f - Pre-Algebra Vol1 Worksheet 6 Multiplying Integers · © 2010 Math TutorDVD.com The Pre-Algebra...

© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 6 – Multiplying Integers

Supplemental Worksheet Problems To Accompany:

The Pre-Algebra Tutor: Volume 1 Section 6 – Multiplying Integers

Please watch Section 6 of this DVD before working these problems.

The DVD is located at:

http://www.mathtutordvd.com/products/item66.cfm


Part 1: Multiplying Positive Integers (Multiplying integers of the same sign)

1) Find the product of the following positive integers.







Part 2: Multiplying Negative Integers (Multiplying integers of the same sign)

7) Find the product of the following negative integers.







Part 3: Multiplying Negative and Positive Integers (Multiplying integers with different signs)

13) Find the product of the following integers.







Part 4: Evaluate and solve for the following expressions

19)

20)

21)

22)

23)

24)

25)

26)


27)

28)

29) 30)

31) 32)

33)

34)


Question

Answer


Begin

(positive)(positive)=(positive)

First we notice we have two positive integers to multiply. Recall that when multiplying positive integers or two integers that have the same sign the result or product will always be positive. Once we realize what sign our result will have we simply multiply the two numbers and include the appropriate sign.

Ans: 16



Begin



Ans: 30



Begin



Ans: 44



Begin



Ans: 48



Begin



Ans: 88



Begin



Ans: 90



Begin

(negative)(negative)=(positive)

First we notice we have two negative integers to multiply. Recall that when multiplying a negative integer to another negative integer or two integers of the same sign the result or product will always be positive. Once we realize what sign our result will have we simply multiply the two numbers and include the appropriate sign.

Ans: 28



Begin



Ans: 35



Begin



Ans: 32



Begin



Ans: 1



Begin



Ans: 45



Begin



Ans: 100



Begin

(negative)(positive)=(negative) OR

(positive)(negative)=(negative)

First we notice we have two integers with opposite signs. Recall that when multiplying a negative to a positive or a positive to a negative integer the result or product will always be negative. So if multiplying two integers with opposite signs, the result will be negative. Once we realize what sign our result will have we simply multiply the two numbers and include the appropriate sign.

Ans: -50



Begin




Ans: -54



Begin




Ans: -93



Begin

(negative)(positive)=(negative)

OR (positive)(negative)=(negative)

Final result:

Since there are three integers, we first begin by multiplying two integers at a time starting from left to right. Each time applying the rules for multiplying positive and negative integers. Once the product is known, we then multiply the product to the remaining integer. The first two integers have different signs so the product or result will be negative. When we take the result and multiply it to the remaining integer we notice they have different signs so the result will be negative.

Ans: -20



Begin



Final result:


Ans: -88



Begin



Final result:


Ans: -60


19)

Begin

First, let’s evaluate the expression by substituting the values expressed by the letters.

Final result:

Next we notice we are multiplying two negative integers together and recall that when multiplying two negative integers or two integers with the same sign we will end up with a positive product or result.

We then simply multiply the two integers together.

Ans: 7


20)

Begin


Final result:

Next, we notice we are multiplying against the number zero. Remember that whenever multiplying anything by zero, your result will always be zero. It doesn’t matter if you are multiplying zero against a positive or a negative integer, the rule is the same.

Ans: 0


21)

Begin


Final result:

Since there are three integers, we first begin by multiplying two integers at a time starting from left to right. Each time applying the rules for multiplying positive and negative integers. Once the product is known, we then multiply the product to the remaining integer. The first two integers are both positive so our result for that will be positive. We then use the result and multiply it against the remaining integer in the expression. In the final multiplication we are multiplying two integers with different signs so the result will be negative.

Ans: -110


22)

Begin

First, we substitute the appropriate integer into the expression.

Final result:

Since there are three integers, we first begin by multiplying two integers at a time starting from left to right. Each time applying the rules for multiplying positive and negative integers. Once the product is known, we then multiply the product to the remaining integer. The first two integers have different signs so our product or result will be negative. We then use the result and multiply it against the remaining integer in the expression. In the final multiplication we are multiplying two integers with different signs so the result will be negative.

Ans: -60


23)

Begin


Final result:

Since there are three integers, we first begin by multiplying two integers at a time starting from left to right. Each time applying the rules for multiplying positive and negative integers. Once the product is known, we then multiply the product to the remaining integer. The first two integers have different signs so our product or result will be negative. We then use the result and multiply it against the remaining integer in the expression. In the final multiplication we are multiplying two integers with the same sign so the result will be positive.

Ans: 150


24)

Begin

(−2)bc8 = (−2)(0)(11)(8)


Final result:

(−2)(0)(11)(8) = 0

Since there are four integers, we first begin by multiplying two integers at a time starting from left to right. Each time applying the rules for multiplying positive and negative integers. Once the product is known, we then multiply the product to the remaining integers until we end up with our final result. We notice we are multiplying against the number zero. Remember that whenever multiplying anything by zero, your result will always be zero. It doesn’t matter if you are multiplying zero against a positive or a negative integer, the rule is the same.

Ans: 0


25)

Begin


Next, we notice we are both multiplying and subtracting. Recall that when there are different operations there is an order we have to follow. We always multiply before we add or subtract. So we will perform all of our multiplication first and then perform the subtraction operation of the products we found to the left and the right of the subtraction sign. Remember that when multiplying integers with different signs (positive with negative or negative to positive) the answer will always be negative.

Now that we are complete with our multiplication we apply what we learned in the previous section for subtracting. We notice we are attempting to subtract a negative number so we will add the opposite (signs cancel out). We are left with an addition of opposite signs. Remember in this scenario we simply subtract and take the sign of the largest absolute value. We notice 30 has the largest absolute value so the final answer will be


Final result:

negative.

Ans: -20


26)

Begin


Next, we notice we are both multiplying and adding. Recall that when there are different operations there is an order we have to follow. We always multiply before we add or subtract. So we perform all of our multiplication first and then perform the addition operation of the products we found to the right of the addition sign. Remember that when multiplying integers with different signs (positive with negative or negative to positive) the answer will always be negative.

Final Result:

Now that we are complete with our multiplication we apply what we learned in the previous sections for adding integers. We notice we are attempting to add a negative number to a positive number. Recall that in these cases when adding opposite signs we simply subtract like we are used to and use the sign of the largest absolute value in the expression which in this case is 70 so our answer will be negative.


Ans: -63


27)

Begin

First, let’s evaluate the expression by substituting the values expressed by the letters. We notice we are both multiplying and doing addition and subtraction. Remember there is order in what we do first. We always multiply before we add or subtract, but we always do what is inside parenthesis before we multiply.

So we need to work whatever operations are inside the parenthesis first and then do what is outside the parenthesis. In the first parenthetical expression we notice we are subtracting a negative so we add the opposite which turns into a simple addition. The second parenthetical expression is a simple addition problem as well. We then plug our results back into our original expression and we see that all that is left is to multiply the two results.

Final result:

Since we are multiplying two positive integers or two integers of the same sign our result will be positive.

Ans: 24


28)

Begin

First, let’s evaluate the expression by substituting the values expressed by the letters. We notice we are both multiplying and doing addition and subtraction. Remember there is order in what we do first. We always multiply before we add or subtract, but we always do what is inside parenthesis before we multiply.

So we need to work whatever operations are inside the parenthesis first and then do what is outside the parenthesis. We notice that we are doing a simple addition inside the parenthesis so we simply add the two integers. Remember to substitute your result back into the original expression and carry out the remaining operations.

Final result:

Now we are left with a multiplication. We notice that our signs our different so we will end up with a negative result.

Ans: -100


29)

Begin


Final result:

Since there are three integers, we first begin by multiplying two integers at a time starting from left to right. Each time applying the rules for multiplying positive and negative integers. Once the product is known, we then multiply the product to the remaining integer. The first two integers have different signs so our product or result will be negative. We then use the result and multiply it against the remaining integer in the expression. In the final multiplication we are multiplying two integers with the same sign so the result will be positive.

Ans: 36


30)

Begin


Next, we notice we are both multiplying and subtracting. Recall that when there are different operations there is an order we have to follow. We always multiply before we add or subtract. So we first multiply and see that we are multiplying two integers with the same sign which means our product or result will be positive.

Final Result:

Now that we are complete with our multiplication we apply what we learned in the previous section for subtracting. We notice we are subtracting a large number from a small number which tells us we will end up owing or with a negative number. We then simply subtract the numbers and place a negative sign on our result.

Ans: -13


31)

Begin


Next, we notice we are both multiplying and subtracting. Recall that when there are different operations there is an order we have to follow. We always multiply before we add or subtract. We see there are three integers to multiply so we multiply two at a time from left to right. The first multiplication we notice we are multiplying two integers of the same sign so our product or result will be positive. Next we use our result and multiply the remaining integer. We notice both integers have the same sign so our product or result will be positive.

Final result:

Now that we are complete with our multiplication we end up with a simply subtraction problem. We notice we are subtracting a smaller number from a bigger number so we simply subtract.

Ans: 2


32)

Begin


Next, we notice we are both multiplying and subtracting. Recall that when there are different operations there is an order we have to follow. We always multiply before we add or subtract. In our first multiplication we notice we are multiplying two integers with different signs which tell us our product or result will be negative. Our second multiplication we notice we are multiplying two integers with the same sign which tells us our product or result will be positive.

Final result:

Now that we are complete with our multiplication we apply what we learned in the previous sections for adding integers. We notice we are attempting to add a negative number to a positive number. Recall that in these cases when adding opposite signs we simply subtract like we are used to and use the sign of the largest absolute value in the expression which in this case is 10 so our answer will be positive.

Ans: 7


33)

Begin


Next, we notice we are both multiplying and subtracting. Recall that when there are different operations there is an order we have to follow. We always multiply before we add or subtract. We see there are three integers to multiply so we multiply two at a time from left to right. The first multiplication we notice we are multiplying two integers with different signs so our product or result will be negative. Next we use our result and multiply the remaining integer. We notice the integers have different signs so our product or result will be negative.

Final result:

Now that we are complete with our multiplication we apply what we learned in the previous sections for adding integers. We notice we are attempting to add two negative integers. Recall that in these cases we will always end up with a negative. We then simply add the absolute values and place the negative sign on our result.

Ans: -70


34) Begin


Next, we notice we are both multiplying and subtracting. Recall that when there are different operations there is an order we have to follow. We always multiply before we add or subtract. We see there are three integers to multiply so we multiply two at a time from left to right. The first multiplication we notice we are multiplying two integers with different signs so our product or result will be negative. Next we use our result and multiply the remaining integer. We notice the integers have the same sign so our product or result will be positive.

Final result:

Now that we are complete with our multiplication we end up with a simply addition problem.

Ans: 73

f - Pre-Algebra Vol1 Worksheet 6 Multiplying Integers · © 2010 Math TutorDVD.com The Pre-Algebra...

Documents

Transcript of f - Pre-Algebra Vol1 Worksheet 6 Multiplying Integers · © 2010 Math TutorDVD.com The Pre-Algebra...