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| 12 Theory slides |
| 10 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
Multiplication is the same as repeated addition. However, when multiplying integers, the signs of the factors determine whether the product is positive or negative.
LaShay is a brilliant pianist. One day, she is asked to play at her school concert. She is excited to showcase her talent in front of her peers. She now wants to calculate how long it would take her to play her piece.
She has a total of 8 songs to play and each song is an average of 3 minutes long. How long would it take her to play all the songs?Multiply the number of songs by the average length of a song to find the total time.
In the afternoons, LaShay takes a break from her studies and piano lessons to help her aunt with her pizza shop.
LaShay's aunt pays her $10 for each day she helps her. However, every time LaShay is late, she loses $3.
The division of integer numbers is similar to the division of whole numbers. However, when dividing integers, the signs of the dividend and the divisor determine whether the quotient is positive or negative.
LaShay wants to buy a new dress for her upcoming performance with her earnings for helping her aunt at the pizza shop. She and her parents are at the shopping center. They must take the elevator to the sixth floor to get to LaShay's favorite clothing store.
They are at the end of a line of 35 people waiting for the elevator. The elevator can only carry seven people at a time. How many elevator trips will it take for LaShay and her parents to get into the elevator?Divide the number of people in line by the number of people that can ride in the elevator per trip.
LaShay's concert went so well that she decided to play one of her favorite pieces for an upcoming competition.
She made 6 mistakes while playing for the competition and lost -96 points. If each mistake was worth the same number of points, how much was each mistake worth? Give the answer as a negative integer.Divide the number of points lost by the number of mistakes made.
Find the product of each multiplication.
Consider the given multiplication. -10*-1 We can see that this is a multiplication of two negative integers. Recall that the result is always positive when multiplying two integers with the same sign. We can ignore the signs of the factors for now and perform the multiplication as if both integers were whole numbers. -10*-1 ⇒ 10* 1 Our multiplication simplifies to the multiplication of 10 and 1. We can use the fact that the multiplication of any number and 1 is the number itself to get the product of the multiplication. 10*1=1 ⇒ -10*-1=10
Let's look at the given expression.
-2*12
We have the multiplication of negative 2 by 12. Because both factors have different signs, their product is negative. Let's perform this multiplication as if both numbers were whole numbers and then include the negative sign in the result. We will perform the multiplication using a number line.
We made 2 jumps of 12 units on the number line and ended at 24. This means that 2* 12= 24. We now change this product to its opposite to get the product of the initial multiplication. 2*12=24 ⇒ -2*12=-24
Consider the given multiplication of integers.
13* 15
We have a multiplication of two positive integers, so their product will also be positive. Because both are two-digit numbers, we can use digit by digit multiplication to find their product.
The product of 13 and 15 is 195.
Calculate each division of integers.
Consider the given division expression. 84÷(-6) The division of two integers with different signs is always negative. We can calculate the quotient by ignoring the signs of the dividend and divisor and perform the division as if both numbers were whole numbers. 84÷(-6) ⇒ 84÷6 We then add the negative sign to the result to get the quotient of the original division of integers. Let's first find the quotient of the whole numbers by using long division.
The quotient is 14. Let's change it to its opposite to get the result of the initial division. 84÷6= 14 ⇒ 84÷(-6)= -14
The given expression is also a division of two integers with different signs.
-16÷4
Let's ignore the signs of the integers and perform the division as if both integers were whole numbers again.
-16÷4 ⇒ 16÷4
The resulting division gives how many intervals of 4 are needed to reach 16 on a number line. Let's find it!
We needed 4 jumps of 4 to reach 16. This means that the result of the division is 4. If we change this number to its opposite -4, we get the result of the initial division of integers with different signs. 16÷ 4= 4 ⇒ - 16÷ 4=- 4
We have now a division of two negative integers.
-38÷(-2)
The result of dividing two integers with the same sign is always positive. With this in mind, we can ignore the signs of the integers in the given division and perform the division as if they were whole numbers.
-38÷(-2) ⇒ 38÷2
Now, we can use long division to find the result of this division.
The quotient of dividing 38 by 2 is 19. 38÷2= 19 ⇒ -38÷(-2)= 19
We are asked to determine which of the given options has the same product as 6*10. 6* 10 We have a multiplication of two positive integers, so the product is also positive. Let's use a shortcut to find this product. Because we have a multiplication of an integer by 10, we can add a 0 to the end of the other factor to get the product. 6*10= 6 0 Next, let's find the product of the given options to find which ones are also 60, starting with the first option. 4* 15 We can use digit by digit multiplication to find this product.
The product of 4* 15 is also 60. This means that the expression 4*15 has the same product as 6*10. Let's now find the products of the remaining options using a similar process.
Expression | Product | Equals 60? |
---|---|---|
4*15 | 60 | ✓ |
7*8 | 56 | * |
5*12 | 60 | ✓ |
2*31 | 62 | * |
We conclude that the expressions 4*15 and 5*12 have the same product as 6*10.
We will begin by finding the quotient of 63÷(-7). Note that this is a division of two integers with different signs. We can calculate this quotient by temporarily ignoring the signs of the values and finding their quotient. 63÷(-7) ⇒ 63÷7 Let's use a number line to find the quotient. In this case, the quotient is the number of jumps of 7 that are needed to reach 63.
The quotient is 9. Remember to change this result to its opposite to get the result of the initial division of integers with different signs. 63÷7= 9 ⇒ 63÷(-7)= -9 We now know that we need to determine which of the given options also has a quotient of -9. Consider the first expression. -36÷ 4 We can see that this quotient will also be negative because we have a division of integers with different signs. Again, we first find the quotient of the numbers without considering their signs. -36÷4 ⇒ 36÷4 Let's use another number line to find the quotient!
The quotient is 9, so we change it to its opposite to find the quotient of the original division expression. 36÷4= 9 ⇒ -36÷4= -9 Let's calculate the quotient of the remaining options by following a similar fashion.
Option | Quotient | Equals -9? |
---|---|---|
-36÷4 | -9 | ✓ |
18÷6 | 3 | * |
72÷8 | 9 | * |
54÷(-6) | -9 | ✓ |
The options with the same quotient as 63÷(-7) are -36÷4 and 54÷(-6).