# 10.5 Subtraction of signed numbers

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to subtract signed numbers. By the end of the module students should understand the definition of subtraction, be able to subtract signed numbers and be able to use a calculator to subtract signed numbers.

## Section overview

• Definition of Subtraction
• The Process of Subtraction
• Calculators

## Definition of subtraction

We know from experience with arithmetic that the subtraction $5-2$ produces 3, that is $5-2=\text{3}$ . We can suggest a rule for subtracting signed numbers by illus­trating this process on the number line.

Begin at 0, the origin.

Since 5 is positive, move 5 units to the right.

Then, move 2 units to the left to get to 6. (This reminds us of addition with a negative number.)

From this illustration we can see that $5-2$ is the same as $\text{5}+\left(-2\right)$ . This leads us directly to the definition of subtraction.

## Definition of subtraction

If $a$ and $b$ are real numbers, $a-b$ is the same as $a+\left(-b\right)$ , where $-b$ is the opposite of $b$ .

## The process of subtraction

From this definition, we suggest the following rule for subtracting signed numbers.

## Subtraction of signed numbers

To perform the subtraction $a-b$ , add the opposite of $b$ to $a$ , that is, change the sign of $b$ and add.

## Sample set a

Perform the indicated subtractions.

$5-3=5+\left(-3\right)=2$

$4-9=\text{4}+\left(-9\right)=-5$

$-4-6=-4+\left(-6\right)=-\text{10}$

$-3-\left(-\text{12}\right)=-3+\text{12}=9$

$0-\left(-15\right)=\text{0}+\text{15}=\text{15}$

The high temperature today in Lake Tahoe was 26°F. The low temperature tonight is expected to be -7°F. How many degrees is the temperature expected to drop?

We need to find the difference between 26 and -7.

$26-\left(-7\right)=\text{26}+\text{7}=\text{33}$

Thus, the expected temperature drop is 33°F.

$\begin{array}{ccc}-6-\left(-5\right)-10& =& -6+5+\left(-10\right)\hfill \\ & =& \left(-6+5\right)+\left(-10\right)\hfill \\ & =& -1+\left(-10\right)\hfill \\ & =& -11\hfill \end{array}$

## Practice set a

Perform the indicated subtractions.

$9-6$

3

$6-9$

-3

$0-7$

-7

$1-\text{14}$

-13

$-8-\text{12}$

-20

$-\text{21}-6$

-27

$-6-\left(-4\right)$

-2

$8-\left(-\text{10}\right)$

18

$1-\left(-\text{12}\right)$

13

$\text{86}-\left(-\text{32}\right)$

118

$0-\text{16}$

-16

$0-\left(-\text{16}\right)$

16

$0-\left(8\right)$

-8

$5-\left(-5\right)$

10

$\text{24}-\left[-\left(-\text{24}\right)\right]$

0

## Calculators

Calculators can be used for subtraction of signed numbers. The most efficient calculators are those with a key.

## Sample set b

Use a calculator to find each difference.

$3,\text{187}-8,\text{719}$

 Display Reads Type 3187 3187 Press - 3187 Type 8719 8719 Press = -5532

Thus, $3,\text{187}-8,\text{719}=-5,\text{532}$ .

$-\text{156}-\left(-\text{211}\right)$

Method A:

 Display Reads Type 156 156 Press -156 Type - -156 Press 211 211 Type -211 Press = 55

Thus, $-\text{156}-\left(-\text{211}\right)=\text{55}$ .

Method B:

We manually change the subtraction to an addition and change the sign of the number to be subtracted.

$-\text{156}-\left(-\text{211}\right)$ becomes $-\text{156}+\text{211}$

 Display Reads Type 156 156 Press -156 Press + -156 Type 211 211 Press = 55

## Practice set b

Use a calculator to find each difference.

$\text{44}-\text{315}$

-271

$\text{12}\text{.}\text{756}-\text{15}\text{.}\text{003}$

-2.247

$-\text{31}\text{.}\text{89}-\text{44}\text{.}\text{17}$

-76.06

$-0\text{.}\text{797}-\left(-0\text{.}\text{615}\right)$

-0.182

## Exercises

For the following 18 problems, perform each subtraction. Use a calculator to check each result.

$8-3$

5

$\text{12}-7$

$5-6$

-1

$\text{14}-\text{30}$

$-6-8$

-14

$-1-\text{12}$

$-5-\left(-3\right)$

-2

$-\text{11}-\left(-8\right)$

$0-6$

-6

$0-\text{15}$

$0-\left(-7\right)$

7

$0-\left(-\text{10}\right)$

$\text{67}-\text{38}$

29

$\text{142}-\text{85}$

$\text{816}-\text{1140}$

-324

$\text{105}-\text{421}$

$-\text{550}-\left(-\text{121}\right)$

-429

$-\text{15}\text{.}\text{016}-\left(4\text{.}\text{001}\right)$

For the following 4 problems, perform the indicated operations.

$-\text{26}+7-\text{52}$

-71

$-\text{15}-\text{21}-\left(-2\right)$

$-\text{104}-\left(-\text{216}\right)-\left(-\text{52}\right)$

164

$-0\text{.}\text{012}-\left(-0\text{.}\text{111}\right)-\left(0\text{.}\text{035}\right)$

When a particular machine is operating properly, its meter will read 34. If a broken bearing in the machine causes the meter reading to drop by 45 units, what is the meter reading?

-11

The low temperature today in Denver was $-4°$ F and the high was $-\text{42}°$ F. What is the temperature difference?

## Exercises for review

( [link] ) Convert $\text{16}\text{.}\text{02}\frac{1}{5}$ to a decimal.

16.022

( [link] ) Find 4.01 of 6.2.

( [link] ) Convert $\frac{5}{\text{16}}$ to a percent.

31.25%

( [link] ) Use the distributive property to compute the product: $\text{15}\cdot \text{82}$ .

( [link] ) Find the sum: $\text{16}+\left(-\text{21}\right)$ .

-5

#### Questions & Answers

How does cognition and memory links with perception?
let's talk Sigmund Freud psychosexual theory and psychoanalytic theory.
Catalina
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Ruth
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Ximax
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Sz
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Ruth
you need to looks for clues. otherwise there is no ready-made answer to your question.
Paul
what if they were acting weird and want to talk but can't
Ruth
also clues like what
Ruth
how to ready human mind
how to read human behaviour
Sujeet
Describe frontal lobe syndrome
Frontal lobe syndrome is an impairment of the frontal lobe that occurs due to disease or head trauma.
Zafar
what does the bell curve represent in intelligence testing?
average
Angela
I'M A VERY CURIOUS PERSON WHO LOVES TO LEARN ABOUT DIFFERENT TYPES
I AM A PERSON WHO IS NOT CHOOSING TO LET MY MENTAL HEALTH AFFECT ME AND I AM AN
Sheri
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rilek
Indeed....different types means what exactly and how does these different types transpire into our lives? there are many different ways of allowing ourselves to accommodate and continiously play out the fact we have mental illnesses!!!
Elizabeth
social learning theory
how we know the people are telling lie
Vasu
human brain
SERAJ
if you want to learn how to detect the lie you have to observe their behaviour...
Aayan
that's common things..
MOHD
anything specially, tht we can say either person is telling yes or no..?
MOHD
Yes
rochell
I believe there are many factors that play into being a human lie detector.
Tasha
all of which is governed by the human brain.
Tasha
There's no accurate method of telling someone is lying unless we know the truth ourselves. Some people, especially people with manipulative tendencies, will make a lie as believable as possible. Behaviors could tell the person is hiding something or may be feeling uncomfortable while being observed.
agii
Ex. Talking too fast while explaining a story might indicate that the person is indeed hiding something. Other than that, people, usually with histrionic personality disorder, also tend to exaggerate stories.
agii
DORFRLYN It's not easier to feel lied at first moment of talking to someone you know or you don't know. The person will be guilty of what they tell in the first sentence.They first find a way to hide the the truth. By so doing, the movement, and the head knock, this symbloyz the shift of origin
dorfrlyn
for one to tell lies, should first read the mind of the listener.
dorfrlyn
I agree with you Agil.Usually a person talks too fast,is hiding something true. But also talking too slow will mean creation of new story rather than the truth.
dorfrlyn
some people have the habit of speaking too fast, so in that case how can we identify whether the person is lying or not?
Labdhee
pay attention on facial expressions
El
When people talk too fast to the point that it's incomprehensible, it could mean that that person is trying to have you move one from one topic to another to prevent you from asking questions.
agii
observe micro expressions
Zafar
thanks to all for giving ans😃
Vasu
MsPam
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Shanelle
Just wrapped a blackboard discussion on that! Theory is a great class. :)
Rachael
what if somebody answers questions quickly because they have social anxiety
Ashley
detecting lies is easier than many think. the dynamics of listening, body language, facial expression, story line, deductive reasoning and most of all analytical skills all play a role in determining if someone is lying. micro expressions can be very hard to discern requiring close analysis!
Kyth
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intresting I mean
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Sometimes if you type "positive psychology " in your play store, you'll get some good ones
Tahmetrea
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Andrew
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Rachael
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tonya
HI I'M SHERI AND IN ANSWER TO THE QUESTION ABOUT THE BIPOLAR SUPPORT GROUPS I LIVE IN SACRAMENTO CALIFORNIA AND I DO KNOW THAT THERE ARE MANY DIFFERENT GROUPS 1) WELLNESS RECOVERY PROGRAMS AND I KNOW OF 2 LOCATIONS ONE ON MARCONI IN NORTH SACRAMENTO AND ON BOWLING OFF FLORIN IN SOUTH SACRAMENTO
Sheri
what's the most common cause of suicide in adolescents
depression
Irfan
yes. it's depression.
Paul
Especially when adolescents go through identity issues. Not knowing if this boy wants to be a girl or vice or versa. Social awkwardness, depression and cruelty of other adolescents in my opinion, brings a lot of suicidal tendencies into the minds of them.
Tahmetrea
reasons that lead to depression caused by many reasons like rape, abusive parents or guardians, bullying and more causes for a person to suicide
Diana
not accepting the fact or situation or the reality. the adolescents can't face rejections, as soon as they are rejected , they commit suicide.
Labdhee
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Jody
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Thuy
well, I've a problem. I feel very conscious when I'm in a crowd. when I'm partying with friends, I feels like everyone is looking at me. when I look at them, each one of them have their eyes on me. I don't know how I should deal with this? can someone help me with that ?
puneet
Hey Puneet! I think it's the matter of time and getting comfortable in that kind of situation after you try to get out of your comfort zone and slowly get used to it. I used to have that problem too but then I acted to not give a 💩 and tried my best to pretend I didn't care at all. And it worked!
Thuy
*Fake it till you make it* in this case worked for me the best. Maybe you could try to start talking to one of the more open/friendly people in that group so you don't get that self-conscious. I'm sure they don't think they will judge you at all! Just do it!
Thuy
Bullying that leads to anxiety, shame and depression, sadly.
Rachael
Where do I go to find research or tips for integrating sex and mental heath?
integrating a sexual routine and a mental illness that has kept o e from intimacy for a prolonged time? can u be a Lil more specific
lindsay
I have experience with both
lindsay
y only these two.?
MOHD
yes
Abu
y only these two sex and mental
MOHD
knowledge some practice practical
Abu
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MOHD
u can explain
Abu
u can't find good sex partner....
MOHD
no
Abu
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Abu
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MOHD
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Abu
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MOHD
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Abu
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Abu
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Wendy
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Abu
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Wendy
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Abu
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Wendy
what's going on?
@lindsay I want to show how sexuality and mental health correlate. How one affects the other.
Felicia
I can help on these subjects
Abiral
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Felicia
Hello
Irfan
Spending quiet time alone, with nature can improve mental health. Offer your opinions?
mmmm but me i cn not spend time alone
Different strokes for different folks 🤷🏽‍♂️
tsav
what do u mean
Some people prefer a quiet life to a busy, bright city life. Some lead very stressful lives. Those people often don't pay attention to how they feel apart from the obvious fact that they're tired and stressed
tsav
nature can be clarifying and soothing because it can be a mixture of just natural beauty and why else are nature sounds an option for white noise
Twisted
You're absolutely right
tsav
what is with human being brain that we don't know?
I guess there are lots of things we don't know, but perhaps your referring to that thing called Consciousness
GoldenWizard
Anything that happens, question it!
tsav
in addition we may ask the doctor's
the science of many feelings and emotions can be hard to describe. our brains light up at some things but we can't always understand why
Twisted
But yet we must persist
tsav
Using relevant examples discuss challenges encounter by the beginning teachers during the learning and teaching process
how do I know when someone is using psychology on me?
If yes, it would always bring a solution.
Professor
Psychology cannot be used *on* something. You can use your *knowledge* of psychology to help tackle a situation. But I think I know what you're asking: pay attention to someone when you're talking, if they are looking at you up and down, they're analysing you
tsav
reasons for studying psychology in schools
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7hours 36 min - 4hours 50 min