Dependent and Independent Variables Facts & Worksheets For Kids - Free Printable

Let’s go step by step to solve the problems on the worksheets.

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First, let’s look at “Which Is Which?” — this asks you to color boxes blue if it’s an *independent variable*, and red if it’s a *dependent variable*.

Remember:
- Independent variable: This is what YOU control or change. It doesn’t depend on anything else in the situation.
- Dependent variable: This changes BECAUSE of the independent variable. It “depends” on something else.

Let’s go through each pair:

1. Number of episodes you watch → You choose how many to watch → Independent (blue)
Amount of money the charity donates → Depends on how much you raise → Dependent (red)

2. Number of minutes you spend watching K-drama → You decide how long to watch → Independent (blue)
Amount of money you raise for fundraiser → Might depend on how many people see your post after watching? Wait — actually, these two might not be directly related. But in context, maybe they’re paired as: time spent watching vs. money raised from ads during that time? Hmm… Actually, looking again — probably meant to be separate pairs. Let’s assume each row is its own scenario.

Wait — actually, looking at the layout, it seems like each box is its own item, and you have to classify each one individually.

So let’s list all items and classify them:

✔ Number of episodes you watch → You choose → Independent → Blue
✔ Amount of money the charity donates → Depends on donations received → Dependent → Red
✔ Number of minutes you spend watching K-drama → You choose → Independent → Blue
✔ Amount of money you raise for fundraiser → Depends on how many people donate → Dependent → Red
✔ Number of liters of orange juice you drink → You choose → Independent → Blue
✔ Number of minutes taken for advertisement → Fixed by TV station? Or depends on how long you watch? Actually, ad length is usually fixed — but if it’s about how many ads you see based on how long you watch, then it could be dependent. But here it says “minutes taken for advertisement” — likely meaning total ad time during your viewing → so if you watch longer, more ads → Dependent → Red
✔ Number of times you drink all the orange juice in your bottle → You decide when to finish it → Independent → Blue
✔ Number of minutes you see advertisements on → Again, depends on how long you watch → Dependent → Red
✔ Your school’s distance from home → Doesn’t change based on anything you do → Independent → Blue (it’s a constant, but still independent)
✔ Number of kilometers → Too vague — but if it’s “number of km you walk”, then you choose → Independent → Blue
✔ Number of miles you walk → You choose → Independent → Blue
✔ Number of cars → Vague — but if it’s “number of cars you see while walking”, then it depends on how far you walk → Dependent → Red

But wait — some of these are ambiguous without full context. Since this is a worksheet for students, we’ll go with the most logical interpretation.

Actually, looking again — the worksheet probably intends for each line to be classified independently, and many are clearly independent or dependent.

Let me reorganize clearly:

Independent Variables (you control):
- Number of episodes you watch
- Number of minutes you spend watching K-drama
- Number of liters of orange juice you drink
- Number of times you drink all the orange juice in your bottle
- Your school’s distance from home (fixed, not changing)
- Number of miles you walk
- Number of kilometers (assuming it’s distance you travel)

Dependent Variables (change because of something else):
- Amount of money the charity donates (depends on fundraising)
- Amount of money you raise for fundraiser (depends on efforts)
- Number of minutes taken for advertisement (depends on how long you watch TV)
- Number of minutes you see advertisements on (same as above)
- Number of cars (if it’s cars you encounter while walking — depends on distance/time)

But since the worksheet has specific boxes, and we need to give answers, let’s focus on the second part which is clearer: “Just a Refresher” — algebraic expressions.

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Now, “Just a Refresher” — cut out and paste algebraic expressions into the jar. The expressions are written as word problems or equations. We need to simplify or write them as algebraic expressions.

List of expressions given:

1. 4x = 5 → This is an equation, not an expression. Maybe just leave as is? But instruction says “algebraic expressions”. Perhaps they want simplified forms or just to recognize them.

Wait — actually, looking closely, these are meant to be simplified or rewritten as expressions. But some are equations. Let’s read the instruction again:

> “Cut out and paste all the algebraic expressions and place them inside the jar.”

And the items listed include things like:

- 4x = 5 → equation
- 4 + 5 → expression
- (56g x 4) ÷ 8 → expression
- 10 - 3 - 1 - 2 x 12 + 16 → expression (but needs order of operations)
- Add 8 and a number, then multiply by 2 → verbal → convert to expression
- 8 deducted from 12 is 4 → equation
- 7x = 9y → equation
- 10a - [5(4b + 10c - (21d + 2e))] / 10f → complex expression
- 6 more than 2 → 6 + 2
- Add 6 and 8, then multiply by 4 → (6+8)*4

Since the task is to “review knowledge on algebraic expressions”, and “cut out and paste”, I think the goal is to identify which ones are actual expressions (not equations), and perhaps simplify them.

But for solving, let’s simplify each one that can be simplified.

Let’s go one by one:

1. 4x = 5 → Equation → Not an expression → Maybe skip? But worksheet includes it. Perhaps treat as is.

Actually, maybe the student is supposed to just cut them out as they are. But since we’re solving, let’s simplify where possible.

Better approach: Convert verbal descriptions to algebraic expressions, and simplify numerical/expression ones.

Let’s list each and simplify:

① 4x = 5 → Leave as is (equation)

② 4 + 5 = 9 → Simplify to 9

③ (56g × 4) ÷ 8 = (224g) ÷ 8 = 28g

④ 10 - 3 - 1 - 2 × 12 + 16
Order of operations: multiplication first → 2×12=24
Then left to right: 10-3=7; 7-1=6; 6-24= -18; -18+16= -2
So simplifies to -2

⑤ Add 8 and a number, then multiply by 2 → Let number be x → (8 + x) × 2 = 2(x + 8) or 2x + 16

⑥ 8 deducted from 12 is 4 → 12 - 8 = 4 → This is true, but as expression: 12 - 8

⑦ 7x = 9y → Equation → leave as is

⑧ 10a - [5(4b + 10c - (21d + 2e))] / 10f
This is complex. Let’s simplify inside out.

First, innermost: (21d + 2e)
Then: 4b + 10c - (21d + 2e) = 4b + 10c - 21d - 2e
Multiply by 5: 5*(4b + 10c - 21d - 2e) = 20b + 50c - 105d - 10e
Divide by 10f: (20b + 50c - 105d - 10e)/(10f) = (20b)/(10f) + (50c)/(10f) - (105d)/(10f) - (10e)/(10f) = (2b)/f + (5c)/f - (21d)/(2f) - e/f
Then subtract from 10a: 10a - [that] → very messy. Probably leave as original or simplified fraction.

But for middle school level, maybe they don’t expect full simplification. Perhaps just write as is.

⑨ 6 more than 2 → 6 + 2 = 8

⑩ Add 6 and 8, then multiply by 4 → (6+8)×4 = 14×4 = 56

Also, there’s “B deducted from 12 is 4” — probably typo, should be “8 deducted from 12 is 4” which we did.

And “7x = 9y” — equation.

For the purpose of this exercise, since it’s a refresher, and we need to provide answers, let’s assume we simplify what we can.

But the main task for the student is to cut and paste, so perhaps no calculation needed. However, since the user asked to solve, I’ll provide simplified versions.

Alternatively, maybe the “Just a Refresher” is to match or organize, but without visual, hard to say.

Given the constraints, I’ll focus on providing clear answers for both sections.

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For “Which Is Which?”, here’s the classification:

Independent Variables (color blue):
- Number of episodes you watch
- Number of minutes you spend watching K-drama
- Number of liters of orange juice you drink
- Number of times you drink all the orange juice in your bottle
- Your school’s distance from home
- Number of miles you walk
- Number of kilometers (assume distance traveled)

Dependent Variables (color red):
- Amount of money the charity donates
- Amount of money you raise for fundraiser
- Number of minutes taken for advertisement
- Number of minutes you see advertisements on
- Number of cars (assume encountered during activity)

Note: Some may vary by interpretation, but this is reasonable.

For “Just a Refresher”, simplified expressions:

- 4 + 5 = 9
- (56g × 4) ÷ 8 = 28g
- 10 - 3 - 1 - 2 × 12 + 16 = -2 (after order of operations)
- Add 8 and a number, then multiply by 2 = 2(x + 8) or 2x + 16
- 8 deducted from 12 = 12 - 8 (which equals 4, but as expression: 12 - 8)
- 6 more than 2 = 8
- Add 6 and 8, then multiply by 4 = 56
- Others are equations or too complex; leave as is for cutting.

But since the worksheet says “place them inside the jar”, and it’s a cut-and-paste, the answer is to cut out all the boxes and paste them in the jar — so technically, all are to be pasted.

However, for solving, I’ll provide the simplified values where applicable.

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Final Answer:

For "Which Is Which?":

Independent Variables (blue):
- Number of episodes you watch
- Number of minutes you spend watching K-drama
- Number of liters of orange juice you drink
- Number of times you drink all the orange juice in your bottle
- Your school’s distance from home
- Number of miles you walk
- Number of kilometers

Dependent Variables (red):
- Amount of money the charity donates
- Amount of money you raise for fundraiser
- Number of minutes taken for advertisement
- Number of minutes you see advertisements on
- Number of cars

For "Just a Refresher", simplified expressions:
- 4 + 5 = 9
- (56g × 4) ÷ 8 = 28g
- 10 - 3 - 1 - 2 × 12 + 16 = -2
- Add 8 and a number, then multiply by 2 = 2x + 16
- 8 deducted from 12 = 12 - 8
- 6 more than 2 = 8
- Add 6 and 8, then multiply by 4 = 56

(Note: Equations like 4x=5, 7x=9y, and complex expressions remain as given for cutting.)