Here are the step-by-step solutions for each problem on the worksheet. Remember to follow PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Left Column:
1.
$3 \times 4 - 4 \times (-7)$
* First, do the multiplication: $3 \times 4 = 12$ and $4 \times (-7) = -28$.
* The equation becomes: $12 - (-28)$.
* Subtracting a negative is the same as adding: $12 + 28 = 40$.
2.
$12 \times (-2) - 11 + 2$
* First, multiply: $12 \times (-2) = -24$.
* Now solve left to right: $-24 - 11 = -35$.
* Then add 2: $-35 + 2 = -33$.
3.
$(-96) \div (-4) + (-9) - (-11)$
* First, divide: $(-96) \div (-4) = 24$ (negative divided by negative is positive).
* The equation becomes: $24 + (-9) - (-11)$.
* Simplify signs: $24 - 9 + 11$.
* Solve left to right: $24 - 9 = 15$.
* Then add: $15 + 11 = 26$.
4.
$(-3) + (-12) - (-3) - (-7)$
* Simplify the double negatives first: $(-3) + (-12) + 3 + 7$.
* Combine the numbers: $-3 - 12 = -15$.
* Then: $-15 + 3 = -12$.
* Finally: $-12 + 7 = -5$.
5.
$2 + 11 + 66 \div 11$
* Division comes before addition: $66 \div 11 = 6$.
* The equation becomes: $2 + 11 + 6$.
* Add them up: $13 + 6 = 19$.
Right Column:
6.
$(-3) \times (-6) - (-12) + (-6)$
* First, multiply: $(-3) \times (-6) = 18$ (negative times negative is positive).
* The equation becomes: $18 - (-12) + (-6)$.
* Simplify signs: $18 + 12 - 6$.
* Add: $18 + 12 = 30$.
* Subtract: $30 - 6 = 24$.
7.
$(-8) - (-66) \div 11 + (-3)$
* Division comes first: $(-66) \div 11 = -6$.
* The equation becomes: $(-8) - (-6) + (-3)$.
* Simplify signs: $-8 + 6 - 3$.
* Solve left to right: $-8 + 6 = -2$.
* Then subtract: $-2 - 3 = -5$.
8.
$5 - 6 \times 3 + 7$
* Multiplication comes first: $6 \times 3 = 18$.
* The equation becomes: $5 - 18 + 7$.
* Solve left to right: $5 - 18 = -13$.
* Then add: $-13 + 7 = -6$.
9.
$(-10) \times (-9) + (-12) \div (-3)$
* Do multiplication and division first.
* Multiply: $(-10) \times (-9) = 90$.
* Divide: $(-12) \div (-3) = 4$.
* The equation becomes: $90 + 4$.
* Add them: $94$.
10.
$4 \times 66 \div 11 + 12$
* Multiplication and division are done from left to right.
* Multiply: $4 \times 66 = 264$.
* Divide: $264 \div 11 = 24$.
* (Alternatively, you can see that $66 \div 11 = 6$, then $4 \times 6 = 24$).
* Add 12: $24 + 12 = 36$.
Final Answer:
Left Column:
1. 40
2. -33
3. 26
4. -5
5. 19
Right Column:
6. 24
7. -5
8. -6
9. 94
10. 36
Parent Tip: Review the logic above to help your child master the concept of integer order of operation worksheet.
