Ratio and Proportion Worksheets | Definitions, Examples, Activities - Free Printable

Let’s solve each part of the “Word Play” worksheet step by step.

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First box:
> To write a ratio in its simplest form, what number should be used to divide the antecedent and consequent?

We know that to simplify a ratio (like 6:9), we divide both numbers by their greatest common factor — but the question is asking for the *name* of the number you use. Actually, it’s more general: you divide by any common factor, but to get to simplest form, you usually divide by the GCF. However, looking at the letter choices:

Letters given:
H F R P Z
I C O J B

We need to pick letters to form a word. The blank has 3 dashes → so 3-letter word.

What 3-letter word fits? Let’s think:
You divide by a common divisor? Too long.
Actually, the key term here is “factor” — but that’s 6 letters. Wait — maybe they mean “divisor”? Also too long.

Wait — perhaps it’s “GCF”? But GCF isn’t among the letters.

Look again: the answer might be “HCF” — Highest Common Factor. That’s 3 letters! And H, C, F are all available.

Check: H, C, F — yes, all in the grid.

So first answer: HCF

But let’s confirm: In some curricula, especially British-influenced ones, they say “HCF” instead of “GCF”. So this makes sense.

✔ First answer: HCF

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Second box:
> A ratio consists of two terms. What is the name of the second term?

In a ratio like a:b,
- ‘a’ is called the antecedent
- ‘b’ is called the consequent

So the second term is the consequent.

How many letters? Blank has 8 dashes → 8 letters.

“Consequent” = 10 letters → too long.

Wait — maybe they want just “conseq”? No.

Wait — look at the letters provided:

Q C N U N
O E S E T

We have: Q, C, N, U, N, O, E, S, E, T

Try to spell “consequent” — c-o-n-s-e-q-u-e-n-t → 10 letters. Not matching.

Wait — maybe it’s “second”? 6 letters — no.

Another thought: sometimes the second term is called the “latter”? Not standard.

Wait — perhaps it’s “term”? Too short.

Hold on — maybe I miscounted the dashes.

Looking back: “________” — that’s 8 underscores? Or is it variable?

Actually, in the image description, it says “--------” which likely means 8 letters.

But “consequent” is 10. Hmm.

Alternative idea: Maybe it’s “denominator”? No, that’s for fractions.

Wait — let’s try to unscramble from the letters.

Available letters: Q, C, N, U, N, O, E, S, E, T

Let’s sort them: C, E, E, N, N, O, Q, S, T, U

Can we make “conquest”? C-O-N-Q-U-E-S-T → 8 letters! Yes!

Is “conquest” related to ratios? No — that doesn’t make sense.

Wait — perhaps it’s “sequence”? S-E-Q-U-E-N-C-E → 8 letters. Still not right.

Another approach: Maybe the answer is “conseq” — but that’s not a real word.

Wait — let’s think differently. Perhaps the second term is called the “following”? No.

Actually, in some contexts, people refer to the parts as “first term” and “second term”, but the technical names are antecedent and consequent.

Perhaps the worksheet expects “consequent”, even if the dash count is off? But we must match the letters.

Wait — let’s count the dashes again. In the user’s text: “--------” — that’s 8 characters.

But “consequent” is 10. Unless... maybe it’s abbreviated?

Another idea: Maybe it’s “latter” — L-A-T-T-E-R — but L and A aren’t in the letters.

Letters available: Q,C,N,U,N,O,E,S,E,T — no L or A.

Try “tenure”? T-E-N-U-R-E — R not available.

“Quest”? Too short.

Wait — what about “conset”? Not a word.

Perhaps I made a mistake earlier.

Let me search my knowledge: Is there another name for the second term in a ratio?

Actually, no — it’s consistently “consequent”.

But let’s look at the letters again: Q, C, N, U, N, O, E, S, E, T

What if we arrange them to spell “conquest”? C-O-N-Q-U-E-S-T — uses C,O,N,Q,U,E,S,T — that’s 8 letters. We have two N’s and two E’s — so yes, we can do C,O,N,Q,U,E,S,T — leaving out one N and one E.

But “conquest” has nothing to do with ratios.

Unless... is this a trick? Maybe the answer is not mathematical?

No, the topic is ratio and proportion.

Wait — perhaps it’s “second” — S-E-C-O-N-D — D not available.

Another thought: Maybe the answer is “term” — but only 4 letters.

I’m stuck.

Let’s move to the third box and come back.

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Third box:
> It is referred to as the equality of two ratios.

That’s the definition of a proportion.

Blank has 9 dashes → 9 letters.

“Proportion” = 10 letters — too long.

“Ratio” = 5 — too short.

“Equal” = 5.

Wait — “proportional”? 12 letters.

Hmm.

Letters given:
P I P O N
T O R O R

So: P,I,P,O,N,T,O,R,O,R

Sort: I, N, O, O, O, P, P, R, R, T

We need a 9-letter word meaning “equality of two ratios” — that’s proportion.

“Proportion” is 10 letters: P-R-O-P-O-R-T-I-O-N

We have: P,P,O,O,O,R,R,T,I,N — that’s exactly the letters for “proportion” minus one O? Wait:

“Proportion” requires: P,R,O,P,O,R,T,I,O,N → that’s 3 O’s, 2 P’s, 2 R’s, 1 T, 1 I, 1 N — total 10 letters.

Our letters: P,I,P,O,N,T,O,R,O,R → that’s 2 P’s, 3 O’s, 2 R’s, 1 T, 1 I, 1 N — same as needed for “proportion” except we have an extra O? No:

Count:

Given: P, I, P, O, N, T, O, R, O, R → that’s 10 letters.

“Proportion” is 10 letters: positions: 1:P, 2:r, 3:o, 4:p, 5:o, 6:r, 7:t, 8:i, 9:o, 10:n

So letters needed: P,R,O,P,O,R,T,I,O,N — which matches our set: we have P,P; R,R; O,O,O; T; I; N — perfect.

And the blank is “---------” — 9 dashes? But “proportion” is 10 letters.

In the user’s text: “---------” — let’s count: 9 underscores.

But “proportion” is 10. Contradiction.

Unless the blank is actually 10? Maybe typo in description.

Perhaps it’s “ratio” — but that’s not equality of two ratios.

Another possibility: “equation”? E-Q-U-A-T-I-O-N — not matching letters.

Or “balance”? No.

Wait — maybe it’s “proport” — not a word.

I think there’s a mismatch. Let’s assume the blank is for 10 letters, and the answer is proportion.

Because it’s the correct term.

Similarly, for the second box, maybe “consequent” is intended, even if dash count is off.

But let’s check the fourth box.

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Fourth box:
> It is known as an expression that can form a solution (proportion)

This is vague. “An expression that can form a solution” — in context of proportion, perhaps it’s referring to a ratio itself? Because a proportion is made of two ratios.

Or maybe “equation”?

Blank has 5 dashes → 5 letters.

Letters: T M R Y I K C A O E

We need a 5-letter word.

Possible words: “ratio” — R,A,T,I,O — all available? T,M,R,Y,I,K,C,A,O,E — yes, R,A,T,I,O are all there.

“Ratio” is 5 letters.

And a ratio is an expression that, when set equal to another ratio, forms a proportion (solution).

So this could be ratio.

Also, “mean” — M,E,A,N — N not available.

“Term” — T,E,R,M — M is there, but “term” is 4 letters.

“Value” — V not available.

So “ratio” seems good.

Now back to second box.

Second box: second term of a ratio is “consequent” — 10 letters, but blank is 8? Letters available allow “conquest” but that’s wrong.

Wait — what if it’s “conseq” — not valid.

Another idea: in some old texts, the second term is called the “subsequent”? S-U-B-S-E-Q-U-E-N-T — too long, and B not available.

Perhaps it’s “latter” — but L not available.

Let’s list all possible 8-letter words from the letters: Q,C,N,U,N,O,E,S,E,T

Sorted: C,E,E,N,N,O,Q,S,T,U

Possible combinations:

- conquest: C,O,N,Q,U,E,S,T — uses 8 letters, leaves E,N — possible.

- sequence: S,E,Q,U,E,N,C,E — needs three E’s, we have only two? We have E,E — so S,E,Q,U,E,N,C — that’s 7, need one more — not enough E’s.

- tenounce? Not a word.

- conetune? No.

Perhaps it’s “conquest” and it’s a play on words? But that doesn’t fit math.

Wait — maybe the answer is “second” — but D not available.

Another thought: perhaps the second term is called the “following” — F not available.

I recall that in some contexts, especially in older math books, the second term is called the “consequent”, and perhaps the worksheet has a typo in the dash count.

Maybe the blank is for 10 letters, and “consequent” is intended.

Letters for “consequent”: C,O,N,S,E,Q,U,E,N,T — 10 letters.

Our letters: Q,C,N,U,N,O,E,S,E,T — that’s C,O,N,S,E,Q,U,E,N,T — yes! Exactly the letters for “consequent”.

C,O,N,S,E,Q,U,E,N,T — that’s 10 letters.

And the blank is shown as “--------” which might be a representation, not exact count. In many worksheets, the number of dashes may not be precise.

Similarly for “proportion” — 10 letters, blank might be approximate.

For the first box, “HCF” is 3 letters, and blank is “---” — 3 dashes, perfect.

For fourth box, “ratio” is 5 letters, blank “-----” — 5 dashes, perfect.

For third box, “proportion” is 10 letters, blank “---------” — 9 dashes? Close enough, probably meant to be 10.

For second box, “consequent” is 10 letters, blank “--------” — 8 dashes? Inconsistent.

But since the letters match “consequent” perfectly, and it’s the correct term, I’ll go with that.

Perhaps the dash count is not literal.

So:

1. HCF

2. CONSEQUENT

3. PROPORTION

4. RATIO

Now, let’s verify the letters for each.

First box: H,C,F — available: H,F,R,P,Z,I,C,O,J,B — yes, H,C,F are there.

Second box: C,O,N,S,E,Q,U,E,N,T — from Q,C,N,U,N,O,E,S,E,T — yes, all present.

Third box: P,R,O,P,O,R,T,I,O,N — from P,I,P,O,N,T,O,R,O,R — yes, P,P,O,O,O,R,R,T,I,N — matches.

Fourth box: R,A,T,I,O — from T,M,R,Y,I,K,C,A,O,E — yes, R,A,T,I,O are there.

Perfect.

So the answers are:

1. HCF

2. CONSEQUENT

3. PROPORTION

4. RATIO

Now, for the final answer, since the user didn't specify how to present, but typically for such puzzles, we list the words.

The instruction is to provide the final answer after reasoning.

Since it's a worksheet with four blanks, I'll list them in order.

Final Answer:
HCF, CONSEQUENT, PROPORTION, RATIO