Download Grade 6 Integers - multiple multiplication operations

ID : pk-6-Integers-multiple-multiplication-operations [1]
Grade 6
Integers - multiple multiplication operations
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Fill in t he blanks
(1)
Find the value of f ollowing :
A)
B)
C)
D)
E)
(2)
16 × 16 × 16 × 10 =
13 × ( -17 ) × 3 =
( -20 ) × ( -2 ) × ( -1 ) =
( -18 ) × 7 × 19 =
What will be the sign (answer : positive or negative) of the product if we multiply together:
A)
B)
C)
D)
E)
(3)
( -9 ) × 19 × ( -16 ) × 16 × ( -5 ) =
15 negative integers and 4 positive integers =
27 negative integers and 1 positive integers =
9 negative integers and 7 positive integers =
20 negative integers and 10 positive integers =
21 negative integers and 9 positive integers =
Find the value of f ollowing :
A)
B)
C)
D)
10 × 11 × ( -7 ) - ( -12 ) × ( -15 ) × ( -4 ) =
18 × 0 + 0 × ( -8 ) × ( -2 ) =
( -5 ) × ( -16 ) × 7 + 3 × 16 =
( -12 ) × ( -1 ) × 5 + 3 × 3 =
E)
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ID : pk-6-Integers-multiple-multiplication-operations [2]
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ID : pk-6-Integers-multiple-multiplication-operations [3]
Answers
(1)
A)
-218880
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
T o solve ( -9 ) × 19 × ( -16 ) × 16 × ( -5 ), f irst of all we have to multiply f irst two
numbers af ter that we have to multiply result with the next number and so on as
shown below:
( -9 ) × 19 × ( -16 ) × 16 × ( -5 )
= -171 × ( -16 ) × 16 × ( -5 )
= 2736 × 16 × ( -5 )
= 43776 × ( -5 )
= -218880
Step 3
T heref ore the value of ( -9 ) × 19 × ( -16 ) × 16 × ( -5 ) is -218880.
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ID : pk-6-Integers-multiple-multiplication-operations [4]
B)
40960
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
T o solve 16 × 16 × 16 × 10, f irst of all we have to multiply f irst two numbers
af ter that we have to multiply result with the next number and so on as shown
below:
16 × 16 × 16 × 10
= 256 × 16 × 10
= 4096 × 10
= 40960
Step 3
T heref ore the value of 16 × 16 × 16 × 10 is 40960.
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ID : pk-6-Integers-multiple-multiplication-operations [5]
C)
-663
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
T o solve 13 × ( -17 ) × 3, f irst of all we have to multiply f irst two numbers af ter
that we have to multiply result with the next number and so on as shown below:
13 × ( -17 ) × 3
= -221 × 3
= -663
Step 3
T heref ore the value of 13 × ( -17 ) × 3 is -663.
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ID : pk-6-Integers-multiple-multiplication-operations [6]
D)
-40
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
T o solve ( -20 ) × ( -2 ) × ( -1 ), f irst of all we have to multiply f irst two numbers
af ter that we have to multiply result with the next number and so on as shown
below:
( -20 ) × ( -2 ) × ( -1 )
= 40 × ( -1 )
= -40
Step 3
T heref ore the value of ( -20 ) × ( -2 ) × ( -1 ) is -40.
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ID : pk-6-Integers-multiple-multiplication-operations [7]
E)
-2394
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
T o solve ( -18 ) × 7 × 19, f irst of all we have to multiply f irst two numbers af ter
that we have to multiply result with the next number and so on as shown below:
( -18 ) × 7 × 19
= -126 × 19
= -2394
Step 3
T heref ore the value of ( -18 ) × 7 × 19 is -2394.
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ID : pk-6-Integers-multiple-multiplication-operations [8]
(2)
A)
negative
Step 1
Multiplication of two positive integers make a positive integer:
f or example 4 × 5 = 20
Multiplication of two negative integers make a positive integer:
f or example (−4) × (−5) = 20
Multiplication of a negative and a positive integer make a negative integer:
f or example (−4) × 5 = −20
Step 2
If number of negative integers are even then the product of integers are positive
else the product of negative integers are negative.
Step 3
Multiplication of 15 negative numbers and 4 positive numbers,
= (Multiplication of 15 negative numbers) × (Multiplication of 4 positive numbers)
= (Multiplication of 14 negative numbers) × (Negative number) × (Multiplication of
4 positive numbers)
= (Positive number) × (Negative number) × (Positive number)
= Negative number
B)
negative
Step 1
Multiplication of two positive integers make a positive integer:
f or example 4 × 5 = 20
Multiplication of two negative integers make a positive integer:
f or example (−4) × (−5) = 20
Multiplication of a negative and a positive integer make a negative integer:
f or example (−4) × 5 = −20
Step 2
If number of negative integers are even then the product of integers are positive
else the product of negative integers are negative.
Step 3
Multiplication of 27 negative numbers and 1 positive numbers,
= (Multiplication of 27 negative numbers) × (Multiplication of 1 positive numbers)
= (Multiplication of 26 negative numbers) × (Negative number) × (Multiplication of
1 positive numbers)
= (Positive number) × (Negative number) × (Positive number)
= Negative number
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ID : pk-6-Integers-multiple-multiplication-operations [9]
C)
negative
Step 1
Multiplication of two positive integers make a positive integer:
f or example 4 × 5 = 20
Multiplication of two negative integers make a positive integer:
f or example (−4) × (−5) = 20
Multiplication of a negative and a positive integer make a negative integer:
f or example (−4) × 5 = −20
Step 2
If number of negative integers are even then the product of integers are positive
else the product of negative integers are negative.
Step 3
Multiplication of 9 negative numbers and 7 positive numbers,
= (Multiplication of 9 negative numbers) × (Multiplication of 7 positive numbers)
= (Multiplication of 8 negative numbers) × (Negative number) × (Multiplication of
7 positive numbers)
= (Positive number) × (Negative number) × (Positive number)
= Negative number
D)
positive
Step 1
Multiplication of two positive integers make a positive integer:
f or example 4 × 5 = 20
Multiplication of two negative integers make a positive integer:
f or example (−4) × (−5) = 20
Multiplication of a negative and a positive integer make a negative integer:
f or example (−4) × 5 = −20
Step 2
If number of negative integers are even then the product of integers are positive
else the product of negative integers are negative.
Step 3
Multiplication of 20 negative numbers and 10 positive numbers,
= (Multiplication of 20 negative numbers) × (Multiplication of 10 positive
numbers)
= (Positive number) × (Positive number)
= Positive number
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ID : pk-6-Integers-multiple-multiplication-operations [10]
E)
negative
Step 1
Multiplication of two positive integers make a positive integer:
f or example 4 × 5 = 20
Multiplication of two negative integers make a positive integer:
f or example (−4) × (−5) = 20
Multiplication of a negative and a positive integer make a negative integer:
f or example (−4) × 5 = −20
Step 2
If number of negative integers are even then the product of integers are positive
else the product of negative integers are negative.
Step 3
Multiplication of 21 negative numbers and 9 positive numbers,
= (Multiplication of 21 negative numbers) × (Multiplication of 9 positive numbers)
= (Multiplication of 20 negative numbers) × (Negative number) × (Multiplication of
9 positive numbers)
= (Positive number) × (Negative number) × (Positive number)
= Negative number
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ID : pk-6-Integers-multiple-multiplication-operations [11]
(3)
A)
-50
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
Now 10 × 11 × ( -7 ) - ( -12 ) × ( -15 ) × ( -4 ) can be expressed as:
10 × 11 × ( -7 ) - ( -12 ) × ( -15 ) × ( -4 )
= (-770) - (-720)
= -770 + 720
= -50
Step 3
T heref ore the value of 10 × 11 × ( -7 ) - ( -12 ) × ( -15 ) × ( -4 ) is -50.
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ID : pk-6-Integers-multiple-multiplication-operations [12]
B)
0
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
Now 18 × 0 + 0 × ( -8 ) × ( -2 ) can be expressed as:
18 × 0 + 0 × ( -8 ) × ( -2 )
= (0) + (0)
=0
Step 3
T heref ore the value of 18 × 0 + 0 × ( -8 ) × ( -2 ) is 0.
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ID : pk-6-Integers-multiple-multiplication-operations [13]
C)
608
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
Now ( -5 ) × ( -16 ) × 7 + 3 × 16 can be expressed as:
( -5 ) × ( -16 ) × 7 + 3 × 16
= (560) + (48)
= 608
Step 3
T heref ore the value of ( -5 ) × ( -16 ) × 7 + 3 × 16 is 608.
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ID : pk-6-Integers-multiple-multiplication-operations [14]
D)
69
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
Now ( -12 ) × ( -1 ) × 5 + 3 × 3 can be expressed as:
( -12 ) × ( -1 ) × 5 + 3 × 3
= (60) + (9)
= 69
Step 3
T heref ore the value of ( -12 ) × ( -1 ) × 5 + 3 × 3 is 69.
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ID : pk-6-Integers-multiple-multiplication-operations [15]
E)
-26
Step 1
We can multiply two numbers by the f ollowing steps:
1. First of all we have to multiply sign of the numbers. we use negative sign
bef ore the negative numbers and we can't use any sign bef ore the positive
numbers.
We can multiply sign as:
+×+=+
+×- =- ×- =+
2. Now we have to multiply numbers.
f or example 3 × 2 = 6,
3 × (-2) = (-6),
(-3) × 2 = (-6),
(-3) × (-2) = 6.
Step 2
Now 16 × 13 + 18 × ( -13 ) can be expressed as:
16 × 13 + 18 × ( -13 )
= (208) + (-234)
= 208 -234
= -26
Step 3
T heref ore the value of 16 × 13 + 18 × ( -13 ) is -26.
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