OPERATIONS ON INTEGERS
Summary
TLDRIn this educational video from Field Korean TV's Math Corner, viewers are introduced to the fundamentals of integer operations. The video explains the concept of integers, including positive, negative, and zero. It then delves into addition and subtraction rules for integers, emphasizing the importance of absolute values and the signs of the numbers involved. The tutorial also covers multiplication and division, illustrating how to determine the sign of the result based on the signs of the operands. Each operation is accompanied by clear examples, making the lesson accessible for learners.
Takeaways
- π’ Integers are whole numbers that can be positive, negative, or zero, and include both counting numbers and their negative counterparts.
- β When adding integers with the same sign, simply add the numbers and keep the common sign.
- β For integers with different signs, subtract the smaller absolute value from the larger and keep the sign of the integer with the larger absolute value.
- π Positive numbers are written without a sign, as it's understood that they are positive by default.
- π Subtracting integers involves changing the subtraction sign to addition and then applying the rules for adding integers.
- π« When the subtrahend is greater than the minuend and both are positive, the result is negative, and vice versa for negative numbers.
- βοΈ In multiplication, multiply the absolute values of the integers and then apply the sign rule: same signs result in a positive product, different signs result in a negative product.
- β For division, divide the absolute values and apply the same sign rule as in multiplication: same signs give a positive quotient, different signs give a negative quotient.
- π Dividing by a smaller number results in a decimal or fraction, and the sign is determined by the original signs of the dividend and divisor.
- π The video provides a comprehensive guide to performing basic arithmetic operations with integers, emphasizing the importance of understanding integer properties and the rules for handling different signs.
Q & A
What are integers?
-Integers are whole numbers that can be positive, negative, or zero. They include counting numbers like 1, 2, 3, etc., and their negative counterparts like -1, -2, -3, etc., as well as zero.
What is the rule for adding two positive integers?
-When adding two positive integers, you simply add the numbers together without the need to write a plus sign before the first number, as it is understood to be positive.
How do you add two negative integers?
-To add two negative integers, you add the numbers and then apply a negative sign to the result.
What is the process for adding integers with different signs?
-When adding integers with different signs, you subtract the number with the smaller absolute value from the one with the larger absolute value and then apply the sign of the integer with the larger absolute value to the result.
What is the meaning of absolute value in the context of adding integers?
-The absolute value of a number is the distance of that number from zero, disregarding its sign. For example, the absolute value of both 6 and -6 is 6.
How do you subtract a positive integer from a negative integer?
-To subtract a positive integer from a negative integer, you change the subtraction sign to addition, take the opposite sign of the subtrahend, and then apply the rules for adding integers with different signs.
What is the shortcut for subtracting a smaller positive integer from a larger one?
-The shortcut for subtracting a smaller positive integer from a larger one is to simply subtract the smaller number from the larger one and then apply a negative sign to the result.
What is the rule for multiplying integers?
-When multiplying integers, you first multiply their absolute values and then apply the following rules to determine the sign: if the signs are the same, the result is positive; if the signs are different, the result is negative.
How do you divide two integers with the same sign?
-When dividing two integers with the same sign, the result is positive. You divide the absolute values of the numbers.
What is the outcome when dividing two integers with different signs?
-When dividing two integers with different signs, the result is negative. You divide the absolute values of the numbers and then apply a negative sign to the result.
Outlines
π Introduction to Integers and Their Operations
This paragraph introduces the concept of integers, defining them as whole numbers that can be positive, negative, or zero. Examples of integers are given, such as 35, -20, -100, 7, and 0. The paragraph emphasizes that integers include all counting numbers and their negative counterparts, as well as zero. It then transitions into explaining how to add integers, starting with the addition of two positive integers (e.g., 6 + 9 = 15), followed by the addition of two negative integers (e.g., -6 + (-9) = -15). The rules for adding integers with different signs are also outlined, where the integer with the larger absolute value determines the sign of the sum after subtracting the smaller absolute value from the larger (e.g., 6 + (-9) = -3 and -6 + 9 = 3). The absolute value is defined as the distance of a number from zero, disregarding its sign.
π’ Subtracting Integers: Steps and Examples
This paragraph explains the process of subtracting integers, outlining a four-step method: keeping the first number (minuend), changing the subtraction sign to addition, getting the opposite sign of the second number (subtrahend), and applying the rules of integer addition. Examples are provided to illustrate the process, including subtracting both positive and negative integers. The technique is also discussed for when the subtrahend is greater than the minuend, simplifying the process by directly subtracting the smaller number from the larger and applying the appropriate sign. The paragraph concludes with examples of subtracting a negative number from a positive number and vice versa, demonstrating how to determine the sign of the result based on the absolute values of the integers involved.
π Multiplication and Division of Integers
The rules for multiplying and dividing integers are discussed in this paragraph. The process involves first multiplying or dividing the absolute values of the integers and then determining the sign of the result based on the signs of the original numbers: same signs yield a positive result, while different signs yield a negative result. Several examples are provided to illustrate these rules, including multiplying positive and negative integers, as well as dividing them. The paragraph covers various scenarios, such as multiplying negative six by positive four (resulting in -24) and dividing negative eight by positive two (resulting in -4). The importance of considering the absolute values and the signs of the integers when performing these operations is emphasized.
π Final Examples and Conclusion
This final paragraph presents additional examples of dividing integers, including dividing negative two by positive eight, which results in a negative 0.25 or -25 hundredths. The paragraph concludes with a summary of the key points covered in the video, highlighting the rules for integer operations and expressing a hope that viewers have gained a better understanding of the topic. The video ends with a sign-off and a blessing, accompanied by closing music.
Mindmap
Keywords
π‘Integers
π‘Addition of Integers
π‘Subtraction of Integers
π‘Absolute Value
π‘Multiplication of Integers
π‘Division of Integers
π‘Minuend
π‘Subtrahend
π‘Positive Integers
π‘Negative Integers
Highlights
Integers are whole numbers that can be positive, negative, or zero.
Positive and negative integers represent counting numbers in their respective directions from zero.
The addition of two positive integers is performed by simply adding their values together.
When adding two negative integers, the numbers are added and the result retains the negative sign.
Adding integers with different signs involves subtracting the absolute values and taking the sign of the integer with the larger absolute value.
The absolute value of a number is the distance from zero, disregarding the sign.
Subtraction of integers is converted to addition by changing the sign of the second integer and applying addition rules.
When subtracting a smaller positive integer from a larger one, the result is negative.
Subtracting a larger negative integer from a smaller positive integer results in a positive number.
Multiplication of integers follows rules based on the signs of the numbers involved: same signs result in positive, different signs result in negative.
Division of integers also follows sign rules similar to multiplication: same signs are positive, different signs are negative.
When multiplying or dividing, first calculate the absolute values and then apply the sign rules.
Parentheses in mathematics indicate multiplication.
Integer multiplication and division rules apply to both positive and negative numbers.
The video provides practical examples to illustrate the rules of integer operations.
The video concludes with a summary of the rules for integer operations and a sign-off.
Transcripts
hi welcome to field korean tv
math corner in this video
we will tackle the operations on
integers
first we must know the meaning of
integers
when we say integer it is a whole number
not a fractional number that can be
positive
negative or zero examples
35 negative 20
negative 100 7
and 0. just keep in mind
that integers are all counting numbers
1 2 3 4 5 and so on
and also the negative counting numbers
negative 1 negative 2
negative 3 and so on as well as
zero now let's proceed
to addition of integers
okay let's add first both positive
integers
example 6 plus
9 the numbers are both
positive so we will just add 6 plus 9
equals
15 so positive 6 plus positive 9
equals positive 15 but in writing
positive numbers
we don't need to put the plus sign
because it is understood that a number
without a sign
is a positive number
next let's add both negative
integers okay let's add negative
six plus negative nine
to add integers with the same negative
signs we just add the numbers
then we copy the negative sign in the
answer so negative 6 plus negative 9
equals
negative 15. this time
we will add integers with unlike or
different
signs let's get the sum
of positive six plus negative
nine to add integers
with unlike or different signs just
subtract
the number with a smaller absolute value
from the number with higher absolute
value and copy the sign of the number
with higher absolute value
when we say absolute value it is at the
distance of a number from
0 regardless of its sign
examples the absolute value of six
and negative six is six
the absolute value of nine and negative
nine
is nine as you can see
positive 6 and negative 6 have the same
absolute
value that means that when we get the
absolute value of
a number we disregard the sign
okay let's go back to the problem
okay let's add now so the rule is we
will subtract this
number with smaller absolute value from
the
number with higher absolute value so we
will subtract six from
9 9 minus 6 equals 3
and then to put the sign in our answer
we need to copy the sign of the number
with higher
absolute value so since negative 9 has a
higher absolute
value so we will copy its sign and it is
negative therefore positive 6
plus negative 9 equals negative
3. how about if we add
negative six plus positive nine
the signs of the addends are different
so the rule is to subtract we will
subtract the smaller number
to a higher number in terms of absolute
value
so we will subtract nine minus
six equals three
then to put the sign in the sum we need
to copy the
sign of the number with a higher
absolute
value and since 9 is higher than
6 so we will copy the sign of 9 and it
is
positive so negative
6 plus positive nine equals positive
three as i've said we don't need
to put the sign in writing the answer
when it is positive
let's proceed to subtraction of integers
okay let's know first the steps in
subtracting integers
first keep the first number or
minuend second change the subtraction
sign
into addition sign so that means
minus will become plus third
get the opposite sign of the second
number or
subtrahend and fourth
proceed to the rules in adding integers
to get the answer okay
let's follow these steps in subtracting
integers
so let's have our first example positive
seven minus positive two or
seven minus two it's very easy
so we will just subtract seven minus two
equals
5 in this example
we can get immediately the answer
without changing
the subtraction sign into addition sign
because we only subtract whole numbers
or natural numbers
now let's solve another problem this one
positive two minus positive
seven okay let's follow the steps in
subtracting
integers so we will keep
the first number or the minuend
the two then we will change the
subtraction sign
into a addition sign then we will get
the
opposite sign of the subtrahend so the
subject is positive 7
so then the opposite is negative
7 the last step is to apply
the rules in adding integers as you can
see
the problem becomes positive 2
plus negative 7 the signs
are different so we need to subtract
the smaller number to a higher number in
terms of
absolute value so that means that we
will subtract two
from seven okay let's do it
seven minus two equals
5 then to put the sign in the
answer we need to copy the sign of
the number with a higher absolute value
and that is 7 the sine of 7
is negative so we will copy the negative
sign so the answer for
positive 2 minus positive 7
or 2 minus 7 equals negative
5 but there is a technique in
subtracting
both positive integers in which the
subtrahend
is greater than the minuend
so the technique is just subtract the
smaller number from the higher number
and then put the negative sign in the
answer
so that's it you don't need to do
step by step to save time
but for both negative numbers
and the subtrahend is greater than in
the minuend in terms of absolute value
the answer is positive
ok let's have another example positive
seven
minus negative two okay let's solve this
step by step
first keep the minuend seven
then change the subtraction sign into
addition
so minus will become plus and then get
the opposite
sign of the subtrahend so negative 2
will become
positive 2 and then
apply the rules in adding integers
so the problem becomes 7 plus
2 or positive 7 plus positive 2
so the answer is 9 we will just add
because the numbers
are both positive so
seven minus negative two equals
positive nine
last example negative two
minus positive seven
okay so first step keep the minuend
negative two second change
minus two plus third
get the opposite of the subtrahend
positive seven so will be it will become
negative seven okay
the problem now becomes negative two
plus negative seven
so we will apply the rules in adding
integers
with both negative signs
okay so we will just add the numbers and
then
copy the negative sign 2 plus 7 equals 9
and copy the negative sign so negative
two minus
positive seven the answer is negative
nine
now let's proceed to multiplication
and division of integers
the rules in multiplying and dividing
integers
are the same first multiply
or divide the absolute values of
the numbers next apply the following
rules
in determining the sign of the product
or
quotient so positive
times or divide positive the answer is
always positive negative
times or divide negative the answer is
always positive and when we
multiply or divide integers with
different or unlike signs the answer is
always negative okay
let's solve some problems for you to
better understand the rules
okay let's multiply 6
times 4 or positive 6 times positive 4
okay both positive so we will just
multiply the numbers
and the answer is always positive so 6
times 4
equals 24
next example negative 6
times negative 4 in this problem
i use parenthesis because in mathematics
parenthesis means multiplication
okay so we will multiply negative six by
negative
four the absolute value of negative six
is six
the absolute value of negative 4 is 4
so multiply the absolute value 6 times 4
equals
24 same sign so the answer is
always positive another example
negative six times positive four
the signs here are different so the
answer
must be negative so we will multiply the
absolute value of negative
six and positive 4. so
just multiply 6 times 4 the answer
is 24 and since the
signs are different so the answer must
be
negative so the answer is negative
twenty-four same with if we multiply
positive six times negative four
different signs so the answer is
negative twenty-four
this time we will divide integers
first example 8 divided by
2 or positive 8 divided by
positive 2 the signs are the same
so the answer must be positive we will
just divide the numbers
eight divided by two equals four
okay next problem negative
8 divided by negative 2
again the signs are the same
both negative so the answer must be
positive we will just divide the
absolute value of
the numbers the absolute value of
negative eight is eight
and absolute value of negative two is
two so eight divided by two equals
four next example
negative eight divided by positive two
okay different signs so the answer must
be
negative we will just divide the
absolute value of
negative eight and two so eight divided
by two
equals four and the sign must be
negative so the answer is negative
four last example
negative 2 divided by positive 8
okay so we will divide the absolute
value
of negative 2 which is 2 by the absolute
value of 8 which is 8. okay let's divide
2 divided by
8 so since 2 is less than 8 we will add
0 it will become 20
20 divided by 8 equals 2
two times eight equals sixteen
then subtract twenty minus sixteen
equals
four okay let's add another zero
it will become forty forty divided by
eight equals five
five times eight equals forty
forty minus forty equals zero the answer
is
twenty five hundredths or point twenty
five
but since the signs are different
so we need to use the negative sign
therefore negative 2 divided by positive
8 equals negative 25
hundredths or negative 0.25
that's all for this topic i hope
you learned in this video see you next
time
god bless
[Music]
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