Math / Algebra

QuestionWhen writi- algebraic expressions, using the symbol 'x' for multiplication can cause confusion. Look at the expressions below using ' $x$ '. $x+x+x$
1. How are the expressions similar?

Studdy Solution

STEP 1

What is this asking? How are $x + x + x$ , $3 \cdot x$ , and $3x$ similar? Watch out! Don't mix up adding variables with multiplying them!

STEP 2

1. Repeated Addition
2. Multiplication as Shorthand
3. The Invisible Multiplication Sign

STEP 3

Think of $x$ like a delicious pizza slice. $x + x + x$ means you have three pizza slices!
We're adding the same thing, $x$ , three times.

STEP 4

Instead of writing $x + x + x$ , we can use multiplication as a shortcut! $3 \cdot x$ means the same thing: three groups of $x$ .
The ' $\cdot$ ' symbol clearly shows we're multiplying.

STEP 5

Now, mathematicians are a bit lazy (in a good way!). Sometimes, they skip the ' $\cdot$ ' symbol altogether.
So, $3x$ means exactly the same as $3 \cdot x$ .
It's still three groups of $x$ , just written more compactly.

STEP 6

All three expressions, $x + x + x$ , $3 \cdot x$ , and $3x$ , represent the same value: three times the variable $x$ .
They just show it in different ways!

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QuestionWhen writi- algebraic expressions, using the symbol 'x' for multiplication can cause confusion. Look at the expressions below using ' $x$ '. $x+x+x$
1. How are the expressions similar?

Studdy Solution

STEP 1

What is this asking? How are $x + x + x$ , $3 \cdot x$ , and $3x$ similar? Watch out! Don't mix up adding variables with multiplying them!

STEP 2

1. Repeated Addition
2. Multiplication as Shorthand
3. The Invisible Multiplication Sign

STEP 3

Think of $x$ like a delicious pizza slice. $x + x + x$ means you have three pizza slices!
We're adding the same thing, $x$ , three times.

STEP 4

Instead of writing $x + x + x$ , we can use multiplication as a shortcut! $3 \cdot x$ means the same thing: three groups of $x$ .
The ' $\cdot$ ' symbol clearly shows we're multiplying.

STEP 5

Now, mathematicians are a bit lazy (in a good way!). Sometimes, they skip the ' $\cdot$ ' symbol altogether.
So, $3x$ means exactly the same as $3 \cdot x$ .
It's still three groups of $x$ , just written more compactly.

STEP 6

All three expressions, $x + x + x$ , $3 \cdot x$ , and $3x$ , represent the same value: three times the variable $x$ .
They just show it in different ways!

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QuestionWhen writi- algebraic expressions, using the symbol 'x' for multiplication can cause confusion. Look at the expressions below using ' xxx '. x+x+xx+x+xx+x+x1. How are the expressions similar?

Studdy Solution

STEP 1

What is this asking? How are x+x+xx + x + xx+x+x, 3⋅x3 \cdot x3⋅x, and 3x3x3x similar? Watch out! Don't mix up adding variables with multiplying them!

STEP 2

1. Repeated Addition2. Multiplication as Shorthand3. The Invisible Multiplication Sign

STEP 3

Think of xxx like a delicious pizza slice. x+x+xx + x + xx+x+x means you have **three** pizza slices!We're adding the same thing, xxx, three times.

STEP 4

Instead of writing x+x+xx + x + xx+x+x, we can use multiplication as a shortcut! 3⋅x3 \cdot x3⋅x means the **same** thing: **three** groups of xxx.The '⋅\cdot⋅' symbol clearly shows we're multiplying.

STEP 5

Now, mathematicians are a bit lazy (in a good way!). Sometimes, they skip the '⋅\cdot⋅' symbol altogether.So, 3x3x3x means *exactly* the same as 3⋅x3 \cdot x3⋅x.It's still **three** groups of xxx, just written more compactly.

STEP 6

All three expressions, x+x+xx + x + xx+x+x, 3⋅x3 \cdot x3⋅x, and 3x3x3x, represent the same value: **three** times the variable xxx.They just show it in different ways!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhen writi- algebraic expressions, using the symbol 'x' for multiplication can cause confusion. Look at the expressions below using ' $x$ '. $x+x+x$
1. How are the expressions similar?

What is this asking? How are $x + x + x$ , $3 \cdot x$ , and $3x$ similar? Watch out! Don't mix up adding variables with multiplying them!

1. Repeated Addition
2. Multiplication as Shorthand
3. The Invisible Multiplication Sign

Think of $x$ like a delicious pizza slice. $x + x + x$ means you have three pizza slices!
We're adding the same thing, $x$ , three times.

Instead of writing $x + x + x$ , we can use multiplication as a shortcut! $3 \cdot x$ means the same thing: three groups of $x$ .
The ' $\cdot$ ' symbol clearly shows we're multiplying.

Now, mathematicians are a bit lazy (in a good way!). Sometimes, they skip the ' $\cdot$ ' symbol altogether.
So, $3x$ means exactly the same as $3 \cdot x$ .
It's still three groups of $x$ , just written more compactly.

All three expressions, $x + x + x$ , $3 \cdot x$ , and $3x$ , represent the same value: three times the variable $x$ .
They just show it in different ways!