This worksheet uses visual fraction models to help students understand and solve for equivalent fractions by filling in the missing numerators.

Let’s solve each problem step by step. These are about equivalent fractions — meaning different fractions that represent the same amount.

We’ll go one box at a time, top to bottom, left to right.

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First Box (Top Left):

It shows:
- Top row: two halves → ½ + ½ = 1 whole
- Bottom row: four quarters → ¼ + ¼ + ¼ + ¼ = 1 whole

So, 2/4 equals ? / 2

Wait — actually, it says:

□ / 2 = 2 / 4

We need to find what number goes in the box so that the fraction is equal to 2/4.

But 2/4 simplifies to 1/2.

So □ / 2 = 1/2 → therefore, □ = 1

✔ Answer for first box: 1

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Second Box (Top Right):

Shows:
- Top: four 1/4s → 4 × 1/4 = 1
- Bottom: eight 1/8s → 8 × 1/8 = 1

Equation: □ / 4 = 2 / 8

Simplify 2/8 → divide numerator and denominator by 2 → 1/4

So □ / 4 = 1/4 → □ = 1

✔ Answer for second box: 1

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Third Box (Middle Left):

Shows:
- Top: six 1/6s → 6 × 1/6 = 1
- Bottom: three 1/3s → 3 × 1/3 = 1

Equation: 2/6 = □ / 3

Simplify 2/6 → divide by 2 → 1/3

So 1/3 = □ / 3 → □ = 1

✔ Answer for third box: 1

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Fourth Box (Middle Right):

Shows:
- Top: two 1/2s → 2 × 1/2 = 1
- Bottom: six 1/6s → 6 × 1/6 = 1

Equation: □ / 2 = 3 / 6

Simplify 3/6 → divide by 3 → 1/2

So □ / 2 = 1/2 → □ = 1

✔ Answer for fourth box: 1

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Fifth Box (Bottom Left):

Shows:
- Top: eight 1/8s → 8 × 1/8 = 1
- Bottom: two 1/2s → 2 × 1/2 = 1

Equation: 4/8 = □ / 2

Simplify 4/8 → divide by 4 → 1/2

So 1/2 = □ / 2 → □ = 1

✔ Answer for fifth box: 1

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Sixth Box (Bottom Right):

Shows:
- Top: three 1/3s → 3 × 1/3 = 1
- Bottom: six 1/6s → 6 × 1/6 = 1

Equation: □ / 3 = 2 / 6

Simplify 2/6 → 1/3

So □ / 3 = 1/3 → □ = 1

✔ Answer for sixth box: 1

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Seventh Box (Very Bottom Left):

Shows:
- Top: one 1/8 block (but only part of the bar? Wait — let's look again)

Actually, this one is different. It has:

Top row: one small box labeled “1/8” — but then below it, there’s a big rectangle split into two parts, each labeled “1/2”

And equation: 4/8 = □ / 2

Wait — we already did this! This is the same as Fifth Box.

4/8 = 1/2 → so □ = 1

✔ Answer: 1

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Eighth Box (Very Bottom Right):

Shows:
- Top: one 1/4 block
- Below: a rectangle split into two halves, each labeled “1/2”

Equation: □ / 4 = □ / 2

Wait — both boxes are blank? Let me read carefully.

Looking back at original image description:

Last box says:

□ / 4 = □ / 2

But from the diagram:

Top: one 1/4 → so maybe they mean 1/4?

Bottom: two 1/2s → but that would be 1 whole, not matching.

Wait — perhaps the diagram is showing equivalence between 1/4 and something over 2?

But 1/4 is not equal to any simple fraction over 2 unless we use decimals or other forms.

Wait — let’s think differently.

Maybe the diagram is meant to show that 1/4 is half of 1/2? But that doesn’t help with equality.

Alternatively — perhaps it’s asking: what fraction over 4 equals what fraction over 2?

But without more context, let’s assume it’s similar to others.

Wait — looking again at the structure:

In previous boxes, the diagrams showed how many pieces make a whole, and the equation matched the shaded or grouped parts.

In this last box:

Top: one piece labeled “1/4” — so maybe representing 1/4

Bottom: two pieces each labeled “1/2” — but that’s 1 whole, which is too much.

Perhaps it’s misdrawn? Or maybe it’s saying: if you have 1/4, what is it equal to over 2?

But 1/4 = ? / 2 → multiply numerator and denominator by 0.5? Not integer.

Wait — perhaps it’s 2/4 = 1/2? That makes sense.

Look: if top is two 1/4s? But it only shows one.

Wait — re-examining the user’s image description:

The last box says:

“□ / 4 = □ / 2”

And the diagram has:

Top: one box labeled “1/4”

Bottom: two boxes each labeled “1/2”

That doesn’t match numerically.

But perhaps it’s a trick? Or maybe I misread.

Another possibility: maybe the bottom is not two 1/2s making a whole, but rather, the whole is divided into two parts, each being 1/2, and we’re comparing to 1/4.

But 1/4 is half of 1/2.

So 1/4 = (1/2) / 2 → but that’s not standard fraction form.

Wait — let’s think of equivalent fractions.

What fraction over 4 equals what fraction over 2?

For example: 2/4 = 1/2 → that works.

Or 1/4 = ? / 2 → no integer solution.

But in the diagram, if top is one 1/4, and bottom is... perhaps it’s implying that 1/4 is half of 1/2, so maybe they want 1/4 = 0.5 / 2? But that’s not typical for elementary level.

Wait — perhaps the diagram is incorrect, or I’m misinterpreting.

Let me check the very first instruction: “Solve the problem accurately.”

Given that all previous answers were 1, and this might be a pattern, but let’s do math.

Suppose the equation is: A/4 = B/2

We need to find integers A and B such that this holds, based on the diagram.

Diagram: top has one 1/4 → so A=1?

Bottom has two 1/2s → but that’s 1 whole, while top is 1/4, so not equal.

Unless the bottom is meant to represent 1/2 total? But it shows two separate 1/2 blocks.

Perhaps it’s a mistake, and it should be like the others.

Another idea: in some worksheets, they show that 2/4 = 1/2, so maybe here it’s 2/4 = 1/2.

And the diagram might have intended to show two 1/4s on top? But it says “1/4” singular.

Looking back at user’s text:

" \frac{ }{4} = \frac{ }{2} "

And diagram: top has one cell with "1/4", bottom has two cells each with "1/2"

This is confusing.

Perhaps the bottom is not the value, but the division.

Let’s think differently.

In the context of the worksheet, all other problems had the answer 1 for the blank when simplified.

For this one, if we assume it’s 2/4 = 1/2, then blanks are 2 and 1.

But the diagram doesn't clearly show two 1/4s.

Wait — in the seventh box, it was 4/8 = □/2, and we said 1.

Similarly, here, perhaps it's 2/4 = 1/2.

And the diagram might be poorly drawn, but logically, 2/4 reduces to 1/2.

So likely, the intended answer is 2 and 1.

But the equation has two blanks: □/4 = □/2

So if 2/4 = 1/2, then first blank is 2, second is 1.

Yes, that makes sense.

And in the diagram, even though it shows one "1/4", perhaps it's a typo, or perhaps the "1/4" label is for the size, but there are two such blocks? The description says "one box labeled '1/4'", but maybe in the actual image, there are two.

Given the pattern, and to be consistent, I'll go with 2/4 = 1/2.

So blanks are 2 and 1.

✔ Answer for eighth box: 2 and 1

But let's confirm with calculation.

2/4 = 0.5

1/2 = 0.5

Equal.

If it were 1/4 = ?/2, then ? = 0.5, not integer.

So must be 2/4 = 1/2.

Therefore, for the last box: first blank is 2, second blank is 1.

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Now, compiling all answers:

1. First box: 1
2. Second box: 1
3. Third box: 1
4. Fourth box: 1
5. Fifth box: 1
6. Sixth box: 1
7. Seventh box: 1
8. Eighth box: 2 and 1

But the seventh box was duplicate of fifth, still 1.

In the user's list, there are 8 problems.

Let me list them as per order:

From top to bottom, left to right:

Row 1:
- Left: □/2 = 2/4 → □=1
- Right: □/4 = 2/8 → □=1

Row 2:
- Left: 2/6 = □/3 → □=1
- Right: □/2 = 3/6 → □=1

Row 3:
- Left: 4/8 = □/2 → □=1
- Right: □/3 = 2/6 → □=1

Row 4 (bottom):
- Left: 4/8 = □/2 → same as above, □=1 (seventh problem)
- Right: □/4 = □/2 → we say 2 and 1 (eighth problem)

In the user's initial description, the last two are:

" \frac{4}{8} = \frac{ }{2} " → this is seventh, answer 1

" \frac{ }{4} = \frac{ }{2} " → eighth, answer 2 and 1

Yes.

So final answers for each blank:

1. 1
2. 1
3. 1
4. 1
5. 1
6. 1
7. 1
8. First blank: 2, second blank: 1

But since the question is to solve the problem, and each box has its own answer, we need to provide all.

However, in the response, we should list them clearly.

Since the user didn't specify how to present, but given the format, perhaps list the answers in order.

But for the Final Answer section, we need to box the answers.

Given that most are 1, and last is 2 and 1, we can write:

Final Answer:
1, 1, 1, 1, 1, 1, 1, 2 and 1

But to be precise, let's specify per box.

Since the worksheet has 8 separate equations, we can list the missing numbers.

Box 1: 1
Box 2: 1
Box 3: 1
Box 4: 1
Box 5: 1
Box 6: 1
Box 7: 1
Box 8: 2 (for numerator over 4), 1 (for numerator over 2)

In box 8, it's □/4 = □/2, so two numbers.

For consistency, in the final answer, we can write the sequence.

I think it's fine.

All calculations verified.

Final Answer:
1, 1, 1, 1, 1, 1, 1, 2, 1

But that's nine numbers? No.

Boxes 1 to 7 have one blank each, box 8 has two blanks.

So total 9 blanks? Let's count:

From user's description:

First line: two boxes, each with one blank → 2 blanks

Second line: two boxes, each with one blank → 2 blanks

Third line: two boxes, each with one blank → 2 blanks

Fourth line: two boxes: first has one blank (4/8 = □/2), second has two blanks (□/4 = □/2) → 3 blanks

Total: 2+2+2+3 = 9 blanks.

Answers:

Blank 1 (box1): 1
Blank 2 (box2): 1
Blank 3 (box3): 1
Blank 4 (box4): 1
Blank 5 (box5): 1
Blank 6 (box6): 1
Blank 7 (box7): 1
Blank 8 (box8 first): 2
Blank 9 (box8 second): 1

So the answers are: 1,1,1,1,1,1,1,2,1

But in the context, perhaps list per box.

Since the problem is to fill in the blanks, and for clarity, we can state:

The missing numbers are:
For the first seven equations: 1 each
For the last equation: 2 and 1 respectively.

But for Final Answer section, we need concise.

I think listing the values in order is fine.

Final Answer:
1, 1, 1, 1, 1, 1, 1, 2, 1