0:00
Multiplying and Dividing Negative Numbers
Select the skills to practice, and then click Go!
Foundational skills
State the sign of a result
\[ (-5) \times (-3) \rightarrow \text{Positive} \]
Work out whether the answer will be positive or negative.
Predict sign of longer calculation
\[ (-4) \times 3 \times (-2) \rightarrow \text{Positive} \]
Predict the sign of a calculation involving multiple negatives.
Multiplication
Multiply positive by negative
\[ 6 \times (-4) \]
Calculate result of positive × negative.
Multiply negative by positive
\[ (-5) \times 9 \]
Calculate result of negative × positive.
Multiply negative by negative
\[ (-4) \times (-7) \]
Calculate result of negative × negative.
Multiply negative by zero
\[ (-8) \times 0 \]
Calculate result of negative × zero.
Division
Divide positive by negative
\[ 24 \div (-6) \]
Calculate result of positive ÷ negative.
Divide negative by positive
\[ (-35) \div 7 \]
Calculate result of negative ÷ positive.
Divide negative by negative
\[ (-36) \div (-4) \]
Calculate result of negative ÷ negative.
Divide zero by negative
\[ 0 \div (-5) \]
Calculate result of 0 ÷ negative.
Missing number problems
Positive × □ = Negative
\[ 7 \times \square = -42 \]
Find missing negative multiplier.
Negative × □ = Positive
\[ (-8) \times \square = 48 \]
Find missing negative multiplier.
Negative × □ = Negative
\[ (-5) \times \square = -35 \]
Find missing positive multiplier.
□ ÷ Negative = Positive
\[ \square \div (-6) = 8 \]
Find missing negative dividend.
□ ÷ Negative = Negative
\[ \square \div (-4) = -7 \]
Find missing positive dividend.
Negative ÷ □ = Result
\[ (-54) \div \square = 9 \]
Find the divisor.
Multiplication grids
Complete grid (1 negative)
\[ \begin{array}{c|c} \times & -2 \\ \hline 3 & \square \end{array} \]
Complete a multiplication grid with negatives.
Complete grid (Multi-negative)
\[ \begin{array}{c|c} \times & -5 \\ \hline -4 & \square \end{array} \]
Grid with multiple negative headers.
Find missing header
\[ \begin{array}{c|c} \times & 5 \\ \hline \square & -20 \end{array} \]
Work backwards to find a missing header.
Combined operations (BIDMAS)
Multiply then add
\[ (-3) \times 4 + 5 \]
BIDMAS with negatives.
Multiply then subtract
\[ 6 \times (-2) – 7 \]
BIDMAS with negatives.
Divide then add/sub
\[ (-20) \div 4 + 8 \]
BIDMAS with negatives.
Brackets then multiply
\[ (5 – 8) \times (-3) \]
Brackets with negatives.
Chain calculation
\[ (-2) \times (-3) \times (-4) \]
Multiple operations left to right.
Midpoints
Midpoint: Positive & Negative
\[ -8 \leftrightarrow 4 \]
Halfway between positive and negative.
Midpoint: Two Negatives
\[ -3 \leftrightarrow -11 \]
Halfway between two negatives.
Midpoint: Negative & Zero
\[ -6 \leftrightarrow 0 \]
Halfway between negative and zero.
Find endpoint given midpoint
\[ \text{Midpoint of } \square \text{ and } 6 \text{ is } 1 \]
Work backwards from midpoint.
Powers of negatives
Square a negative
\[ (-5)^2 \]
Calculate (-x)².
Cube a negative
\[ (-3)^3 \]
Calculate (-x)³.
Compare powers
\[ (-2)^4 \text{ vs } (-2)^3 \]
Compare even and odd powers.
Special cases
Multiply/Divide by -1
\[ 7 \times (-1) \]
Result of operation with -1.
Sum and Product (One Neg)
\[ \text{Sum: } 2, \text{ Prod: } -15 \]
Find numbers given sum and product.
Sum and Product (Both Neg)
\[ \text{Sum: } -7, \text{ Prod: } 12 \]
Find numbers given sum and product.
Timer (Optional)
0:00
Question