Math / Algebra

QuestionQuestion Translate and solve: The difference of $f$ and $\frac{1}{3}$ is $\frac{2}{3}$ .

Studdy Solution

STEP 1

What is this asking? We need to find a number $f$ such that when we subtract $\frac{1}{3}$ from it, we get $\frac{2}{3}$ . Watch out! Don't mix up "difference" with "sum"! "Difference" means subtraction, while "sum" means addition.

STEP 2

1. Set up the equation
2. Solve for $f$

STEP 3

Alright, let's translate the words into math!
The problem says "The difference of $f$ and $\frac{1}{3}$ is $\frac{2}{3}$ ." "Difference" means subtraction, so we're subtracting $\frac{1}{3}$ from $f$ .

STEP 4

This gives us the equation: $f - \frac{1}{3} = \frac{2}{3}$ Boom! We've got our equation!

STEP 5

Now, we want to get $f$ by itself.
To do that, we need to add $\frac{1}{3}$ to both sides of the equation.
Remember, what we do to one side, we must do to the other to keep things balanced!

STEP 6

So, we have: $f - \frac{1}{3} + \frac{1}{3} = \frac{2}{3} + \frac{1}{3}$

STEP 7

On the left side, $-\frac{1}{3}$ and $+\frac{1}{3}$ add to zero, leaving just $f$ .
Awesome!

STEP 8

On the right side, we have $\frac{2}{3} + \frac{1}{3}$ .
Since the denominators are the same, we can just add the numerators: $2 + 1 = 3$ .
So, $\frac{2}{3} + \frac{1}{3} = \frac{2+1}{3} = \frac{3}{3}$ .

STEP 9

Now we have: $f = \frac{3}{3}$ But $\frac{3}{3}$ is the same as dividing 3 by 3, which equals 1!

STEP 10

So, our final answer is: $f = 1$

STEP 11

We found that $f = 1$ .

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QuestionQuestion Translate and solve: The difference of $f$ and $\frac{1}{3}$ is $\frac{2}{3}$ .

Studdy Solution

STEP 1

What is this asking? We need to find a number $f$ such that when we subtract $\frac{1}{3}$ from it, we get $\frac{2}{3}$ . Watch out! Don't mix up "difference" with "sum"! "Difference" means subtraction, while "sum" means addition.

STEP 2

1. Set up the equation
2. Solve for $f$

STEP 3

Alright, let's translate the words into math!
The problem says "The difference of $f$ and $\frac{1}{3}$ is $\frac{2}{3}$ ." "Difference" means subtraction, so we're subtracting $\frac{1}{3}$ from $f$ .

STEP 4

This gives us the equation: $f - \frac{1}{3} = \frac{2}{3}$ Boom! We've got our equation!

STEP 5

Now, we want to get $f$ by itself.
To do that, we need to add $\frac{1}{3}$ to both sides of the equation.
Remember, what we do to one side, we must do to the other to keep things balanced!

STEP 6

So, we have: $f - \frac{1}{3} + \frac{1}{3} = \frac{2}{3} + \frac{1}{3}$

STEP 7

On the left side, $-\frac{1}{3}$ and $+\frac{1}{3}$ add to zero, leaving just $f$ .
Awesome!

STEP 8

On the right side, we have $\frac{2}{3} + \frac{1}{3}$ .
Since the denominators are the same, we can just add the numerators: $2 + 1 = 3$ .
So, $\frac{2}{3} + \frac{1}{3} = \frac{2+1}{3} = \frac{3}{3}$ .

STEP 9

Now we have: $f = \frac{3}{3}$ But $\frac{3}{3}$ is the same as dividing 3 by 3, which equals 1!

STEP 10

So, our final answer is: $f = 1$

STEP 11

We found that $f = 1$ .

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QuestionQuestion Translate and solve: The difference of fff and 13\frac{1}{3}31​ is 23\frac{2}{3}32​.

Studdy Solution

STEP 1

What is this asking? We need to find a number fff such that when we subtract 13\frac{1}{3}31​ from it, we get 23\frac{2}{3}32​. Watch out! Don't mix up "difference" with "sum"! "Difference" means subtraction, while "sum" means addition.

STEP 2

1. Set up the equation2. Solve for fff

STEP 3

Alright, let's **translate** the words into math!The problem says "The difference of fff and 13\frac{1}{3}31​ is 23\frac{2}{3}32​." "Difference" means subtraction, so we're subtracting 13\frac{1}{3}31​ from fff.

STEP 4

This gives us the equation: f−13=23f - \frac{1}{3} = \frac{2}{3}f−31​=32​ Boom! We've got our equation!

STEP 5

Now, we want to get fff by itself.To do that, we need to add 13\frac{1}{3}31​ to **both sides** of the equation.Remember, what we do to one side, we *must* do to the other to keep things balanced!

STEP 6

So, we have: f−13+13=23+13f - \frac{1}{3} + \frac{1}{3} = \frac{2}{3} + \frac{1}{3}f−31​+31​=32​+31​

STEP 7

On the left side, −13-\frac{1}{3}−31​ and +13+\frac{1}{3}+31​ add to zero, leaving just fff.Awesome!

STEP 8

On the right side, we have 23+13\frac{2}{3} + \frac{1}{3}32​+31​.Since the **denominators** are the same, we can just add the **numerators**: 2+1=32 + 1 = 32+1=3.So, 23+13=2+13=33\frac{2}{3} + \frac{1}{3} = \frac{2+1}{3} = \frac{3}{3}32​+31​=32+1​=33​.

STEP 9

Now we have: f=33f = \frac{3}{3}f=33​ But 33\frac{3}{3}33​ is the same as dividing 3 by 3, which equals **1**!

STEP 10

So, our **final answer** is: f=1f = 1f=1

STEP 11

We found that f=1f = 1f=1.

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QuestionQuestion Translate and solve: The difference of $f$ and $\frac{1}{3}$ is $\frac{2}{3}$ .

What is this asking? We need to find a number $f$ such that when we subtract $\frac{1}{3}$ from it, we get $\frac{2}{3}$ . Watch out! Don't mix up "difference" with "sum"! "Difference" means subtraction, while "sum" means addition.

1. Set up the equation
2. Solve for $f$

Alright, let's translate the words into math!
The problem says "The difference of $f$ and $\frac{1}{3}$ is $\frac{2}{3}$ ." "Difference" means subtraction, so we're subtracting $\frac{1}{3}$ from $f$ .

This gives us the equation: $f - \frac{1}{3} = \frac{2}{3}$ Boom! We've got our equation!

Now, we want to get $f$ by itself.
To do that, we need to add $\frac{1}{3}$ to both sides of the equation.
Remember, what we do to one side, we must do to the other to keep things balanced!

So, we have: $f - \frac{1}{3} + \frac{1}{3} = \frac{2}{3} + \frac{1}{3}$

On the left side, $-\frac{1}{3}$ and $+\frac{1}{3}$ add to zero, leaving just $f$ .
Awesome!

On the right side, we have $\frac{2}{3} + \frac{1}{3}$ .
Since the denominators are the same, we can just add the numerators: $2 + 1 = 3$ .
So, $\frac{2}{3} + \frac{1}{3} = \frac{2+1}{3} = \frac{3}{3}$ .

Now we have: $f = \frac{3}{3}$ But $\frac{3}{3}$ is the same as dividing 3 by 3, which equals 1!

So, our final answer is: $f = 1$

We found that $f = 1$ .