Math / Algebra

Question4 Fill in the Blank 1 point Simplify the expression by filling in the blank. $\frac{5 x-y}{20 y}+\frac{x+y}{20 y}$ type your answer... / type your answer...

Studdy Solution

STEP 1

What is this asking? We've got two fractions with the same denominator, and we need to add them together and simplify the result! Watch out! Don't forget that when adding fractions with the same denominator, we only add the numerators!
The denominator stays the same.
Also, make sure to simplify the final fraction as much as possible.

STEP 2

1. Combine the fractions
2. Simplify the numerator
3. Simplify the fraction

STEP 3

Alright, since our fractions have the same denominator, we can add them directly!
Remember, we add the numerators and keep the denominator the same.

STEP 4

So, we have $\frac{5x - y}{20y} + \frac{x + y}{20y}$ .
Let's add those numerators!

STEP 5

That gives us: $\frac{(5x - y) + (x + y)}{20y}$

STEP 6

Now, let's clean up that numerator!
We have $(5x - y) + (x + y)$ .

STEP 7

First, let's remove the parentheses: $5x - y + x + y$ .

STEP 8

Notice we have a $-y$ and a $+y$ .
Adding those together gives us zero!
So, they add to zero and effectively disappear!

STEP 9

That leaves us with $5x + x$ , which simplifies to $6x$ .
Awesome!

STEP 10

Now, our fraction looks like this: $\frac{6x}{20y}$ .

STEP 11

We can simplify this further!
Notice that both $6$ and $20$ are divisible by $2$ .

STEP 12

Dividing both the numerator and the denominator by $2$ gives us: $\frac{6x \div 2}{20y \div 2} = \frac{3x}{10y}$

STEP 13

Our final simplified fraction is $\frac{3x}{10y}$ !
So, the answer is $3x$ / $10y$ .

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Question4 Fill in the Blank 1 point Simplify the expression by filling in the blank. $\frac{5 x-y}{20 y}+\frac{x+y}{20 y}$ type your answer... / type your answer...

Studdy Solution

STEP 1

STEP 2

1. Combine the fractions
2. Simplify the numerator
3. Simplify the fraction

STEP 3

Alright, since our fractions have the same denominator, we can add them directly!
Remember, we add the numerators and keep the denominator the same.

STEP 4

So, we have $\frac{5x - y}{20y} + \frac{x + y}{20y}$ .
Let's add those numerators!

STEP 5

That gives us: $\frac{(5x - y) + (x + y)}{20y}$

STEP 6

Now, let's clean up that numerator!
We have $(5x - y) + (x + y)$ .

STEP 7

First, let's remove the parentheses: $5x - y + x + y$ .

STEP 8

Notice we have a $-y$ and a $+y$ .
Adding those together gives us zero!
So, they add to zero and effectively disappear!

STEP 9

That leaves us with $5x + x$ , which simplifies to $6x$ .
Awesome!

STEP 10

Now, our fraction looks like this: $\frac{6x}{20y}$ .

STEP 11

We can simplify this further!
Notice that both $6$ and $20$ are divisible by $2$ .

STEP 12

Dividing both the numerator and the denominator by $2$ gives us: $\frac{6x \div 2}{20y \div 2} = \frac{3x}{10y}$

STEP 13

Our final simplified fraction is $\frac{3x}{10y}$ !
So, the answer is $3x$ / $10y$ .

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Question4 Fill in the Blank 1 point Simplify the expression by filling in the blank. 5x−y20y+x+y20y\frac{5 x-y}{20 y}+\frac{x+y}{20 y}20y5x−y​+20yx+y​ type your answer... / type your answer...

Studdy Solution

STEP 1

STEP 2

1. Combine the fractions2. Simplify the numerator3. Simplify the fraction

STEP 3

Alright, since our fractions have the *same denominator*, we can add them directly!Remember, we add the numerators and keep the denominator the same.

STEP 4

So, we have 5x−y20y+x+y20y\frac{5x - y}{20y} + \frac{x + y}{20y}20y5x−y​+20yx+y​.Let's add those numerators!

STEP 5

That gives us: (5x−y)+(x+y)20y \frac{(5x - y) + (x + y)}{20y} 20y(5x−y)+(x+y)​

STEP 6

Now, let's clean up that numerator!We have (5x−y)+(x+y)(5x - y) + (x + y)(5x−y)+(x+y).

STEP 7

First, let's remove the parentheses: 5x−y+x+y5x - y + x + y5x−y+x+y.

STEP 8

Notice we have a −y-y−y and a +y +y+y.Adding those together gives us zero!So, they add to zero and effectively disappear!

STEP 9

That leaves us with 5x+x5x + x5x+x, which simplifies to 6x6x6x.Awesome!

STEP 10

Now, our fraction looks like this: 6x20y\frac{6x}{20y}20y6x​.

STEP 11

We can simplify this further!Notice that both 666 and 202020 are divisible by 222.

STEP 12

Dividing both the numerator and the denominator by 222 gives us: 6x÷220y÷2=3x10y \frac{6x \div 2}{20y \div 2} = \frac{3x}{10y} 20y÷26x÷2​=10y3x​

STEP 13

Our final simplified fraction is 3x10y\frac{3x}{10y}10y3x​!So, the answer is 3x3x3x / 10y10y10y.

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Question4 Fill in the Blank 1 point Simplify the expression by filling in the blank. $\frac{5 x-y}{20 y}+\frac{x+y}{20 y}$ type your answer... / type your answer...

1. Combine the fractions
2. Simplify the numerator
3. Simplify the fraction

Alright, since our fractions have the same denominator, we can add them directly!
Remember, we add the numerators and keep the denominator the same.

So, we have $\frac{5x - y}{20y} + \frac{x + y}{20y}$ .
Let's add those numerators!

That gives us: $\frac{(5x - y) + (x + y)}{20y}$

Now, let's clean up that numerator!
We have $(5x - y) + (x + y)$ .

First, let's remove the parentheses: $5x - y + x + y$ .

Notice we have a $-y$ and a $+y$ .
Adding those together gives us zero!
So, they add to zero and effectively disappear!

That leaves us with $5x + x$ , which simplifies to $6x$ .
Awesome!

Now, our fraction looks like this: $\frac{6x}{20y}$ .

We can simplify this further!
Notice that both $6$ and $20$ are divisible by $2$ .

Dividing both the numerator and the denominator by $2$ gives us: $\frac{6x \div 2}{20y \div 2} = \frac{3x}{10y}$

Our final simplified fraction is $\frac{3x}{10y}$ !
So, the answer is $3x$ / $10y$ .