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Fractions, SM-Bank 055

Evaluate the following number sentences, giving your answers in simplest form.

  1. `1/6-5/6`  (1 mark)

  2. `4/9-1/2`  (2 marks)

  3. `-3/4-1/2`  (2 marks)

Show Answers Only

a.    `-2/3`

b.    `-1/18`

c.    `-1 1/4`

Show Worked Solution
a.    `1/6-5/6` `=-4/6`
  `= -2/3`

 

b.    `4/9-1/2` `=(4 xx 2)/(9 xx 2)-(1 xx 9)/(2 xx 9)`
  `= 8/18-9/18`
  `=-1/18`

 

c.    `-3/4-1/2` `=-3/4-2/4`
  `= -5/4`
  `=-1 1/4`

Integers, SM-Bank 071

Aurora had $500 in her bank account at the beginning of September.

During the month she withdrew $415 and deposited $82?

Write and solve a directed number sentence to show the balance of Aurora's account at the end of the month?  (2 marks)

Show Answers Only

` 500-415 + 82= +$167`

Show Worked Solution

`text(Balance)\ = 500-415 + 82 = +167`

`:.\ text(Aurora’s balance)\ = +$167`

Integers, SM-Bank 070

Jamison measured the temperature at sunrise to be `-7\^circ`C.

He measured the temperature again 3 hours later and found it had risen to `5\^circ`C.

  1. By how many degrees had the temperature risen during the 3 hours since sunrise?  (1 mark)

  2. What was the average hourly increase in temperature during this 3 hours period?  (1 mark)

Show Answers Only

a.   `+12^circ`

b.   `4^circ text(/hour)`

Show Worked Solution
a.   `text(Temperature change)` `=5-\-7`  
  `=+12\^circ`  

 

b.   `text(Average temperature)` `=12/3`
  `=4\^circ\text(/hour)`

Integers, SM-Bank 065

Find the values of the following.  (3 marks)

  1. `-3- (-15)`
  2. `7-(-3)`
  3. `-3-(-6)-2`
Show Answers Only

a.   `12`   b.   `10`   c.   `1`

Show Worked Solution

`text(Remember:)\  -\ – = +`

a.   `-3- (-15)= -3 + 15= 12`

b.   `7-(-3)= 7 + 3 = 10`

c.   `-3-(-6)-2 = -3 + 6-2 = 1`

Integers, SM-Bank 049

Complete the following table.  (3 marks)

\begin{array} {|c|c|c|c|}
\hline + & \ \ 4\ \  & -5 & -3 \\
\hline -2 &  &  \\
\hline 7 &  &  \\
\hline -10 &  &  \\
\hline \end{array}

Show Answers Only

\begin{array} {|c|c|c|c|}
\hline + & \ \ 4\ \  & -5 & -3 \\
\hline -2 & 2 & -7 & -5 \\
\hline 7 & 11 & 2 & 4 \\
\hline -10 & -6 & -15 & -13 \\
\hline \end{array}

Show Worked Solution

\begin{array} {|c|c|c|c|}
\hline + & \ \ 4\ \  & -5 & -3 \\
\hline -2 & 2 & -7 & -5 \\
\hline 7 & 11 & 2 & 4 \\
\hline -10 & -6 & -15 & -13 \\
\hline \end{array}

Integers, SM-Bank 048

Find the values of the following.  (3 marks)

  1. `4 -(-7)`
  2. `-1 -(-3)`
  3. `-21-(-16)`
Show Answers Only

a.   `11`   b.   `2`   c.   `-5`

Show Worked Solution

`text(Remember:)\  − − = +`

a.   `4-(-7)= 4 + 7 = 11`

b.   `-1-(-3) = -1 + 3 = 2`

c.   `-21-(-16) = -21 + 16 = -5`

Integers, SM-Bank 046

Evaluate the following.  (3 marks)

  1. `15 + (-8)`
  2. `-7 + 4`
  3. `-7 + 5 + (-2)`
Show Answers Only

a.   `7`   b.   `-3`   c.   `-4`

Show Worked Solution

a.   `15 + (-8) = 15-8 = 7`

b.   `-7 + 4 = -3`

c.   `-7 + 5 + (-2) = -7 + 5-2 = -4`

Integers, SM-Bank 045

Evaluate the following.  (3 marks)

  1. `-1 + (-5)`
  2. `-12 + 5`
  3. `-3 + 4 + (-1)`
Show Answers Only

a.   `-6`   b.   `-7`   c.   `0`

Show Worked Solution

a.   `-1 + (-5) = -1-5 = -6`

b.   `-12 + 5 = -7`

c.   `-3 + 4 + (-1) = -3 + 4-1 = 0`

Integers, SM-Bank 039

Jennifer opened a bank account with $500. Each week for 4 weeks she withdrew $122 for rent. At the end of the month the bank deducted $15 in fees.

What was the balance of Jennifer's bank account at the end of the month? (2 marks)

Show Answers Only

`-$3`

Show Worked Solution

`text(Balance)\ = 500-122 xx 4-15 = 500-488-15 = -3`

`:.\ text(Jennifer’s balance)\ = -$3`

Integers, SM-Bank 037

Jasper is a meteorologist working in Antartica. One of his jobs each week is to upload the daily maximum and minimum temperatures to the Base Camp website.

Jasper has partially completed his log book for this week but will need his additional notes to fill in the missing entries before he can upload them to the website.

Using Jasper's notes below, complete the missing log book entries.  (4 marks)

 Jasper's Additional Notes:

  1. Tuesday's maximum is 3 less than Monday's maximum.
  2. Thursday's temperature range is 12.
  3. Saturday's minimum is 3 times smaller than Wednesday's minimum.
  4. Saturday's maximum is half of Sunday's maximum.
     
    TEMPERATURE LOG BOOK
    \begin{array} {|l|c|c|}
    \hline \textbf{Day} & \textbf{Minimum} &  \textbf{Maximum}  \\
    \hline \text{Monday} & -10°  &  -1° \\
    \hline \text{Tuesday} & -15°  &   \\
    \hline \text{Wednesday} & -7°  &  -2° \\
    \hline \text{Thursday} &   &  -8° \\
    \hline \text{Friday} & -17°  &  -6° \\
    \hline \text{Saturday} &  &   \\
    \hline \text{Sunday} & -19°  &  -4° \\
    \hline \end{array}

Show Answers Only

TEMPERATURE LOG BOOK
\begin{array} {|l|c|c|}
\hline \textbf{Day} & \textbf{Minimum} &  \textbf{Maximum}  \\
\hline \text{Monday} & -10°  &  -1° \\
\hline \text{Tuesday} & -15°  & \colorbox{lightblue}{−4°} \\
\hline \text{Wednesday} & -7°  &  -2° \\
\hline \text{Thursday} &  \colorbox{lightblue}{−20°} &  -8° \\
\hline \text{Friday} & -17°  &  -6° \\
\hline \text{Saturday} & \colorbox{lightblue}{−21°} &  \colorbox{lightblue}{−2°} \\
\hline \text{Sunday} & -19°  &  -4° \\
\hline \end{array}

Show Worked Solution

`1.\   text{Tuesday’s Maximum}\= -1-3 = -4`

`2.\   text{Thursday’s Minimum}\= -8-12 = -20`

`3.\   text{Saturday’s minimum}\= 3 xx -7 = -21`

`4.\   text{Saturday’s maximum}\= -4 ÷ 2 = -2`
  

TEMPERATURE LOG BOOK
\begin{array} {|l|c|c|}
\hline \textbf{Day} & \textbf{Minimum} &  \textbf{Maximum}  \\
\hline \text{Monday} & -10°  &  -1° \\
\hline \text{Tuesday} & -15°  & \colorbox{lightblue}{−4°} \\
\hline \text{Wednesday} & -7°  &  -2° \\
\hline \text{Thursday} &  \colorbox{lightblue}{−20°} &  -8° \\
\hline \text{Friday} & -17°  &  -6° \\
\hline \text{Saturday} & \colorbox{lightblue}{−21°} &  \colorbox{lightblue}{−2°} \\
\hline \text{Sunday} & -19°  &  -4° \\
\hline \end{array}

Integers, SM-Bank 036

James runs a tyre fitting company.

At the beginning of February he took out a `$50\ 000` bank loan to expand his workshop.

In July James had flood damage in his workshop and added `$20\ 000` to his bank loan to pay for repairs. 

By the end September he had made loan repayments totalling `$12\ 000` and had also deposited business profits of `$15\ 000` into his loan account.

Write a number sentence and use it to calculate how much James owed at the end of September. (3 marks)
  

Show Answers Only

`-$43\ 000`

Show Worked Solution
`text(Amount of debt)` `= -50\ 000-20\ 000+12\ 000+15\ 000`  
  `= -70\ 000+27\ 000 `  
  `= -43\ 000`  

`:.\ text(James’ debt at the end of September)\= -$43\ 000`

Integers, SM-Bank 032

The daily high and low temperatures are measured in four ski resorts and recorded in the table below.

\begin{array} {|l|c|c|}
\hline \textbf{Ski Resort} & \textbf{Low} &  \textbf{High}  \\
\hline \text{Thredbo} & -1°  &  6° \\
\hline \text{Charlotte's Pass} & -5°  &  1° \\
\hline \text{Mount Hotham} & -2°  &  3° \\
\hline \text{Perisher} & -4°  &  4° \\
\hline \end{array}

  1. Which resort had the lowest recorded temperature range?  (1 mark)

  2. Which resort had a recorded temperature range of 6 degrees?  (1 mark)

Show Answers Only

a.   `text(Mount Hotham)`

b.   `text(Charlotte’s Pass)`

Show Worked Solution

`text(Considering all options.)`

`text(Thredbo)` `=6-(-1)` `=7`
`text(Charlotte’s Pass)` `=1-(-5)` `=6`
`text(Mount Hotham)` `=3-(-2)` `=5`
`text(Perisher)` `=4-(-4)` `=8`

 
a.   `text(Lowest Range)\ =\text(Mount Hotham)`

b.   `text(Range of)\ 6 = text(Charlotte’s Pass)`

Integers, SM-Bank 021

Rachel lives in Broome where the temperature on a particular day was 46°C.

Rachel's son lives in Winnipeg, Canada, and on the same day the temperature there was −16°C.

What was the temperature difference between the two towns on this day? (2 marks)

Show Answers Only

`62°text(C)`

Show Worked Solution
`text(Temperature difference)` `= 46-(-16)`
  `= 62°text(C)`

Integers, SM-Bank 020 MC

Which of the following changes is the smallest?

  1. `-8°text(C  to)\ -4°text(C)`
  2. `-5°text(C  to)\ -2°text(C)`
  3. `-2°text(C  to)\ 3°text(C)`
  4. `3°text(C  to)\ 7°text(C)`
Show Answers Only

`B`

Show Worked Solution

`text(Consider each option:)`

`-8\ text(to)\ -4` `=\ text(4° change)`
`-5\ text(to)\ -2` `=\ text(3° change)`
`-2\ text(to)\ 3` `=\ text(5° change)`
`3\ text(to)\ 7` `=\ text(4° change)`

 

`:.\ -5^@\ text(C to)\-2^@text(C is the smallest change.)`

`=> B`

Integers, SM-Bank 019

Death Valley is the lowest point in the United States at `-`85 metres, which is below sea level.

King's Peak, also in the United States, is 4128 metres above sea level.

What is the difference, in metres, between Death Valley and King's Peak?  (2 marks)

Show Answers Only

`4213\ text(metres)`

Show Worked Solution
`text(Difference)` `= 4128- (-85)`
  `= 4213\ text(metres)`

Integers, SM-Bank 018 MC

Dilbert and Smacka were playing a game where they both started with zero points.

Dilbert's final score was 165 points and Smacka's final score was `-90`.

How many more points did Dilbert have than Smacka?

  1. `-255`
  2. `-75`
  3. `75`
  4. `255`
Show Answers Only

`D`

Show Worked Solution
`text(Difference)` `= 165 – (-90)`
  `= 255`

`=> D`

Integers, SM-Bank 017

Murray lives in Bundaberg, QLD, where the temperature on a particular day was 39°C.

Murray's son lives in Salt Lake City, USA, and on the same day the temperature there was `-`15°C.

What was the temperature difference between the two towns on this day?  (2 marks)

Show Answers Only

`54°text(C)`

Show Worked Solution
`text(Temperature difference)` `= 39-(-15)`
  `= 54°text(C)`

Integers, SM-Bank 016 MC

Manou placed an apple pie into his oven.

The 1st measurement of the apple pie's temperature was  `-` 4°C.

Twenty minutes later, a second temperature reading was taken, which measured 21°C.

What was the change in temperature between the two measurements?

  1. decrease of  25°C
  2. decrease of  17°C
  3. increase of  25°C
  4. increase of  17°C
Show Answers Only

`C`

Show Worked Solution
`text(Change in temperature)` `=21-(-4)`
  `=25^@ text(C)`

 

`:.\ text(An increase of  25°C.)`

`=> C`