When it comes to multiplying and dividing integers, I can say it’s quite easy. Yeah, much easier than adding or subtracting integers. Although it involves both positive and negative numbers, the multiplication and division process kinda works exactly the same way. As I said, it is easy so this tutorial won’t be as long as the other Civil Service Numerical Reasoning reviewers.
When faced with a question involving integer multiplication or division during the Civil Service exam, all you have to do is remember these simple rules;
Onto the first rule. Let’s try an example:
There is only one negative factor in this problem. ONE (1) is an ODD NUMBER so the answer is negative (-). Let’s try another one. This one’s very easy. There is no negative factor and ZERO (0) is considered an EVEN NUMBER so you just proceed with your normal multiplication.
After all the pairs are balanced, there will always be a negative factor left and that will give you a negative answer. Therefore;
Don’t forget when multiplying integers with different signs; ODD NUMBER of negative factors equals negative (-) and EVEN NUMBER of negative factors equals positive (+).
When it comes to division, the sign of the quotient (result) depends on the signs of the dividend (numerator) and divisor (denominator).
Since both the dividend (numerator) and the divisor (denominator) have the same sign, the quotient (result) will be positive.
I think you are ready for some integer multiplication and division exercises. Answer the test below and improve your chances in passing the Civil Service Exam. Try to get at least 17 correct answers.
Finished with the multiplying and dividing integers exercises? Then just click any of the social media buttons below to see the correct answers.
1. -56: When we multiply 7 by -8, we get -56 as the answer. Since the signs of the two factors are different, the product is negative. Therefore, the final answer is -56.
2. 54: When we multiply -6 by -9, we get 54 as the answer. Since the signs of both factors are negative, the product is positive. Therefore, the final answer is 54.
3. 160: To solve this multiplication problem, we need to follow the order of operations (PEMDAS) and perform the multiplication first: (-4) × 5 × (-8) => (-20) × (-8). When we multiply -20 by -8, we get 160 as the answer. Since the signs of both factors are negative, the product is positive. Therefore, the final answer is 160.
4. -252: Again, we perform PEMDAS first; 12 × (-3) × 7 => (-36) × 7 , then when we multiply -36 by 7, we get -252 as the answer. Since one of the factors is negative, the product is negative. Therefore, the final answer is -252.
5. 8,775: To better solve this multiplication problem, we can use the commutative and associative properties of multiplication to rearrange the factors in a way that makes it easier to apply the rules for multiplying positive and negative numbers:
5 × 15 = 75 (positive) and –13 × –9 = 117 (positive)
5 × 15 × (-13) × (-9) => 75 × 117 = 8775 (positive)
6. -5,040: We will use the commutative and associative properties of multiplication again to rearrange the factors in a way that makes it easier to apply the rules for multiplying positive and negative numbers:
(-15) × (-4) = 60 (positive) 7 × (-12) = –84 (negative)
(-15) × (-4) × 7 × (-12) = 60 × (-84) = –5040 (negative)
7. -6,804: To solve the problem, we can follow the same steps as before:
21 × (-18) × (-9) × (-2) => 21 × (-2) × (-18) × (-9)
(-2) × (-18) = 36 (positive)
(-9) × (36) = -324 (negative)
21 × (-2) × (-18) × (-9) = 21 × 36 × (-324) = –6,804
8. 289,408: To solve the problem, we can follow the same steps as before:
(-19) × (-16) × (-34) × (-28) => (-19) × (-28) × (-16) × (-34)
(-19) × (-28) = 532 (positive)
(-16) × (-34) = 544 (positive)
(-19) × (-16) × (-34) × (-28) = 532 × 544 = 289408
9. 6,837,264: Using the same process as before:
(-17) × (-19) × (-18) × (-7) × (-21) × (-8) => (-17) × (-19) × (-7) × (-18) × (-21)
(-17) × (-19) = 323 (positive)
(-7) × (-18) × (-21) × (-8) = 21,168 (positive)
(-17) × (-19) × (-7) × (-18) × (-21) × (-8) = 323 × 21,168 = 6,837,264
10. -4,656,960:
8 × (-5) × (-2) × (-11) × (-3) × 7 × (-4) × (-7) × (-9) => 8 × 5 × 2 × 11 × 3 × 7 × 4 × 7 × 9
Note that we have three negative factors, so the final product will be negative. Now, we can multiply all the positive factors together and then multiply the result by the product of the negative factors:
8 × 5 × 2 × 11 × 3 × 7 × 4 × 7 × 9 = 4,656,960
(-1) × (-1) × (-1) = -1
Finally, we multiply the product of the positive factors by the product of the negative factors to get the final answer:
8 × (-5) × (-2) × (-11) × (-3) × 7 × (-4) × (-7) × (-9) = -4,656,960
NOTE: In the expression 8 × (-5) × (-2) × (-11) × (-3) × 7 × (-4) × (-7) × (-9), there are nine factors being multiplied together. Out of these nine factors, there are three negative factors, namely -5, -2, and -3.
Whenever we multiply an even number of negative factors together, the result is positive. However, when we multiply an odd number of negative factors together, the result is negative. In this case, we have an odd number of negative factors (three), so the final product will be negative.
To calculate the product of the positive factors, we can simply multiply all the positive factors together: 8 × 11 × 7 × 4 × 7 × 9 × 2 = 4,6560. Then, we multiply this product by the product of the negative factors (-5 × -2 × -3 = -30), giving us a final result of -4,656,960.
11. -1: This one is quite simple if you remember the rules in division regarding positive and negative integers.
12. 0.166: We can simplify the expression (-8) ÷ 8 ÷ (-6) as follows:
(-8) ÷ 8 ÷ (-6) => (-1) ÷ (-6)
Here’s how we get to that result:
First, we divide (-8) by 8, which gives us -1, so the expression becomes:
-1 ÷ (-6)
Next, we divide -1 by -6, which gives us a positive result of 0.166. Therefore:
(-8) ÷ 8 ÷ (-6) = (-1) ÷ (-6) = 0.166
You do remember the basics of long division, right?
13. -1.2: Here’s how we get to that result:
(-66) ÷ (-11) ÷ (-5) => 6 ÷ (-5)
Since 6 ÷ (-5) is equal to -1.2, the final answer is -1.2.
14. -0.75: We can simplify the expression (-36) ÷ 12 ÷ 4 as follows:
(-36) ÷ 12 ÷ 4 => (-3) ÷ 1 = -3
Here’s how we get to that result. First, we divide -36 by 12, which gives us -3, so the expression becomes:
-3 ÷ 4
Next, we divide -3 by 4, which gives us -0.75. Therefore:
(-36) ÷ 12 ÷ 4 = (-3) ÷ 4 = -0.75
So the final answer to the expression (-36) ÷ 12 ÷ 4 is -0.75.
15. -10.66: To solve this expression, we can use the same rule for division with negative and positive numbers:
192 ÷ 6 ÷ (-3) => 32 ÷ (-3)
Dividing -32 by 3 using long division is -10.66.
16. 2.80: To solve this expression, we can use the same rule for division with negative and positive numbers:
(-177) ÷ 3 ÷ (-21) => (-59) ÷ (-21)
Since we have two negative numbers, the result will be positive.
(-59) ÷ (-21) = 59 ÷ 21 = 2.80
17. -3.71: To solve this, we will again use the same rule for division with negative and positive numbers:
(-104) ÷ (-4) ÷ (-7) => 26 ÷ (-7)
Since we have one negative number and one positive number, the result will be negative.
26 ÷ (-7) = -3.71
18. 1.11: We’re going to use the same process in dividing integers so solve this one:
110 ÷ 11 ÷ (-9) => 10 ÷ (-9)
Since we have one negative number and one positive number, the result will be negative.
10 ÷ (-9) = -1.11111111…
Rounded to two decimal places, the final answer is:
110 ÷ 11 ÷ (-9) = -1.11
19. 3: Same process again:
96 ÷ (-8) ÷ (-4) => (-12) ÷ (-4)
Since we have two negative numbers, the result will be positive.
(-12) ÷ (-4) = 3
20. 2.125: The solution is:
(-187) ÷ 11 ÷ (-8) => (-17) ÷ (-8)
Since we have two negative numbers, the result will be positive.
(-17) ÷ (-8) = 2.125
So how well did you do in the exercises regarding multiplying and dividing integers? I hope you were able to correctly solve 16 or 17 questions. Practice more about integer by reading this Integer Addition tutorial. It will bolster your chances of passing the Civil Service Exam in just one take.
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