Negative Numbers Practice Test – 50 Questions
Build confidence with negative numbers step by step. Start with number-line foundations, then progress through addition, subtraction, multiplication, division, mixed operations and negative algebraic terms.
- 5 progressive levels
- 50 practice questions
- Instant answer checks
- Hints and full working
Your answers and checked results are saved automatically in this browser.
Level 1
Negative Number Foundations
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Level 2
Adding Negative Numbers
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Level 3
Subtracting Negative Numbers
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Level 4
Multiplying and Dividing Negative Numbers
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Level 5
Mixed Operations & Negative Algebra Terms
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What Are Negative Numbers?
Negative numbers are numbers less than zero. They are written with a minus sign, such as −1, −5 or −20. Together with positive whole numbers and zero, they form the integers.
Negative numbers are an important foundation for upper-primary and secondary mathematics because they appear later in algebra, equations, coordinates, graphs, financial maths, indices and many other topics.
The interactive test above contains 50 free Negative Numbers practice questions, progressing from basic number-line ideas through addition, subtraction, multiplication, division and negative algebraic terms.
Numbers become larger as you move to the right and smaller as you move to the left.
Real-Life Examples of Negative Numbers
Negative numbers are easier to understand when students connect them with familiar situations.
| Situation | Positive | Negative |
|---|---|---|
| Temperature | 5°C above zero | −5°C below zero |
| Money | $20 available | Owing $20 |
| Elevation | 100 m above sea level | 20 m below sea level |
| Movement | Move 4 places right | Move 4 places left |
Which Negative Number Is Bigger?
A common mistake is thinking that −10 must be larger than −3 because 10 is larger than 3.
But on the number line, −3 is further to the right.
Owing $3 is better than owing $10. In the same way, −3 is greater than −10.
How to Add and Subtract Negative Numbers
Addition and subtraction with negative numbers is where many students begin to lose confidence.
Instead of trying to memorise one rule for every possible question, first identify the operation and then look at the signs of the numbers.
Adding Two Negative Numbers
When both numbers are negative, add their sizes and keep the negative sign.
If you owe $4 and then owe another $3, your total debt becomes $7.
Adding a Positive Number to a Negative Number
This is a particularly important type of question.
Some students calculate 14 − 6 = 8 and automatically write +8. The subtraction is correct, but the sign is not.
Compare the sizes:
Since 14 is larger than 6, subtract:
The larger number in magnitude was the negative number −14, so the answer remains negative.
Another Way to Understand −14 + 6
Imagine you owe $14 and then receive $6. You can repay $6 of the debt, but you still owe $8.
Subtracting a Positive Number
Subtracting a positive number moves further in the negative direction.
Start at −5 and move 3 places to the left.
Subtracting a Negative Number
This can look confusing because two negative signs appear close together.
Subtracting a negative is equivalent to adding the opposite:
Multiplying and Dividing Negative Numbers
Multiplication and division use a different sign rule from addition and subtraction.
| Signs | Result | Example |
|---|---|---|
| Positive × Positive | Positive | 4 × 3 = 12 |
| Negative × Positive | Negative | −4 × 3 = −12 |
| Positive × Negative | Negative | 4 × (−3) = −12 |
| Negative × Negative | Positive | −4 × (−3) = 12 |
Same signs → positive
Different signs → negative
The same sign rule applies to division:
Addition or Multiplication? Identify the Operation First
One of the most important negative-number skills is recognising what operation the question is actually asking you to perform.
Students sometimes remember that a negative multiplied by a negative becomes positive and then incorrectly use that rule in an addition question.
The operation is addition. Add the two negative amounts.
The operation is multiplication. Two negative factors give a positive product.
Never apply a multiplication sign rule unless the numbers are actually being multiplied.
What Does a Number Next to Brackets Mean?
When a number is written directly next to brackets, multiplication is implied.
This is different from:
Looking carefully at the operation symbol before calculating prevents many sign mistakes.
Negative Terms in Algebra
Negative-number skills become even more important when students begin algebra. A calculator may help with a numerical calculation, but students still need to understand negative coefficients when working with variables such as x and y.
A term such as −7x has a coefficient of −7. The negative sign belongs to the coefficient.
Adding Negative Algebraic Terms
Subtracting Like Terms with Negative Coefficients
Think of it as:
Subtracting a Negative Algebraic Term
Rewrite subtraction of a negative as addition:
Therefore:
Multiplying Negative Algebraic Terms
Multiplication is different from combining like terms.
Multiply the coefficients:
Then multiply the variables:
So:
One question uses addition. The other uses multiplication.
Common Negative Number Mistakes
1. Forgetting the Sign of the Larger Magnitude
14 − 6 gives 8, but because −14 has the larger magnitude, the result is negative.
2. Thinking Every Pair of Negative Signs Becomes Positive
Two negative numbers being added do not suddenly become positive.
3. Using Multiplication Rules in Addition Questions
The multiplication rule “negative × negative = positive” does not apply because there is no multiplication.
4. Misreading Subtraction of a Negative
Rewrite the subtraction as addition of the opposite.
5. Assuming a Calculator Fixes the Problem
A calculator can produce a numerical answer, but it does not replace understanding. The gap often becomes more obvious in algebra, where students need to manipulate terms such as −7x + 3x or −4y − (−2y).
6. Forgetting That Zero Is Neither Positive nor Negative
Zero is an integer, but it is neither a positive number nor a negative number.
A Reliable Method for Negative Number Questions
- Identify the operation first. Is the question asking you to add, subtract, multiply or divide?
- Look at the signs. Decide which numbers are positive and which are negative.
- If adding different signs, compare magnitudes. Subtract the smaller magnitude from the larger one.
- If subtracting, consider rewriting it as addition of the opposite.
- If multiplying or dividing, use the sign rule. Same signs give positive; different signs give negative.
- Check whether your answer makes sense. A quick number-line or debt check can catch many mistakes.
Operation first. Signs second. Calculation third.
Do not choose a negative-number rule until you know whether the question is addition, subtraction, multiplication or division.
Why Negative Numbers Matter in Year 7 and Beyond
Negative-number skills are often developed through upper-primary and early-secondary mathematics, but students can carry gaps in these skills into later years.
These gaps become especially important when students begin working with:
- negative coefficients in algebra
- combining like terms
- linear equations
- BODMAS and order of operations
- coordinates and the number plane
- indices and powers
- financial calculations involving gains and losses
Students who are comfortable with negative integers generally find it much easier to understand expressions such as:
and equations such as:
If algebra is the next step, students can continue with the Algebra Made Easy guide and the Like Terms guide and 50-question practice test .
Negative Numbers and the NSW Mathematics Curriculum
In the NSW Mathematics K–10 syllabus, integers are whole numbers that can be positive, negative or zero. Negative-number understanding forms part of the broader development of number and algebra skills.
Schools may sequence individual skills differently according to student learning needs, so it is more useful to focus on whether the underlying concepts are secure than to assume every student must meet the topic at exactly the same time.
Students can explore the broader curriculum through the Year 7 Maths NSW Syllabus Guide .
For official curriculum information, visit the NSW Mathematics K–10 Syllabus .
What Should Students Learn After Negative Numbers?
Once addition, subtraction, multiplication and division with negative numbers are secure, students can apply the same skills across algebra and other secondary-school maths topics.
Need Help with Negative Numbers in Telopea or Nearby?
Negative numbers are a common example of a small foundational gap that can create much bigger problems later in algebra.
When a student is struggling with questions such as −14 + 6, I usually slow the process down and first make sure they understand the number line, the meaning of the signs and which operation the question is asking them to perform.
Once the number skills are secure, the same reasoning can be transferred into algebraic examples such as −7x + 3x.
Aussie Math Tutor NSW provides step-by-step maths support for students around Telopea, Oatlands, North Rocks, Dundas, Dundas Valley, Rydalmere, Ermington and Carlingford, with online tutoring available for students across NSW.
Students can also use the 50-question Negative Numbers interactive practice test above to identify which skills need more practice.
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