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Percentages, SM-Bank 057 MC

A fishing boat returns with 16 flathead, 7 bream and 9 flounder.

About what percentage of the fish are bream?

  1. 50%
  2. 28%
  3. 22%
  4. 21%
Show Answers Only

\(C\)

Show Worked Solution
\(\text{Percentage of bream}\) \(=\dfrac{\text{number of bream}}{\text{total fish}}\)
  \(=\dfrac{7}{16+7+9}\)
  \(=\dfrac{7}{32}\)
  \(=0.21875=21.875\%\)
  \(\approx 22\%\)

  
\(\Rightarrow C\)

 

Percentages, SM-Bank 056

In a classroom there are 24 boys and 36 girls.

What percentage of the students in the classroom are girls?  (2 marks)

Show Answers Only

\(60\%\)

Show Worked Solution
\(\text{Percentage of girls}\) \(=\dfrac{\text{number of girls}}{\text{total students}}=\dfrac{36}{24+36}\)
  \(=\dfrac{36}{60}=0.6=60\%\)

  

Percentages, SM-Bank 052 MC

Which set of numbers is arranged from the smallest to the largest?

  1. \(-6\ ,\ -7\ ,\ 80\text{%}\ ,\ \dfrac{5}{3}\)
  2. \(-7\ ,\ -6\ ,\ 80\text{%}\ ,\ \dfrac{5}{3}\)
  3. \(-6\ ,\ -7\ ,\ \dfrac{5}{3}\ ,\ 80\text{%}\)
  4. \(-7\ ,\ -6\ ,\ \dfrac{5}{3}\ ,\ 80\text{%}\)
Show Answers Only

\(B\)

Show Worked Solution

\(-7\text{ is less than}\ -6\)

\(80\text{%} = \dfrac{4}{5}\ \text{which is less than}\ \dfrac{5}{3}\)

\(\therefore\ \text{Smallest to largest is }\rightarrow -7\ ,\ -6\ ,\ 80\text{%}\ ,\ \dfrac{5}{3}\)

\(\Rightarrow B\)

Percentages, SM-Bank 051 MC

Which set of numbers is arranged from the smallest to the largest?

  1. \(-3\ ,\ -2\ ,\ 25\text{%}\ ,\ \dfrac{5}{4}\)
  2. \(-2\ ,\ -3\ ,\ 25\text{%}\ ,\ \dfrac{5}{4}\)
  3. \(-3\ ,\ -2\ ,\ \dfrac{5}{4}\ ,\ 25\text{%}\)
  4. \(-2\ ,\ -3\ ,\ \dfrac{5}{4}\ ,\ 25\text{%}\)
Show Answers Only

\(A\)

Show Worked Solution

\(-3\text{ is less than}\ -2\)

\(25\text{%} = \dfrac{1}{4}\ \text{which is less than}\ \dfrac{5}{4}\)

\(\therefore\ \text{Smallest to largest is }\rightarrow -3\ ,\ -2\ ,\ 25\text{%}\ ,\ \dfrac{5}{4}\)

\(\Rightarrow A\)

Percentages, SM-Bank 045

John uses concrete in his landscaping business.

He makes a dry mix using 1 part cement, 2 parts sand and 3 parts gravel.

  1. Express the amount of gravel as a fraction of the total mix. Give your answer in simplest form.  (1 mark)
  2. Express the amount of sand as a percentage of the total mix.  (2 marks)
  3. Express the amount of cement compared to the total mix. Give your answer as a recurring decimal.  (2 marks)

 

Show Answers Only

a.     \(\dfrac{1}{2}\)

b.     \(33\dfrac{1}{3}\%\)

c.     \(0.1\dot{6}\)

Show Worked Solution
a.    \(\text{Gravel as fraction of total}\) \(=\dfrac{3}{6}=\dfrac{1}{2}\)

 

b.     \(\text{Sand as percentage of total}\) \(=\dfrac{2}{6}\times 100=\dfrac{1}{3}\times 100=33\dfrac{1}{3}\%\)

 

c.     \(\text{Cement compared to total}\) \(=\dfrac{1}{6}=0.16666\ldots\approx 0.1\dot{6}\)

Percentages, SM-Bank 044

Express the number of red building bricks above as:

  1. a fraction of the total number of building bricks, in simplest form.  (1 mark)

  2. a percentage of the total number of building bricks.  (1 mark)

 

Show Answers Only

a.     \(\dfrac{5}{8}\)

b.     \(62.5\%\)

Show Worked Solution
a.    \(\text{Fraction of total bricks}\) \(=\dfrac{5}{8}\)

 

b.     \(\text{Percentage of total bricks}\) \(=\dfrac{5}{8}\times 100=\dfrac{125}{2}\)
  \(=62.5\%\)

Percentages, SM-Bank 043

Express the shaded area above as:

  1. a fraction of the total area, in simplest form.  (1 mark)

  2. a percentage of the total area.  (1 mark)

 

Show Answers Only

a.     \(\dfrac{2}{5}\)

b.     \(40\%\)

Show Worked Solution
a.    \(\text{Fraction of total area}\) \(=\dfrac{4}{10}=\dfrac{2}{5}\)

 

b.     \(\text{Percentage of total area}\) \(=\dfrac{4}{10}\times 100=40\%\)

Percentages, SM-Bank 042

Graham has a bag containing coloured marbles.

There are 5 blue marbles, 4 white marbles and 6 green marbles in the bag.

  1. What percentage of the marbles in the bag are blue? Give your answer as a recurring decimal.  (2 marks)

  2. Graham removed 3 blue marbles. What percentage of the remaining marbles are green?  (2 marks)

 

Show Answers Only

a.     \(33.\dot{3}\text{%}\)

b.     \(50\text{%}\)

Show Worked Solution

a.    \(\text{Total marbles}\ =5+4+6=15\)

\(\text{Percentage  Blue}\) \(=\dfrac{5}{15}\times 100\)
  \(=33.33333…\text{%}\)
  \(=33.\dot{3}\text{%}\)

 
b.    \(\text{Total marbles after 3 removed}=12\)

\(\text{Percentage Green}\) \(=\dfrac{6}{12}\times 100\)
  \(=50\text{%}\)

Percentages, SM-Bank 041

Geordie achieved a mark of 31 out of 42 in his English essay.

Convert his mark to a percentage, correct to the nearest whole number.  (2 marks)

 

Show Answers Only

\(74\text{%}\)

Show Worked Solution
\(\text{Conversion}\) \(=\dfrac{31}{42}\times 100\)
  \(=73.809…\text{%}\)
  \(\approx 74\text{%}\)

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

 
\(\Rightarrow D\)