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Percentages, SM-Bank 040 MC

The population of Australian states in 2015 and 2016 is recorded in the table below.

Some data for Western Australia is not shown.
 

 
What was the population of Western Australia (WA) close to in 2016?

  1. \(2\ 773\ 100\)
  2. \(2\ 710\ 500\)
  3. \(2\ 147\ 600\)
  4. \(2\ 091\ 300\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{WA Population in 2016}\)

\(= 2\ 085\ 021 + \Big(\dfrac{0.3}{100}\times 2\ 085\ 021\Big)=2\ 085\ 021 + 6255.063\)

\(=2\ 091\ 276.063\approx 2\ 091\ 300\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{WA Population in 2016}\)

\(=2\ 085\ 021\times 100.3\%= 2\ 085\ 021\times 1.003\)

\(\approx 2\ 091\ 300\)

 
\(\Rightarrow D\)

Percentages, SM-Bank 039

Max wanted to buy a squash racquet that cost $75.

He has saved $60.

How much extra does he need to save as a percentage of the cost price?   (2 marks)

Show Answers Only

\(20\%\)

Show Worked Solution
\(\text{Percentage}\) \(=\dfrac{15}{75}\times 100=\dfrac{1}{5}\times 100\)
  \(= 20\%\)

 
\(\therefore\ \text{Max needs to save an extra 20%.}\)

Percentages, SM-Bank 038

A candy box contains 6 white chocolate bars and 11 dark chocolate bars.

About what percentage of the candy in the box are white chocolate bars?  Give your answer to the nearest whole percentage.  (2 marks)

Show Answers Only

\(35\text{%}\)

Show Worked Solution

\(\text{Percentage of white chocolate bars}\)

\(=\dfrac{6}{17}\times 100\)

\(=35.294….\text{%}\)

\(\approx 35\text{%   (nearest %)}\)

Percentages, SM-Bank 036 MC

In a water polo season, Vladimir had 330 shots at goal.

He scored 170 goals but missed the rest.

Vladimir's success rate of scoring goals was?

  1. less than 25%
  2. more than 25% but less than 50%
  3. more than 50% but less than 75%
  4. more than 75%
Show Answers Only

\(C\)

Show Worked Solution
\(\text{Success rate}\) \(=\dfrac{170}{330}\)
  \(=0.515…\)
  \(=52\text{%}\)

 

\(\therefore\ \text{His succes rate is more than 50% but less than 75%.}\)

 
\(\Rightarrow C\)

Percentages, SM-Bank 035

Ricky wants to buy a cricket bat that has a normal price of $160.

He is given a 15% discount.

What is the value of the discount?  (2 marks)

Show Answers Only

\($24\)

Show Worked Solution

\(\text{Value of the discount}\)

\(10\text{% of }160 = 16\)

\(\therefore\ 5\text{% of }160=8\)

\(\therefore\ 15\text{% of }160=16 + 8 =24\)

\(\therefore\ \text{The value of the discount was }$24.\)

Percentages, SM-Bank 034 MC

Hoon's camera has a memory card that holds 20 gigabytes.

He has used exactly 16 gigabytes of memory.

What percentage of the memory has not been used?

  1. \(4\text{%}\)
  2. \(20\text{%}\)
  3. \(25\text{%}\)
  4. \(80\text{%}\)
Show Answers Only

\(B\)

Show Worked Solution
\(\text{Memory left}\) \(= 20-16\)
  \(= 4\ \text{GB}\)

 

\(\therefore\ \text{Percentage not used}\)

\(=\dfrac{4}{20}\)

\(= 20\text{%}\)

 
\(\Rightarrow B\)

Percentages, SM-Bank 033 MC

Zoey scored 88% on her Geography exam.

If she achieved the same mark on her French exam, which of these could have been her mark?

  1. \(\dfrac{68}{80}\)
  2. \(\dfrac{45}{50}\)
  3. \(\dfrac{40}{50}\)
  4. \(\dfrac{44}{50}\)
Show Answers Only

\(D\)

Show Worked Solution
\(88\text{%}\) \(=\dfrac{88}{100}\)
  \(=\dfrac{44}{50}\)

 
\(\Rightarrow D\)

Percentages, SM-Bank 032 MC

Santana is buying a guitar string.

Some of the strings are on sale.

Select the string that will be cheapest.

A. B. C. D.

 

Show Answers Only

\(C\)

Show Worked Solution

\(\text{C}\text{ost of each option:}\)

\(\text{A.  }$17\)

\(\text{B.  }$35\ \text{less }50\text{%} = $17.50\)

\(\text{C.  }$20\ \text{less }20\text{%} = 20-4 = $16\)

\(\text{D.  }$24\ \text{less } 25\text{%} = 24-6 = $18\)

\(\therefore\ \text{Sale: take }20\text{% off is the cheapest string.}\)

\(\Rightarrow C\)

Percentages, SM-Bank 031

A local soccer club has 1600 fans.

At a game, one-quarter of the fans wear a yellow jersey and the rest wear red.

25% of the red jerseys have a black stripe down the back.

How many red jerseys have a black stripe?  (2 marks)

Show Answers Only

\(300\)

Show Worked Solution
\(\text{Total red jerseys}\) \(=75\text{%}\times 1600\)
  \(=\dfrac{3}{4}\times 1600=1200\)

 

\(\therefore\ \text{Red jerseys with black stripe}\)
\(=0.25\times 1200=300\)

Percentages, SM-Bank 030

Marty and Paul swam 3 kilometres in an ocean swimming race.

Marty finished in a time of 1 hour and 10 minutes.

Paul took 25% longer than Marty.

How long did Paul take to finish the race?  (2 marks)

Show Answers Only

\(87.5\ \text{minutes}\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Paul’s time}\) \(=1\ \text{hour and 10 minutes}+(25\%\times 1\ \text{hour and 10 minutes})\)
  \(=70+17.5\)
  \(=87.5\ \text{minutes}\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{Paul’s time}\)

\(= (1\ \text{hour and 10 minutes})\times 125\%\)

\(= 70\times 1.25\)

\(= 87.5\ \text{minutes}\)
 

\(\therefore\ \text{Paul took 87.5 minutes to complete the race.}\)

Percentages, SM-Bank 029

Jake bought a mobile phone at 25% off the original price.

The original price was $380.

How much did Jake pay for the mobile phone?  (2 marks)

Show Answers Only

\($285\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Price of mobile}\) \(=380-(25\%\times 380)=380-95\)
  \(=$285\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{Price of mobile}\) \(=0.75\times 380=$285\)

Percentages, SM-Bank 027

Richard bought a second hand snowboard at a cost of $390.

Richard had to spend 65% of his savings to buy the snowboard.

How much did Richard have in his savings after buying the snowboard?  (2 marks)

Show Answers Only

\($210\)

Show Worked Solution
\(65\text{%}\times \text{Savings}\) \(= $390\)
 \(\therefore\ \text{Savings}\) \(=\dfrac{390}{0.65}= $600\)

 

\(\therefore\ \text{Savings left}\) \(= 600-390= $210\)

Percentages, SM-Bank 026

Harrison was saving his money to buy a cricket bat.

After 1 month, he had saved 45% of the bat's cost.

After 2 months, he had saved another $90 and now had 75% of the bat's cost.

How much does the bat cost?  (2 marks)

Show Answers Only

\($300\)

Show Worked Solution
\(75\%-45\%\) \(= $90\)
\(30\%\) \(= $90\)
\(\therefore\ 1\%\) \(= $3\)

 

\(\therefore\ \text{The bat cost}\) \(= 100\times 3= $300\)

Percentages, SM-Bank 025

Michael purchases a 3D printer worth $2 490 000.

He was given a 10% discount.

What was the price paid by Michael after the discount?  (2 marks)

Show Answers Only

\($2\ 241\ 000\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Discount}\) \(= 10\text{%}\times 2\ 490\ 000\)
  \(= $249\ 000\)

 

\(\therefore\ \text{Discounted Price}\) \(= 2\ 490\ 000-249\ 000\)
  \(= $ 2\ 241\ 000\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{Discounted Price}\) \(= 90\%\times 2\ 490\ 000=0.9\times 2\ 490\ 000\)
  \(= $ 2\ 241\ 000\)

Percentages, SM-Bank 024

A box of golf balls normally cost $19.50.

During a sale, the golf shop took 10% off the regular price of the balls.

What is the new sale price of the golf balls?  (2 marks)

Show Answers Only

\($17.55\)

Show Worked Solution
\(10\text{% discount}\) \(=\dfrac{19.50}{10}= $1.95\)

 

\(\therefore\ \text{Sale price}\) \(= $19.50-$1.95= $17.55\)

Percentages, SM-Bank 023

Don buys a cricket ball, originally marked $30, that is discounted by 25%.

He also has a loyalty card that gives him another 20% off the sale price.

What is the final cost of the ball?   (2 marks)

Show Answers Only

\($18\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Sale price}\) \(= 30-(25\%\times 30)30-7.50= $22.50\)

 

\(\therefore\ \text{Final cost}\) \(= 22.50-(20\%\times 22.50=22.50-4.50)\)
  \(= $18\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{Final cost}\) \(= 30\times 0.75\times 0.8= $18\)

Percentages, SM-Bank 022

Walker is doing an intensive swim program over the summer holidays.

In his first session, he swims 50 laps.

In his second session, he swims 30% more laps than his first session.

In his third session, he swims 20% more laps than his second session.

How many laps does he swim at his third practice?  (2 marks)

Show Answers Only

\(78\ \text{laps}\)

Show Worked Solution

\(\text{1st session} = 50\ \text{laps}\)

\(\text{2nd session}\) \(= 50 + (30\text{%}\times 50)\)
  \(= 50 + 15\)
  \(= 65\ \text{laps}\)

 

\(\text{3rd session}\) \(= 65 + (20\text{%}\times 65)\)
  \(= 65 + 13\)
  \(= 78\ \text{laps}\)

Percentages, SM-Bank 021

A sport store has a sale.
 

What is the difference in the sale prices of these two tents?  (2 marks)

Show Answers Only

\($7.50\)

Show Worked Solution
\(\text{Price of tent 1}\) \(= 85-30\%\times 85\)
  \(= 85-25.5\)
  \(= $59.50\)
\(\text{Price of tent 2}\) \(= 80-35\%\times 80\)
  \(= 80-28.0\)
  \(= $52.00\)

  

\(\therefore\ \text{Price difference}\) \(= 59.50-52\)
  \(= $7.50\)

Percentages, SM-Bank 020

Mary has 60 books and splits them into four categories.

This table shows the percentage of each category.
  

Book Category Percentage
Textbooks 35%
Sport 30%
Fiction 20%
Travel 15%

 

How many sport books does Mary have?  (2 marks)

Show Answers Only

\(18\)

Show Worked Solution

\(\text{30% of 60 books are sport books.}\)

\(\therefore\ \text{Number of sport books}\) \(= 30\text{%}\times 60\)
  \(=\dfrac{3}{10}\times 60\)
  \(= 18\text{ books}\)

Percentages, SM-Bank 019

A scholarship fund of $1 000 000 is allocated between three scholarships as shown in the table below.
  

  Percentage of $1 million
Academic Scholarship 40%
Sport Scholarship 30%
Hardship Scholarship 30%

  
150 students were given a Hardship Scholarship.

How much did each Hardship Scholarship winner receive?  (2 marks)

Show Answers Only

\($2000\)

Show Worked Solution

\(\text{Hardship Scholarship Funds}\)

\(= 30\text{%}\times 1\ 000\ 000\)

\(= $300\ 000\)
 

\(\therefore\ \text{Amount each winner received}\)

\(= \dfrac{300\ 000}{150}\)

\(= $2000\)

Percentages, SM-Bank 018

Albert has 50 marbles in his bag.

He records the colour of each marble in the table below.
   

Marble Number of Marbles
Blue 20
Red 12
Orange 4
White ?
TOTAL 50

  
What percentage of the marbles are white?  (2 marks)

Show Answers Only

\(28\%\)

Show Worked Solution

\(\text{Number of white marbles}\)

\(= 50-(20 + 12 + 4)= 14\)
   

\(\therefore\ \text{% white}\) \(=\dfrac{14}{50}\times 100= 28\%\)

Percentages, SM-Bank 016 MC

The table below lists the original price and the amount of discount of a pair of jeans at four different shops.
    

JEANS SALE
Shop Original price Discount
A. \($20\) \(25\%\)
B. \($21\) \(\dfrac{1}{3}\)
C. \($18\) \(20\%\)
D. \($17\) \($2\text{ off}\)

    
Which shop has the lowest sale price for the jeans?

Show Answers Only

\(B\)

Show Worked Solution

\(\text{Consider the sale price at each shop:}\)

\(\text{A}\) \(= 20-(25\%\times 20) = $15\)
\(\text{B}\) \(= 21-(1/3\times 21) = $14\)
\(\text{C}\) \(= 18-(20 \text{%}\times 18) = $14.40\)
\(\text{D}\) \(= 17-2 = $15\)

 
\(\Rightarrow B\)

Percentages, SM-Bank 014

Gary is painting his house over 3 days.

    • He paints \(\dfrac{1}{3}\) of the house on the first day.
    • He paints \(\dfrac{5}{12}\) of the house on the second day.

In order to finish, what percentage of the house does Gary need to paint on the third day?  (2 marks)

Show Answers Only

\(25\%\)

Show Worked Solution
\(\text{Fraction painted}\) \(=\dfrac{1}{3}+\dfrac{5}{12}=\dfrac{4 + 5}{12}\)
  \(=\dfrac{9}{12}=\dfrac{3}{4}=75\%\)

 
\(\therefore\ 25\text{% needs to be painted on the third day.}\)

Percentages, SM-Bank 013

Find:

  1. 2% of $14.50.  (2 mark)

  2. 15% of 300 kg.  (2 marks)

  3. \(12\dfrac{1}{2}\%\) of 880 km.  (2 marks)

Show Answers Only

a.     \($0.29\)

b.     \(45\ \text{kg}\)

c.     \(110\ \text{km}\)

Show Worked Solution
a.    \(1\%\ \text{of}\ $14.50\) \(=$0.145\)
\(\therefore\ 2\%\ \text{of}\ $14.50\) \(=2\times $0.145=$0.29\)

 

b.     \(15\%\ \text{of}\ 300\text{ kg}\)  
\(10\text{% of }\ 300\ \text{kg}\) \(=30\ \text{kg}\)
\(\therefore\ 5\text{% of }\ 300\ \text{kg}\) \(=15\ \text{kg}\)
\(\therefore\ 15\text{% of }\ 300\ \text{kg}\) \(=30+15=45\ \text{kg}\)

 

c.     \(12\dfrac{1}{2}\text{% of}\ 880\ \text{km}\)  
 \(25\text{% of}\ 880\ \text{km}\)  \(=220\ \text{km}\)
 \(\therefore\ 12\dfrac{1}{2}\text{% of}\ 880\ \text{km}\) \(=110\ \text{km}\)

Percentages, SM-Bank 012

Find:

  1. 10% of $325.  (1 mark)

  2. 30% of 1200 kg.  (2 marks)

  3. 75% of 500 km.  (2 marks)

Show Answers Only

a.     \($32.50\)

b.     \(360\text{ kg}\)

c.     \(375\text{ km}\)

Show Worked Solution
a.    \(10\text{% of}\ $325\) \(=\dfrac{10}{100}\times 325=\dfrac{1}{10}\times 325\)
  \(=$32.50\)

 

b.     \(30\text{% of }1200\text{ kg}\) \(=\dfrac{30}{100}\times 1200=30\times 12\)
  \(=360\ \text{kg}\)

 

c.     \(75\text{% of}\ 500\) \(=\dfrac{75}{100}\times 500=75\times 5\)
  \(=375\ \text{km}\)

Percentages, SM-Bank 011

Brittany is an apprentice hair dresser who works 8 hours per day.

Yesterday she spent her time in the following way.

    • 0.42 of her day \(\rightarrow\) sweeping and tidying the salon
    • 0.18 of her day \(\rightarrow\) washing hair
    • 0.05 of her day \(\rightarrow\) drying hair

The rest of Brittany's day was spent restocking the shelves with new products.

What percentage of Brittany's day was spent restocking shelves?  (2 marks)

Show Answers Only

\(35\text{%}\)

Show Worked Solution
\(\text{Percentage of day restocking shelves}\) \(=1-(0.42+0.18+0.05)\)
  \(=1-0.65=0.35=35\text{%}\)

 

\(\therefore\ \text{Brittany spent 35% of her day restocking shelves.}\)

Percentages, SM-Bank 010

The breakdown of Joanna's weekly spending is shown in the sector graph below.

What percentage of Joanna's weekly spending was on entertainment?  (2 marks)

Show Answers Only

\(10\text{%}\)

Show Worked Solution
\(\text{Percentage spent on Entertainment}\) \(=100-(20+40+10+20)\)
  \(=10\text{%}\)

 
\(\therefore\ \text{Joanna spent } 10\text{% on Entertainment.}\)

Percentages, SM-Bank 009

Convert the following decimals to percentages.

  1. 0.83  (1 mark)

  2. 0.7  (1 mark)

  3. 0.03  (1 mark)

  4. 1.45  (1 marks)

Show Answers Only

a.     \(83\%\)

b.     \(70\%\)

c.     \(3\%\)

d.     \(145\%\)

Show Worked Solution
a.    \(0.83\) \(=0.83\times 100=83\%\)

 

b.     \(0.7\) \(=0.7\times 100=70\%\)

 

c.    \(0.03\) \(=0.03\times 100=3\%\)

 

d.     \(1.45\) \(=1.45\times 100=145\%\)

Percentages, SM-Bank 008

Convert the following percentages to fractions in simplest form.

  1. 89%  (1 mark)

  2. 55%  (1 mark)

  3. 164%  (2 mark)

  4. 385%  (2 marks)

Show Answers Only

a.     \(\dfrac{89}{100}\)

b.     \(\dfrac{11}{20}\)

c.     \(1\ \dfrac{16}{25}\)

d.     \(3\ \dfrac{17}{20}\)

Show Worked Solution
a.    \(89\%\) \(=\dfrac{89}{100}\)

 

b.     \(55\%\) \(=\dfrac{55}{100}=\dfrac{11}{20}\)

 

c.    \(164\%\) \(=\dfrac{164}{100}=1\dfrac{64}{100}=1\dfrac{16}{25}\)

 

d.     \(385\%\) \(=\dfrac{385}{100}=3 \dfrac{85}{100}=3\ \dfrac{17}{20}\)

Percentages, SM-Bank 007

Convert the following fractions to percentages.

  1. \(\dfrac{51}{100}\)  (1 mark)

  2. \(\dfrac{3}{10}\)  (1 mark)

  3. \(1\dfrac{2}{5}\)  (2 mark)

  4. \(4\dfrac{3}{4}\)  (2 marks)

Show Answers Only

a.     \(51\text{%}\)

b.     \(30\text{%}\)

c.     \(125\text{%}\)

d.     \(475\text{%}\)

Show Worked Solution
a.     \(\dfrac{51}{100}\) \(=51\%\)

 

b.     \(\dfrac{3}{10}\) \(=\dfrac{30}{100}=30\%\)

 

c.    \(1\dfrac{2}{5}\) \(=1\ \dfrac{2\times 20}{5\times 20}=1\dfrac{40}{100}=\dfrac{140}{100}=140\%\)

 

d.     \(4\dfrac{3}{4}\) \(=4 \dfrac{75}{100}=\dfrac{475}{100}=475\%\)

Percentages, SM-Bank 006 MC

Zane bought a soccer ball that was on sale at 50% discount.

He paid $19.95 for the soccer ball.

Which amount below is the best estimate of the original price of the soccer ball?

  1. $40
  2. $25
  3. $20
  4. $10
Show Answers Only

\(A\)

Show Worked Solution

\(19.95\approx $20\ \) and \(\ 50\text{%}=\dfrac{1}{2}\)

\(\therefore\ \dfrac{1}{2}\ \times\ \text{Original Price}\) \(\approx $20\)
\(\therefore\ \text{Original Price}\) \(\approx 2\times 20\)
  \(\approx $40\)

 
\(\Rightarrow A\)

Percentages, SM-Bank 004 MC

Given \(\dfrac{1}{3}=33\dfrac{1}{3}\text{%}\), then \(\dfrac{2}{3}\) written as a percentage is:

  1. \(23\dfrac{2}{3}\text{%}\)
  2. \(33\dfrac{2}{3}\text{%}\)
  3. \(66\text{%}\)
  4. \(66\dfrac{2}{3}\text{%}\)
Show Answers Only

\(D\)

Show Worked Solution
\(\dfrac{2}{3}\) \(= 2\times\dfrac{1}{3}\)
  \(=\Big(2\times 33\dfrac{1}{3}\Big)\text{%}\)
  \(=66\dfrac{2}{3}\text{%}\)

 
\(\Rightarrow D\)

Percentages, SM-Bank 002 MC

Which of the following lists the numbers in decreasing order?

  1. \(35\text {%}\ ,\ 0.3\ ,\ 0.32\ ,\ \dfrac{3}{8}\)
  2. \(\dfrac{3}{8}\ ,\ 35\text{%}\ ,\ 0.32\  ,\ 0.3\)
  3. \(35\text {%}\ ,\ \dfrac{3}{8}\ ,\ 0.3\ ,\ 0.32\)
  4. \(\dfrac{3}{8}\ ,\ 0.32\ ,\ 0.3\ ,\ 35\text {%}\)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Convert to decimals:}\)

\(35\text{%} = \dfrac{35}{100}= 0.35\)

\(\dfrac{3}{8} = 0.375\)

\(\therefore\ \text{descending (decreasing) order is } \rightarrow\dfrac{3}{8}\ ,\ 35\text{%}\ ,\ 0.32\  ,\ 0.3\)

\(\Rightarrow B\)

Percentages, SM-Bank 001 MC

Which of the following lists the numbers in increasing order?

  1. \(65\text {%}\ ,\ 0.7\ ,\ 0.72\ ,\ \dfrac{3}{4}\)
  2. \(\dfrac{3}{4}\ ,\ 0.7\ ,\ 65\text{%}\ ,\ 0.72\)
  3. \(65\text {%}\ ,\ \dfrac{3}{4}\ ,\ 0.7\ ,\ 0.72\)
  4. \(\dfrac{3}{4}\ ,\ 0.72\ ,\ 0.7\ ,\ 65\text {%}\)
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Convert to decimals:}\)

\(65\text{%} = \dfrac{65}{100}= 0.65\)

\(\dfrac{3}{4} = \dfrac{75}{100}=0.75\)

\(\therefore\ \text{ascending (increasing) order is } \rightarrow\  65\text{%}\ ,\ 0.7\ ,\ 0.72\ ,\ \dfrac{3}{4}\)

\(\Rightarrow A\)

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)

Show Answers Only

\(\text{See worked solutions}\)

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

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 081

Evaluate the following:

  1. \(416.48\ ÷\ 200\)  (1 mark)

  2. \(20.645\ ÷\ 50\)  (1 mark)

  3. \(829.715\ ÷ \ 500\)  (2 mark)

  4. \(0.724\ ÷\ 400\)  (2 marks)

Show Answers Only

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:

  1. \(84\ ÷\ 1.2\times 0.3\)  (1 mark)

  2. \(20\times 2.5\ ÷\ 0.1\)  (1 mark)

  3. \(1.8\ ÷ \ 0.2\times 0.6\)  (2 mark)

  4. \(0.8\times 0.03\ ÷\ 1.2\)  (2 marks)

Show Answers Only

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. \(1.2\ ÷\ 4\)  (1 mark)

  2. \(3.2\ ÷\ 0.8\)  (1 mark)

  3. \(42\ ÷\ 0.6\)  (1 mark)

  4. \(1.44\ ÷\ 1.2\)  (1 mark)

Show Answers Only

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. \(1.2\times 8\)  (1 mark)

  2. \(0.8\times 0.7\)  (1 mark)

  3. \(2.5\times 0.04\)  (1 mark)

  4. \(0.05\times 1.6\)  (1 mark)

Show Answers Only

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 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)

Show Answers Only

\(0.75\)

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 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)

Show Answers Only

\(22.8^{\circ}\text{C}\)

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)

Show Answers Only

\($28\)

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)

Show Answers Only

\(60\)

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

  1. \(234.2 ÷ 10\)  (1 mark)

  2. \(1.237 ÷ 100\)  (1 mark)

  3. \(4536.2 ÷ 1000\)  (1 mark)

Show Answers Only

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

  1. \(0.24\times 10\)  (1 mark)
  2. \(13.4\times 100\)  (1 mark)

  3. \(242.52\times 1000\)  (1 mark)

Show Answers Only

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.    \(242.52\times 1000=242\ 520\)

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

Probability, STD1 S2 2023 HSC 8 MC

Four cards marked with the numbers 1, 2, 3 and 4 are placed face down on a table.

One card is turned over as shown.

What is the probability that the next card turned over is marked with an odd number?

  1. \(\dfrac{1}{4}\)
  2. \(\dfrac{1}{3}\)
  3. \(\dfrac{2}{4}\)
  4. \(\dfrac{2}{3}\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Sample space} =1,3,4\)

\(P(\text{odd})=\dfrac{2}{3}\)

  
\(\Rightarrow D\)

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)

Show Answers Only

`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)

Show Answers Only

`$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?

  1. `100`
  2. `500`
  3. `1000`
  4. `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`