461-45-Multiply/Divide 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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$79.185$

Show Worked Solution

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

Decimals, SM-Bank 081

Evaluate the following:

$416.48\ ÷\ 200$ (1 mark)

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$20.645\ ÷\ 50$ (1 mark)

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$829.715\ ÷ \ 500$ (2 mark)

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$0.724\ ÷\ 400$ (2 marks)

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a. $2.0824$

b. $0.4129$

c. $1.65943$

d. $0.00181$

Show Worked Solution

a. $416.48\ ÷\ 200$	$=416.48\ ÷\ 100\ ÷\ 2$
	$=4.1648\ ÷\ 2$
	$=2.0824$

b. $20.645\ ÷\ 50$	$= 20.645\ ÷\ 10\ ÷\ 5$
	$= 2.0645\ ÷\ 5$
	$=0.4129$

c. $829.715\ ÷\ 500$	$=829.715\ ÷\ 100 ÷\ 5$
	$=8.29715\ ÷\ 5$
	$=1.65943$

d. $0.724 ÷\ 400$	$=0.724 ÷\ 100\ ÷\ 4$
	$=0.00724\ ÷\ 4$
	$=0.00181$

Decimals, SM-Bank 080

Evaluate the following, using order of operations:

$84\ ÷\ 1.2\times 0.3$ (1 mark)

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$20\times 2.5\ ÷\ 0.1$ (1 mark)

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$1.8\ ÷ \ 0.2\times 0.6$ (2 mark)

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$0.8\times 0.03\ ÷\ 1.2$ (2 marks)

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a. $21$

b. $500$

c. $5.4$

d. $0.02$

Show Worked Solution

a. $84\ ÷\ 1.2\times 0.3$	$= 840\ ÷\ 12\times 0.3$
	$=70\times 3\ ÷\ 10$
	$=21$

b. $20\times 2.5\ ÷\ 0.1$	$= 50\ ÷\ 0.1$
	$= 500\ ÷\ 1$
	$=500$

c. $1.8\ ÷\ 0.2\times 0.6$	$=18\ ÷\ 2\times 0.6$
	$=9\times 0.6$
	$=9\times 6\ ÷\ 10$
	$=5.4$

d. $0.8\times 0.03\ ÷\ 1.2$	$= 8\times 3\ ÷\ 1000\ ÷\ 1.2$
	$=0.024\ ÷\ 1.2$
	$=0.24\ ÷\ 12$
	$=0.02$

Decimals, SM-Bank 079

Evaluate the following:

$1.2\ ÷\ 4$ (1 mark)

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$3.2\ ÷\ 0.8$ (1 mark)

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$42\ ÷\ 0.6$ (1 mark)

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$1.44\ ÷\ 1.2$ (1 mark)

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a. $0.3$

b. $4$

c. $70$

d. $1.2$

Show Worked Solution

a. $1.2\ ÷\ 4$

$= 0.3$

b. $3.2\ ÷\ 0.8$	$= 32\ ÷\ 8$
	$= 4$

c. $42\ ÷\ 0.6$	$=420\ ÷\ 6$
	$=70$

d. $1.44\ ÷\ 1.2$	$= 14.4\ ÷\ 12$
	$=1.2$

Decimals, SM-Bank 078

Evaluate the following:

$1.2\times 8$ (1 mark)

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$0.8\times 0.7$ (1 mark)

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$2.5\times 0.04$ (1 mark)

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$0.05\times 1.6$ (1 mark)

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a. $9.6$

b. $0.56$

c. $0.1$

d. $0.08$

Show Worked Solution

a. $1.2\times 8$	$= 12\times 8\ ÷\ 10$
	$= 96\ ÷\ 10$
	$=9.6$

b. $0.8\times 0.7$	$= 8\times 7\ ÷\ 100$
	$= 56\ ÷\ 100$
	$=0.56$

c. $2.5\times 0.04$	$= 25\times 4\ ÷\ 1000$
	$= 100\ ÷\ 1000$
	$=0.1$

d. $0.05\times 1.6$	$= 5\times 16\ ÷\ 1000$
	$= 80\ ÷\ 1000$
	$=0.08$

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 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 072

Calculate

$234.2 ÷ 10$ (1 mark)

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$1.237 ÷ 100$ (1 mark)

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$4536.2 ÷ 1000$ (1 mark)

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a. $23.48$

b. $0.01237$

c. $4.5362$

Show Worked Solution

a. $234.2 ÷ 10=23.42$

$\text{(Dividing by 10 “moves” the decimal point 1 place to the left.)}$

b. $1.237 ÷ 100=0.01237$

$\text{(Dividing by 100 “moves” the decimal point 2 places to the left.)}$

c. $4536.2 ÷ 1000=4.5362$

$\text{(Dividing by 1000 “moves” the decimal point 3 places to the left.)}$

Decimals, SM-Bank 071

Calculate

$0.24\times 10$ (1 mark)
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$13.4\times 100$ (1 mark)

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$242.52\times 1000$ (1 mark)

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a. $2.4$

b. $1340$

c. $242\ 520$

Show Worked Solution

a. $0.24\times 10=2.4$

$\text{(Multiplying by 10 “moves” the decimal point 1 place to the right.)}$

b. $13.4\times 100=1340$

$\text{(Multiplying by 100 “moves” the decimal point 2 places to the right.)}$

c. $242.52\times 1000=242\ 520$

$\text{(Multiplying by 1000 “moves” the decimal point 3 places to the right.)}$

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)

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`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 067 MC

Jamie buys a 200 gram bag of pumpkin seeds at the market for making muesli.

Each pumpkin seed has a mass of 0.19 grams.

Which of these is the best estimate for the number of seeds in the 200 gram bag?

`100`
`500`
`1000`
`5000`

Show Answers Only

`C`

Show Worked Solution

`text(Mass of 1 seed) ~~ 0.2 text(g)`

`text(Mass of 10 seeds) ~~ 2 text(g)`

`text(Mass of 100 seeds) ~~ 20 text(g)`

`text(Mass of 1000 seeds) ~~ 200 text(g)`

`:. 1000\ text(is the best estimate.)`

`=> C`

Decimals, SM-Bank 066 MC

`9.634 div 100 =`

`96.34`
`9.634`
`0.9634`
`0.09634`

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`D`

Show Worked Solution

`9.634 div 100 = 0.09634`

`text(When dividing by 100, move the decimal)`

`text(point 2 positions to the left.)`

`=> D`

Decimals, SM-Bank 064

`22.5 ÷`

`= 2.25` (1 mark)

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`10`

Show Worked Solution

`22.5 ÷ 10`	`=22.5/10`
	`=2.25`

Decimals, SM-Bank 063 MC

Which of the following statements is correct for the number sentence `202 xx 0.1`?

`202 xx 0.1` is less than `202`
`202 xx 0.1` is equal to `202`
`202 xx 0.1` is greater than `202`
None of the above

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`A`

Show Worked Solution

`202 xx 0.1`	`= 202 xx 1/10`
	`= 20.2`

`:.\ text(less than 202)`

`=> A`

Decimals, SM-Bank 062

`3.85 div 3.5=`

(2 marks)

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`1.1`

Show Worked Solution

`text(Strategy 1:)`

`3.85 div 3.5`	`=(3.5 + 0.35) div 3.5`
	`=3.5/3.5 + 0.35/3.5`
	`=1 + 0.1`
	`=1.1`

`text(Strategy 2:)`

`3.85 div 3.5`	`=38.5 div 35`
	`=1 3.5/35`
	`=1 1/10`
	`=1.1`

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 015

A flea can jump up to 300 times its body length.

The flea's body length is 1.5 mm.

What is the maximum distance the flea can jump? (2 marks)

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`text(450 mm)`

Show Worked Solution

`text(Maximum distance)`	`=300 xx 1.5`
	`= 3 xx 100 xx 1.5`
	`= 3 xx 150`
	`=450\ text(mm)`

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

a. \(416.48\ ÷\ 200\)	\(=416.48\ ÷\ 100\ ÷\ 2\)
	\(=4.1648\ ÷\ 2\)
	\(=2.0824\)

b. \(20.645\ ÷\ 50\)	\(= 20.645\ ÷\ 10\ ÷\ 5\)
	\(= 2.0645\ ÷\ 5\)
	\(=0.4129\)

c. \(829.715\ ÷\ 500\)	\(=829.715\ ÷\ 100 ÷\ 5\)
	\(=8.29715\ ÷\ 5\)
	\(=1.65943\)

d. \(0.724 ÷\ 400\)	\(=0.724 ÷\ 100\ ÷\ 4\)
	\(=0.00724\ ÷\ 4\)
	\(=0.00181\)

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

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

c. \(1.8\ ÷\ 0.2\times 0.6\)	\(=18\ ÷\ 2\times 0.6\)
	\(=9\times 0.6\)
	\(=9\times 6\ ÷\ 10\)
	\(=5.4\)

c. \(42\ ÷\ 0.6\)	\(=420\ ÷\ 6\)
	\(=70\)