So even if you have a fraction it just means to divide but you should multiply?

Yes exactly so in the last problem you would cancel out the 4 by multiplying it by 4 and what ever you do on one side of the equal sign you have to do on the other so you would multiply 18 by 4 to get 72.

the only one I don't understand is the first one,any tips?

You divide by 8 on each sides so 72/8 =9

i dont get this, it says "what you do to one side, you do to the other" so if you have x/5=7 you have to multiply each side by 5, so is it 5x5=25 and 7x5=35? if so what happened to the 25?

When x/5 is multiplied by 5, the 5's are *not* multiplied together to give 25. Rather, multiplication by 5 undoes (or cancels out) the division by 5 that occurs in the expression x/5. So there's no 25 here. The final result is x = 35.

Is there any way i cant get taught better for inverse operation

If you are looking for another video or some reference to use for inverse operation, I would recommend using Math Antics or Mathceraptops (YouTube channel).This are the places i personally do to for second opinions. I am not sure if Math antics has a video about inverse operation but Mathceraptops sure do.

If a letter is close to a number how do you solve the equation?

I'm assuming your referring to something such as _7x = 14_ in this case, you would use 7x to say that 7 of that variable is equal to 14 in which case x = 2. This works because 7x is used to refer to multiplication easily during algebra since if you tried 7 x X = 14, it can get a bit confusing. While you can also use 7 ⋅ X = 14 (⋅ being another form of multiplication symbol) but it's much less common. TLDR; when a number is by a variable it means to multiply the variable by the number.

how do you do thisss w . 5 = 55 like what is this?

The dot represents multiplication. So "w . 5 = 55" is just "w times 5 is equal to 55."

Main content

6th grade

Course: 6th grade > Unit 7

Lesson 4: One-step multiplication and division equations

One-step multiplication & division equations

CCSS.Math:

6.EE.B.7

Google Classroom

Learn to solve equations like "4x = 20" or "y/3 = 7".

Based on our understanding of the balance beam model, we know that to keep a true equation, we always have to do the same thing to both sides of an equation.

But how do we know what to do to both sides of the equation?

Multiplication and division are inverse operations

Here's an example of how division is the inverse operation of multiplication:

If we start with 7, multiply by 3, then divide by 3, we get back to 7:

7, dot, 3, divided by, 3, equals, 7

Here's an example of how multiplication is the inverse operation of division:

If we start with 8, divide by 4, then multiply by 4, we get back to 8:

8, divided by, 4, dot, 4, equals, 8

Solving a multiplication equation using inverse operations

Let's think about how we can solve for t in the following equation:

6, t, equals, 54

We want to get t by itself on the left hand side of the equation. So, what can we do to undo multiplying by 6?

We should divide by 6 because the inverse operation of multiplication is division!

Here's how dividing by 6 on each side looks:

$\begin{aligned} 6t &= 54 \\\\ \dfrac{6t}{\blueD{6}} &= \dfrac{54}{\blueD{ 6}}~~~~~~~~~~\small\gray{\text{Divide each side by six.}} \\\\ t &= \greenD{9}~~~~~~~~~~\small\gray{\text{Simplify.}} \end{aligned}$

Let's check our work.

It's always a good idea to check our solution in the original equation to make sure we didn't make any mistakes:

\qquad

\begin{aligned} 6t &= 54 \\ 6 \cdot \greenD9 &\stackrel{\large?}{=} 54\\ 54 &= 54 \end{aligned}

Yes, t, equals, start color #1fab54, 9, end color #1fab54 is a solution!

Solving a division equation using inverse operations

Now, let's try to solve a slightly different type of equation:

start fraction, x, divided by, 5, end fraction, equals, 7

We want to get x by itself on the left hand side of the equation. So, what can we do to cancel out dividing by 5?

We can multiply by 5 because the inverse operation of division is multiplication!

Here's how multiplying by 5 on each side looks:

$\begin{aligned} \dfrac x5 &= 7 \\\\ \dfrac x5 \cdot \blueD{5} &= 7 \cdot \blueD{5}~~~~~~~~~~\small\gray{\text{Multiply each side by five.}} \\\\ x &= \greenD{35}~~~~~~~~~~\small\gray{\text{Simplify.}} \end{aligned}$

Let's check our work.

\qquad

\begin{aligned} \dfrac x5 &= 7 \\\\ \dfrac{\greenD{35}}{5} &\stackrel{\large?}{=} 7\\\\ 7 &= 7 \end{aligned}

Yes, x, equals, start color #1fab54, 35, end color #1fab54 is a solution!

Summary of how to solve multiplication and division equations

Awesome! We just solved a multiplication equation and a division equation. Let's summarize what we did:

Type of equation	Example	First step
Multiplication equation	6, t, equals, 54	Divide each side by six.
Division equation	start fraction, x, divided by, 5, end fraction, equals, 7	Multiply each side by five.

Let's try solving equations.

Equation A

Current

Which operation would help solve for w?

8, w, equals, 72

w, equals

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Makayla
Posted 5 years ago. Direct link to Makayla's post “So even if you have a fra...”
So even if you have a fraction it just means to divide but you should multiply?
Button navigates to signup pageComment on Makayla's post “So even if you have a fra...”
(49 votes)
Answer
- TaelorW
  Posted 2 years ago. Direct link to TaelorW's post “Yes exactly so in the las...”
  Yes exactly so in the last problem you would cancel out the 4 by multiplying it by 4 and what ever you do on one side of the equal sign you have to do on the other so you would multiply 18 by 4 to get 72.
  Comment on TaelorW's post “Yes exactly so in the las...”
  (15 votes)
jorge mendoza
Posted 4 years ago. Direct link to jorge mendoza's post “i dont get this, it says ...”
i dont get this, it says "what you do to one side, you do to the other" so if you have x/5=7 you have to multiply each side by 5, so is it 5x5=25 and 7x5=35? if so what happened to the 25?
Button navigates to signup pageComment on jorge mendoza's post “i dont get this, it says ...”
(13 votes)
Answer
- Ian Pulizzotto
  Posted 4 years ago. Direct link to Ian Pulizzotto's post “When x/5 is multiplied by...”
  When x/5 is multiplied by 5, the 5's are not multiplied together to give 25. Rather, multiplication by 5 undoes (or cancels out) the division by 5 that occurs in the expression x/5. So there's no 25 here. The final result is x = 35.
  Comment on Ian Pulizzotto's post “When x/5 is multiplied by...”
  (27 votes)
Bailey
Posted 3 years ago. Direct link to Bailey's post “the only one I don't unde...”
the only one I don't understand is the first one,any tips?
Button navigates to signup pageComment on Bailey's post “the only one I don't unde...”
(14 votes)
Answer
- Brian
  Posted 2 years ago. Direct link to Brian's post “You divide by 8 on each s...”
  You divide by 8 on each sides so 72/8 =9
  Comment on Brian's post “You divide by 8 on each s...”
  (2 votes)
samaimoore126
Posted 3 years ago. Direct link to samaimoore126's post “Is there any way i cant g...”
Is there any way i cant get taught better for inverse operation
Button navigates to signup pageComment on samaimoore126's post “Is there any way i cant g...”
(10 votes)
Answer
- Azza Safa
  Posted 3 years ago. Direct link to Azza Safa's post “If you are looking for an...”
  If you are looking for another video or some reference to use for inverse operation, I would recommend using Math Antics or Mathceraptops (YouTube channel).This are the places i personally do to for second opinions. I am not sure if Math antics has a video about inverse operation but Mathceraptops sure do.
  Button navigates to signup page
  (10 votes)
vaca,Natalia
Posted 5 years ago. Direct link to vaca,Natalia's post “If a letter is close to a...”
If a letter is close to a number how do you solve the equation?
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Maggie
  Posted 5 months ago. Direct link to Maggie's post “I'm assuming your referri...”
  I'm assuming your referring to something such as 7x = 14
  in this case, you would use 7x to say that 7 of that variable is equal to 14 in which case x = 2. This works because 7x is used to refer to multiplication easily during algebra since if you tried 7 x X = 14, it can get a bit confusing. While you can also use
  7 ⋅ X = 14 (⋅ being another form of multiplication symbol) but it's much less common.
  
  TLDR; when a number is by a variable it means to multiply the variable by the number.
  Comment on Maggie's post “I'm assuming your referri...”
  (5 votes)
Hakase
Posted a year ago. Direct link to Hakase's post “About the "what you do to...”
About the "what you do to one side, you do to the other".
To understand the logic behind this, first let's imagine a beam balance in front of you, it has two blocks on each side each weighing 200 grams, thus the two sides are equal.

However if you add another 100g block on one side, the balance becomes uneven, as in 200g < 300g . To solve this we add another 100g block to the other side, so the beam balance becomes even again, as in 300g = 300g . That's why what you do on one side you also do to the other, when solving an equation.

TL:DR; We do that to avoid a false equation.
Button navigates to signup pageButton navigates to signup page
(7 votes)
Answer
Aidan H
Posted 2 years ago. Direct link to Aidan H's post “how do you do thisss w . ...”
how do you do thisss w . 5 = 55 like what is this?
Button navigates to signup pageComment on Aidan H's post “how do you do thisss w . ...”
(4 votes)
Answer
- BruinWarrior
  Posted 2 years ago. Direct link to BruinWarrior's post “The dot represents multip...”
  The dot represents multiplication. So "w . 5 = 55" is just "w times 5 is equal to 55."
  Button navigates to signup page
  (6 votes)
KATHERINE S
Posted 2 years ago. Direct link to KATHERINE S's post “It is the same question s...”
It is the same question so will the answer change or stay the same?
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(6 votes)
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atevanlozano
Posted a month ago. Direct link to atevanlozano's post “Thank you, Khan! You made...”
Thank you, Khan! You made math easier for me! When get rich, I will donate to Khan Academy to help many people, students, and children that do not have easy access to education.
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(7 votes)
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- martha_frenck579
  Posted a month ago. Direct link to martha_frenck579's post “You post this in question...”
  You post this in questions not tips and thanks. Did you know that?
  Button navigates to signup page
  (0 votes)
Victoria
Posted 6 years ago. Direct link to Victoria's post “I don't get any of this. ...”
I don't get any of this. ... I tried to understand it but I can't.
;-; Can someone help me please? I am confused how u get a fraction number when ur doing this. Help please :/
Button navigates to signup pageComment on Victoria's post “I don't get any of this. ...”
(6 votes)
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- TechGuru2000
  Posted a month ago. Direct link to TechGuru2000's post “Ok, let's start simply, w...”
  Ok, let's start simply, with this equation:w5=55, which can also be written as w.5=55.
  
  The dot represents the multiplication sign, and if the letter and the number are joined together, that also represents multiplication.
  
  In this Lesson, we were taught that to solve for w in w.5=55, we need to use the inverse operation, which basically means the opposite of the operations, addition is the opposite of subtraction, and multiplication is the opposite of division.
  
  We were also taught that we need to use the inverse for both places, not just one, so it can be a balanced equation, an example of that is w.5=55 if the . represents multiplication, we divide instead.
  
  So we would do 55/5, which is the same as a fraction (a fraction is another form of showing division, the / represents division and fractions, and the numerator is divided by the denominator), and 55/5 or 55 divided by 5 is equal to 11, so w is equal to 11, or w=11.
  
  Now for division, for the equation t/6=7, or 7=t/6 (they are the same thing, just put in a different format, keep that in mind), we use inverse operation, as shown in the Lesson, and we know what type of inverse operation it is because t/6 is division -because it's a fraction-, so we use multiplication instead so to solve for t in t/6=7, we multiply 7 by 6, which, keep in mind, can be represented as 7 . 6, or 7 X 6, and 7 X 6 is equal to 42, so t=42
  Button navigates to signup page
  (1 vote)