 # Negative Numbers Level 7

## Use negative numbers in basic arithmetic and algebraic calculations.

##### Level 1Level 2Level 3Level 4Level 5Level 6Level 7DescriptionHelpMore

This is level 7: mixed You can earn a trophy if you get at least 9 correct and you do this activity online.

 1. Find the fifth term of the linear sequence which begins 18, 13, 8...  2. Subtract ten squared from four squared.  3. The temperature at noon was $$12^\circ$$C. The temperature at midnight was $$-6^\circ$$C. What is the difference in degrees between those two temperatures?   4. What is the missing number in the calculation $$(-7) - \blacksquare = 12$$?  5. What is the missing number in the calculation $$\blacksquare - (-4) = 9$$?  6. Cristina got these scores 12 -11 12 -4What was her total score?  7. What is negative six cubed?  8. What is the cube root of negative five hundred and twelve?  9. Find the average (mean) of the following set of numbers.$$\{ -7, 7, -11, -6, 27, \}$$  10. What gives the answer negative five when divided by negative eight?  11. A bank account is considered to be 'in the black' or 'in credit' when it contains a positive amount of money. An account is considered to be 'in the red' or 'in debt' when it contains a negative amount of money.     $$\oplus$$ Saturday, September 7, 2019: Opening balance £35     $$\oplus$$ Monday, September 9, 2019: A withdrawl of £84 was made.     $$\oplus$$ Thursday, September 12, 2019: A deposit of £31 was made.     $$\oplus$$ Saturday, September 14, 2019: A withdrawl of £88 was made.What was the final balance (How many pounds are in the account after these transactions)?  12. Here are the transactions for a different account.     $$\oplus$$ Thursday, September 5, 2019: Opening balance £186     $$\oplus$$ Friday, September 6, 2019: A deposit of £348 was made.     $$\oplus$$ Sunday, September 8, 2019: A withdrawl of £585 was made.     $$\oplus$$ Friday, September 13, 2019: A withdrawl of £892 was made.What was the final balance?  Check

This is Negative Numbers level 7. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6

Or here are some other negative number exercises to try:
Temperatures Negative Magic Reading Scales Inequalities

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions. ## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

#### Practice Papers Mathematics GCSE(9-1) Higher style questions and worked solutions presented as twenty short, free, practice papers to print out.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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© Transum Mathematics :: This activity can be found online at:
www.transum.org/software/SW/Starter_of_the_day/Students/Negative_Numbers.asp?Level=7

## Description of Levels

Close Level 1 - Simple subtraction

Example: 5 - 12

Level 2 - Adding to a negative number

Example: -7 + 9

Level 3 - Addition and Subtraction

Example: -10 + -2

Level 4 - Multiplication

Example: -3 x 2

Level 5 - Division

Example: -10 ÷ 5

Level 6 - Substitution

Example: If a=-3 and b=-7 evaluate 7a - 8b - 6

Level 7 - Mixed

Example: A mixed set of word problems

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

### Adding and Subtracting Negative Numbers

The video above is from MathsWatch

### Multiplying and Dividing Negative Numbers

When multiplying or dividing negative numbers remember this:

Same Signs $$\rightarrow$$ Positive Answer

Different Signs $$\rightarrow$$ Negative Answer

Example 1: Same signs (a positive multiplied by a positive) gives a positive answer:

$$12 \times 6 = 72$$

Example 2: Different signs (a positive multiplied by a negative) gives a negative answer:

$$12 \times (-6) = -72$$

Example 3: Different signs (a negative divided by a positive) gives a negative answer:

$$(-12) \div 6 = -2$$

Example 4: Same signs (a negative divided by a negative) gives a positive answer:

$$(-12) \div (-6) = 2$$

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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