Year 7 Negative numbers: free practice test with answers

Sample negative numbers questions with answers

Try each one before you open the answer.

1. Introduction to negative integers

   In each pair, which number is greater?

   (a) $-3$ or $-7$

   (b) $-\frac{1}{2}$ or $-\frac{1}{4}$

   Show the answer

   Answer: (a) $-3$ (b) $-\frac{1}{4}$

2. Adding and subtracting positive integers

   Calculate $-8 + 3$.

   Show the answer

   Key idea: When adding integers with opposite signs, find the difference between their absolute values and keep the sign of the integer with the larger absolute value.

   1. Find the absolute values: $\lvert -8 \rvert = 8$ and $\lvert 3 \rvert = 3$.
   2. Subtract the smaller from the larger: $8 - 3 = 5$.
   3. Keep the sign of the integer with the larger absolute value (negative, since $\lvert -8 \rvert > \lvert 3 \rvert$): the answer is $-5$.

   Answer: $-8 + 3 = -5$

3. Adding and subtracting negative integers

   Calculate $-4 - (-9)$.

   Show the answer

   Key idea: Subtracting a negative is the same as adding the positive: $a - (-b) = a + b$.

   1. Rewrite the subtraction of a negative as addition: $-4 - (-9) = -4 + 9$.
   2. The two integers now have opposite signs. Find the difference of the absolute values: $\lvert 9 \rvert - \lvert -4 \rvert = 9 - 4 = 5$.
   3. Keep the sign of the integer with the larger absolute value (positive, since $\lvert 9 \rvert > \lvert -4 \rvert$): the answer is $5$.

   Answer: $-4 - (-9) = 5$

4. Multiplying and dividing integers

   Evaluate: (a) $(-7) \times 8$ (b) $(-6) \times (-9)$

   Show the answer

   Key idea: Different signs give a negative product; the same signs give a positive product.

   1. (a) $7 \times 8 = 56$; signs differ, so $-56$
   2. (b) $6 \times 9 = 54$; signs are the same, so $54$

   Answer: (a) $-56$ (b) $54$

5. Order of operations with integers

   Evaluate $-3 + 4 \times (-2)$.

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   Key idea: Multiplication comes before addition.

   1. $4 \times (-2) = -8$
   2. $-3 + (-8) = -11$

   Answer: $-11$

6. Substituting integers

   If $a = -3$, evaluate $5a + 2$.

   Show the answer

   Key idea: Substitute using brackets around the negative number, then use the order of operations.

   1. $5 \times (-3) + 2$
   2. $= -15 + 2 = -13$

   Answer: $-13$

7. The Cartesian plane

   The points $A(-5, 2)$ and $B(3, 2)$ are plotted on a Cartesian plane.

   (a) Find the length of $AB$.

   (b) Write the coordinates of the point halfway between $A$ and $B$.

   Show the answer

   Key idea: Points with the same $y$-coordinate lie on a horizontal line, so the distance is the difference of the $x$-coordinates.

   1. $AB = 3 - (-5) = 8$ units.
   2. Halfway is 4 units right of $A$: $x = -5 + 4 = -1$, and $y$ stays $2$, giving $(-1, 2)$.

   Answer: (a) $8$ units (b) $(-1, 2)$

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 7 integers worksheet
• Year 7 algebra worksheet
• Year 7 tables of values and plotting points worksheet
• Year 7 transformations on the cartesian plane worksheet