Adding and Subtracting Integers: A Step-By-Step Review | How to Add and Subtract Integers

Summary

In this educational video, Mr. J teaches how to add and subtract integers, focusing on both positive and negative numbers. He explains two methods for each operation: one using absolute values and the other a mental math approach. For addition, with different signs, you take the greater absolute value, subtract the smaller, and the result takes the sign of the larger absolute value. For the same signs, you add the absolute values and keep the common sign. In subtraction, you add the opposite of the number being subtracted, which essentially increases the value. The video provides clear examples and encourages viewers to think about starting points and changes in value for better understanding.

Takeaways

• 📚 The video teaches how to add and subtract integers, focusing on both positive and negative numbers.
• 🔢 When adding integers with different signs, take the greater absolute value and subtract the lesser, then adopt the sign of the number with the greater absolute value.
• 📈 The absolute value represents the distance a number is from zero, which is crucial for adding integers with different signs.
• ➕ For adding integers with the same sign, simply add their absolute values and keep the common sign.
• 🤔 A mental math approach is suggested for adding integers, which involves thinking about the starting point and the change in value.
• ➖ When subtracting integers, the process is effectively adding the opposite of the number being subtracted.
• 💡 Subtracting a negative is akin to removing a debt or expense, which increases the value and results in a positive outcome.
• 🔄 The concept of 'opposite' is important in subtraction; the opposite of a negative number is positive, and vice versa.
• 📉 Subtracting a positive number is like decreasing in value, which results in a more negative outcome when starting with a negative number.
• 🔗 Additional resources for learning how to add and subtract integers are provided in the video description for further assistance.

Q & A

What is the first step when adding integers with different signs?

The first step is to determine the signs of the integers and take the greater absolute value, then subtract the lesser absolute value.

How do you determine the sign of the answer when adding integers with different signs?

The answer takes the sign of the integer with the greater absolute value.

What is the mental math approach to adding integers with different signs?

You can think of it as starting at the positive integer and decreasing in value by the absolute value of the negative integer.

What happens when you add two negative integers?

When adding two negative integers, you add their absolute values and the result takes the same sign, which is negative.

How do you calculate the sum of negative 8 and negative 10?

You add the absolute values (8 + 10 = 18) and since both integers are negative, the result is negative 18.

What is the rule for subtracting integers?

When subtracting integers, you add the opposite of the integer you are subtracting.

Why does subtracting a negative integer result in a positive value?

Subtracting a negative integer is equivalent to adding its positive counterpart, which increases the value.

How do you interpret the subtraction of a negative number in terms of money?

Subtracting a negative number can be thought of as removing a debt or expense, which is a positive action in terms of money.

What is the result of subtracting 20 from negative 3?

You add the opposite of 20 (which is negative 20) to negative 3, resulting in negative 23.

What additional resources does Mr. J provide for further help with integer operations?

Mr. J provides links to more videos and examples in the description of the video for further assistance.

Outlines

00:00

📚 Adding and Subtracting Integers

This paragraph introduces a tutorial on how to add and subtract integers, focusing on both positive and negative values. The instructor explains two methods for adding integers with different signs. The first method involves calculating the absolute values and subtracting the smaller from the larger, taking the sign of the number with the greater absolute value. The example given is 12 + (-7), which results in a positive 5 after subtracting 7 from 12. The second method is a mental math approach, visualizing the operation as starting at 12 and decreasing by 7 to reach 5. The paragraph emphasizes understanding the starting point and the change in value when adding negative numbers.

05:02

🔢 Advanced Integer Operations

The second paragraph continues the tutorial with examples of adding integers with the same sign and subtracting integers by converting the operation into addition. When adding two negative numbers, such as -8 + (-10), the absolute values are added, and the result takes the same sign, yielding -18. The instructor suggests thinking of this as starting at -8 and decreasing by 10 to reach -18. For subtraction, the concept is flipped: subtracting a negative is like adding a positive, which increases the value. An example is given with 5 - (-9), which is equivalent to 5 + 9, resulting in 14. The explanation connects this to the idea of removing debt or expense, which positively impacts the value. Another example, -3 - 20, is also covered, leading to a decrease in value from -3 to -23. The paragraph concludes with an invitation for further learning and a thank you for watching.

Keywords

💡Integers

Integers are whole numbers that can be either positive, negative, or zero. In the context of the video, integers are the primary mathematical objects being manipulated. The video focuses on how to add and subtract integers, which is fundamental for understanding arithmetic operations. For instance, the script mentions adding '12 plus negative 7' and 'negative 8 plus negative 10', showcasing the application of integer arithmetic.

💡Positive Integers

Positive integers are numbers greater than zero and are represented with a '+' sign or no sign at all. The video discusses the rules for adding and subtracting integers, including positive ones. An example from the script is '12 plus negative 7', where '12' is a positive integer, and understanding its role is crucial for determining the correct outcome of the addition.

💡Negative Integers

Negative integers are numbers less than zero and are represented with a '-' sign. The video script includes operations with negative integers, such as 'negative 8 plus negative 10', to demonstrate how their signs affect the result of arithmetic operations. Negative integers are essential for understanding the concept of debt or loss, as alluded to in the script.

💡Absolute Value

The absolute value of a number is the distance between that number and zero on the number line, disregarding its sign. It is a key concept in the video when adding integers with different signs. For example, the script explains calculating the absolute values of '12' and '-7' as part of the process to find the result of '12 plus negative 7'.

💡Addition

Addition is one of the four basic arithmetic operations, combining two numbers to find their total. The video script provides several examples of adding integers, such as '12 plus negative 7', emphasizing the rules for handling different signs and absolute values to reach the correct sum.

💡Subtraction

Subtraction is the arithmetic operation of removing one number from another. The video script explains that subtracting an integer is equivalent to adding its opposite, as shown in the example 'five minus negative nine', which is rephrased as '5 plus 9' to clarify the concept.

💡Opposite Numbers

Opposite numbers are pairs of numbers that have the same absolute value but different signs. The video uses the concept of opposite numbers to explain subtraction, stating that to subtract a number, you add its opposite. For instance, 'negative 9' is the opposite of 'positive 9', and the script uses this in the context of the subtraction example.

💡Mental Math

Mental math involves performing arithmetic calculations in one's mind without using a calculator or writing. The video suggests a mental math approach to adding integers, such as visualizing starting at 'positive 12' and decreasing by '7' to reach '5', which helps in understanding the process without formal computation.

💡Greater Absolute Value

When adding integers with different signs, the result takes the sign of the number with the greater absolute value. The video script illustrates this with the example '12 plus negative 7', where the absolute value of '12' is greater than that of '-7', hence the answer is positive.

💡Same Signs

The video script mentions that when adding integers with the same signs, you add their absolute values and keep the common sign. This is demonstrated in the example 'negative 8 plus negative 10', where both numbers are negative, so their absolute values are added, resulting in '-18'.

Highlights

Introduction to adding and subtracting integers with both positive and negative values.

Explanation of the process for adding integers with different signs.

Rule for determining the sign of the result when adding integers with different signs.

Example calculation: Adding 12 and negative 7, emphasizing the concept of absolute values.

Mental math approach to adding integers, focusing on the change in value.

Guidance on how to think about the starting point and direction of change in integer addition.

Process for adding integers with the same signs, specifically two negative numbers.

Example calculation: Adding negative 8 and negative 10, demonstrating the rule for same signs.

Conceptual approach to understanding integer addition by considering starting and ending values.

Introduction to the concept of integer subtraction as the addition of the opposite number.

Example calculation: Subtracting negative 9 from 5, illustrating the addition of the opposite.

Practical analogy of subtracting a negative as removing a debt or expense, resulting in a positive outcome.

Example calculation: Subtracting 20 from negative 3, showing the decrease in value.

Summary of how to add and subtract integers, emphasizing the importance of understanding the process.

Offer of additional resources for further help with integer operations.

Closing remarks and sign-off, encouraging viewers to seek more examples if needed.

Transcripts

[Music]

welcome to math with mr j

[Music]

in this video i'm going to go through a

review of how to add and subtract

integers and we're going to be working

with both positive and negative integers

we'll start with adding integers now

when it comes to these types of problems

there are different ways to think

through these we will go through two

ways for each of our examples let's jump

into number one where we have 12 plus

negative 7. we'll start this problem by

taking a look at the signs we have a

positive 12 and a negative 7. so we have

different signs a positive and a

negative since we have

different signs

we are going to take the greater

absolute value and subtract the lesser

our answer will take the sign of the

greater absolute value let's start by

writing the absolute value of both 12

and negative 7 and remember absolute

value is the distance a number is from

0. the absolute value

of 12

is 12.

the absolute value of negative 7

is 7.

now we take the greater absolute value

and subtract the lesser

these are already in order so we can

subtract if the larger absolute value

comes second you can always switch the

order to find the difference if need be

let's subtract

so 12 minus 7

is 5.

now we need to determine if our answer

is going to be positive or negative so

we need to take a look at the larger

absolute value which is this 12.

so we take the sign of the larger

absolute value from the original problem

so the larger absolute value is 12 let's

take a look at the 12 in the original

problem and that 12 is positive that

means our answer is going to be positive

so our final answer a positive 5.

so a quick recap here basically we

forgot about any negatives because we

were working with absolute values we

then found the difference between the

absolute values

and the answer takes the sine of the

greater absolute value from the original

problem

now let's think through this another way

and this way is going to be more of a

mental math approach just basically

thinking about what's going on in this

problem so let me rewrite 12

plus

negative 7 here

so our original problem so we are

starting at a positive 12 and we are

adding a negative seven by adding a

negative by adding that negative seven

we are decreasing in value by seven from

that twelve we can basically think of

this as 12 minus 7 or 12 take away 7

that gives us our answer of 5. so 12

plus negative 7 we are decreasing that

12 by a value of 7

so we get a positive 5.

so again we started at a positive 12.

always think about where you are

starting and where you are going from

that starting point so we are adding a

negative 7 which is decreasing our 12 in

value by 7 and we end up with 5.

let's move on to number 2 where we have

negative 8

plus negative 10. here we have two

negatives so the same signs so we're

going to add the absolute values and use

the same sign so let's start by taking a

look at the absolute value of negative 8

and negative 10. the absolute value of

negative eight is eight

plus

the absolute value of negative ten

which is ten

now we add those absolute values because

again we have the same signs

eight plus ten is eighteen

we use the same sign

from the original problem which those

are negatives there so our answer

is negative

final answer

negative 18.

now if we were to think through this we

can think that we are starting at

negative eight so let me rewrite here

negative 8

plus

negative 10.

so again starting at negative 8 and we

are adding a negative 10. so that means

we are decreasing in value by 10. that

leaves us at negative 18. like i

mentioned earlier think about your

starting point so the number you are

starting with we have a negative 8 and

then adding that negative 10 tells us we

are decreasing in value and end up at

negative 18 negative 18

is our final answer that's how we add

integers let's move on to subtraction

so here are our examples for subtracting

integers let's jump into number one

where we have five minus negative nine

now when we subtract integers we're

actually going to add the opposite so if

you're able to add integers you're going

to be able to subtract

the opposite of subtraction is addition

and then we take the opposite of the

number we are subtracting so this gives

us an equivalent problem and we are able

to use this strategy so we have 5

and then let's add the opposite of

negative 9. the opposite of negative 9

is

positive 9 so 5 plus 9 that gives us

14

a positive 14 and that's our

final answer now that answer may not

make sense at first but let's think

about how we end up with a positive 14

in this subtraction problem whenever we

subtract a negative we actually increase

in value i like to think of this in

terms of money a negative represents a

debt or an expense when it comes to

money so that negative 9 would be a 9

debt or expense

think of subtracting a negative like

subtracting or taking away that debt or

expense and getting that money back that

is a good positive thing and increases

the value of that problem so something

to think about let's move on to number

two where we have negative three minus

twenty so let's add the opposite

negative 3

plus the opposite of positive 20 is

negative 20.

so we have negative 3 plus negative 20.

now adding that negative 20 we are

decreasing in value by 20 so we're

starting at negative 3 and then

decreasing in value by 20. that's going

to give us negative

23

and that's our final answer

so there you have it there's how you add

and subtract integers if you need any

more help or examples i dropped links to

more videos and examples down in the

description

i hope that helped

thanks so much for watching

until next time

peace

you