Reciprocal Fraction Worksheets - Free Printable

Let's solve the "Reciprocal Match" activity step by step.

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🔍 What is a reciprocal?

The reciprocal of a number is 1 divided by that number. For fractions, you just flip the numerator and denominator.

For example:
- Reciprocal of $ \frac{a}{b} $ is $ \frac{b}{a} $
- Reciprocal of a whole number $ n $ is $ \frac{1}{n} $
- Reciprocal of a mixed number: first convert to an improper fraction, then flip.

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🧩 Step 1: List all the given numbers in the grid

We’ll go through each box and find its reciprocal, then match it with the cut-out cards (like $ \frac{3}{4}, \frac{4}{3}, \frac{5}{8}, \frac{8}{5} $, etc.).

Here are the numbers in the grid:

| Fraction/Number | Reciprocal |
|------------------|-----------|
| $ \frac{8}{33} $ | $ \frac{33}{8} $ ✔ |
| $ \frac{33}{8} $ | $ \frac{8}{33} $ ✔ |
| $ 5\frac{3}{5} $ | Convert to improper: $ \frac{28}{5} $ → reciprocal = $ \frac{5}{28} $ |
| $ \frac{1}{16} $ | $ 16 $ ✔ |
| $ \frac{16}{1} $ | $ \frac{1}{16} $ ✔ |
| $ 16 $ | $ \frac{1}{16} $ ✔ |
| $ \frac{11}{15} $ | $ \frac{15}{11} $ |
| $ 15 $ | $ \frac{1}{15} $ |
| $ \frac{14}{17} $ | $ \frac{17}{14} $ |
| $ 4\frac{1}{8} $ | Convert: $ \frac{33}{8} $ → reciprocal = $ \frac{8}{33} $ |
| $ \frac{2}{7} $ | $ \frac{7}{2} $ |
| $ \frac{7}{16} $ | $ \frac{16}{7} $ |
| $ \frac{4}{7} $ | $ \frac{7}{4} $ |

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Now, look at the cut-out cards shown:
- $ \frac{3}{4} $
- $ \frac{4}{3} $
- $ \frac{5}{8} $
- $ \frac{8}{5} $

Wait — these don’t seem to match most of the reciprocals we just found. But let’s see if any of them do appear.

Let’s check which of the cut-outs are reciprocals of numbers in the grid.

🔎 Check for matches:

1. $ \frac{3}{4} $ → reciprocal is $ \frac{4}{3} $
- Is $ \frac{3}{4} $ in the grid? No.
- Is $ \frac{4}{3} $ in the grid? No.
- But wait — maybe one of the original numbers has reciprocal $ \frac{3}{4} $? Let’s reverse it.

If reciprocal is $ \frac{3}{4} $, original number is $ \frac{4}{3} $. So $ \frac{4}{3} $ must be in the grid?

Looking back: no $ \frac{4}{3} $ in the grid.

2. $ \frac{4}{3} $ → reciprocal is $ \frac{3}{4} $

3. $ \frac{5}{8} $ → reciprocal is $ \frac{8}{5} $

4. $ \frac{8}{5} $ → reciprocal is $ \frac{5}{8} $

But none of these appear in the grid directly.

Wait — perhaps the cut-outs are the reciprocals, and we need to match them to their original numbers.

So maybe the task is: Which original number has reciprocal equal to $ \frac{3}{4} $?

That would be $ \frac{4}{3} $ — but $ \frac{4}{3} $ isn't in the grid.

Wait — look again at the grid. We have:

- $ \frac{8}{33} $ → reciprocal $ \frac{33}{8} $
- $ \frac{33}{8} $ → reciprocal $ \frac{8}{33} $
- $ 5\frac{3}{5} = \frac{28}{5} $ → reciprocal $ \frac{5}{28} $
- $ \frac{1}{16} $ → $ 16 $
- $ \frac{16}{1} = 16 $ → $ \frac{1}{16} $
- $ 16 $ → $ \frac{1}{16} $
- $ \frac{11}{15} $ → $ \frac{15}{11} $
- $ 15 $ → $ \frac{1}{15} $
- $ \frac{14}{17} $ → $ \frac{17}{14} $
- $ 4\frac{1}{8} = \frac{33}{8} $ → $ \frac{8}{33} $
- $ \frac{2}{7} $ → $ \frac{7}{2} $
- $ \frac{7}{16} $ → $ \frac{16}{7} $
- $ \frac{4}{7} $ → $ \frac{7}{4} $

Now, none of the cut-out cards ($ \frac{3}{4}, \frac{4}{3}, \frac{5}{8}, \frac{8}{5} $) are among these reciprocals.

But wait — could there be a mistake? Or perhaps the cut-outs are meant to be glued into the boxes?

Let’s suppose the cut-outs are the reciprocals, and we need to find which original number they belong to.

So:

- Cut-out: $ \frac{3}{4} $ → original number = $ \frac{4}{3} $ → not in grid
- Cut-out: $ \frac{4}{3} $ → original = $ \frac{3}{4} $ → not in grid
- Cut-out: $ \frac{5}{8} $ → original = $ \frac{8}{5} $ → not in grid
- Cut-out: $ \frac{8}{5} $ → original = $ \frac{5}{8} $ → not in grid

Hmm — so none of the cut-outs match any reciprocal from the grid.

Wait — but look at this:
Is $ \frac{8}{5} $ in the grid? No.
Is $ \frac{5}{8} $? No.

But what about $ \frac{33}{8} $ and $ \frac{8}{33} $? They are reciprocals.

And $ \frac{16}{1} $ and $ \frac{1}{16} $ are reciprocals.

And $ 16 $ and $ \frac{1}{16} $ are reciprocals.

So perhaps the cut-outs are not the ones shown — or maybe only some are visible.

Wait — the image shows only four cut-outs: $ \frac{3}{4}, \frac{4}{3}, \frac{5}{8}, \frac{8}{5} $

But those aren't matching anything in the grid.

Unless... maybe the task is incomplete, or I’m missing something.

Wait — look again at the grid.

There’s a blank next to $ 5\frac{3}{5} $. What is its reciprocal?

$ 5\frac{3}{5} = \frac{28}{5} $ → reciprocal = $ \frac{5}{28} $

Not in cut-outs.

Next: $ \frac{11}{15} $ → $ \frac{15}{11} $

No.

Wait — what about $ \frac{4}{7} $? Reciprocal is $ \frac{7}{4} $

Still not matching.

Wait — what if the cut-outs are meant to be matched to other numbers not in the grid? That doesn’t make sense.

Alternatively — perhaps the cut-outs are the reciprocals, and the original numbers are in the grid, and we need to match them.

But again, none of the cut-outs are reciprocals of numbers in the grid.

Wait — unless one of the numbers in the grid is $ \frac{4}{3} $? Let’s scan again.

Grid has:
- $ \frac{8}{33}, \frac{33}{8}, 5\frac{3}{5}, \frac{1}{16}, \frac{16}{1}, 16, \frac{11}{15}, 15, \frac{14}{17}, 4\frac{1}{8}, \frac{2}{7}, \frac{7}{16}, \frac{4}{7} $

No $ \frac{4}{3} $, $ \frac{3}{4} $, $ \frac{5}{8} $, $ \frac{8}{5} $

So unless the cut-outs are extras, or the image is cropped, or I'm missing something...

Wait — perhaps the cut-outs are meant to be placed in the blank boxes, and the original numbers are already in the grid, and we’re to match the reciprocal card to the correct number.

But again, none of the cut-outs are reciprocals of the numbers in the grid.

Unless…

Wait — is $ \frac{8}{5} $ the reciprocal of $ \frac{5}{8} $? Yes.

But $ \frac{5}{8} $ is not in the grid.

Wait — what about $ \frac{2}{7} $? Its reciprocal is $ \frac{7}{2} = 3\frac{1}{2} $

Not in cut-outs.

Wait — maybe the cut-outs are not the reciprocals, but the original numbers?

No — the instruction says: “Cut out the reciprocals and glue them into the box next to the correct fraction…”

So the cut-outs are the reciprocals, and we glue them next to the original number.

So for example:
- If a number in the grid is $ \frac{8}{33} $, its reciprocal is $ \frac{33}{8} $
- So we should glue $ \frac{33}{8} $ next to $ \frac{8}{33} $

Similarly:
- $ \frac{33}{8} $ → $ \frac{8}{33} $
- $ 5\frac{3}{5} = \frac{28}{5} $ → $ \frac{5}{28} $
- $ \frac{1}{16} $ → $ 16 $
- $ \frac{16}{1} $ → $ \frac{1}{16} $
- $ 16 $ → $ \frac{1}{16} $
- $ \frac{11}{15} $ → $ \frac{15}{11} $
- $ 15 $ → $ \frac{1}{15} $
- $ \frac{14}{17} $ → $ \frac{17}{14} $
- $ 4\frac{1}{8} = \frac{33}{8} $ → $ \frac{8}{33} $
- $ \frac{2}{7} $ → $ \frac{7}{2} $
- $ \frac{7}{16} $ → $ \frac{16}{7} $
- $ \frac{4}{7} $ → $ \frac{7}{4} $

Now, the cut-outs shown are:
- $ \frac{3}{4} $
- $ \frac{4}{3} $
- $ \frac{5}{8} $
- $ \frac{8}{5} $

None of these appear in the list above.

So either:
1. The image is incomplete — more cut-outs exist off-screen.
2. There’s a typo or error.
3. Or I misread the grid.

Wait — look at the grid again.

In the top row:
- $ \frac{8}{33} $, $ \frac{33}{8} $, $ 5\frac{3}{5} $, [blank], $ \frac{1}{16} $, $ \frac{16}{1} $

Then second row:
- $ 16 $, $ \frac{1}{16} $, $ \frac{11}{15} $, $ 15 $, [blank], [blank]

Third row:
- $ \frac{14}{17} $, [blank], $ 4\frac{1}{8} $, [blank], [blank], [blank]

Fourth row:
- $ \frac{2}{7} $, $ \frac{7}{16} $, $ \frac{4}{7} $, [blank], [blank], [blank]

So there are many blanks — and the cut-outs are likely meant to fill some of them.

But the cut-outs shown are $ \frac{3}{4}, \frac{4}{3}, \frac{5}{8}, \frac{8}{5} $

Are any of these reciprocals of numbers in the grid?

Let’s test:

- Is $ \frac{3}{4} $ the reciprocal of any number in the grid?

That would mean: $ \frac{1}{x} = \frac{3}{4} $ → $ x = \frac{4}{3} $

Is $ \frac{4}{3} $ in the grid? No.

- $ \frac{4}{3} $ → $ x = \frac{3}{4} $ → not in grid.

- $ \frac{5}{8} $ → $ x = \frac{8}{5} $ → not in grid.

- $ \frac{8}{5} $ → $ x = \frac{5}{8} $ → not in grid.

So none of these cut-outs are reciprocals of any number in the grid.

But perhaps the cut-outs are the original numbers, and we're supposed to glue the reciprocals in the blank boxes?

No — the instruction says: "Cut out the reciprocals and glue them..."

So the cut-outs are the reciprocals.

Therefore, they must be the reciprocals of the numbers in the grid.

But they don't match.

Unless...

Wait — is $ \frac{4}{7} $ in the grid? Yes!

Its reciprocal is $ \frac{7}{4} $

But $ \frac{7}{4} $ is not among the cut-outs.

But $ \frac{7}{4} = 1\frac{3}{4} $

Not shown.

Wait — what about $ \frac{8}{5} $? Could it be the reciprocal of $ \frac{5}{8} $? Yes.

But $ \frac{5}{8} $ is not in the grid.

Wait — look at $ \frac{7}{16} $ → reciprocal is $ \frac{16}{7} $

Not shown.

Wait — $ \frac{2}{7} $ → $ \frac{7}{2} = 3\frac{1}{2} $

Not shown.

Wait — perhaps the cut-outs are not for the numbers in the grid, but for other numbers?

Or maybe the image is partially cropped, and there are more cut-outs.

But based on what we can see, the four cut-outs shown do not match any reciprocals of the numbers in the grid.

However, there is one possibility:

Look at $ \frac{8}{33} $ and $ \frac{33}{8} $ — they are reciprocals.

Similarly, $ \frac{1}{16} $ and $ 16 $, $ \frac{16}{1} $ and $ \frac{1}{16} $, etc.

But none of the cut-outs match.

Wait — what if the cut-outs are meant to be used for a different part of the worksheet?

Or perhaps the numbers in the grid are not all the original numbers — maybe some are reciprocals and some are originals.

But the instruction says: "glue them into the box next to the correct fraction, whole number, or mixed number."

So the numbers in the grid are the originals, and the cut-outs are the reciprocals.

But since none of the cut-outs match, perhaps the image is missing some cut-outs.

Alternatively, maybe the cut-outs shown are examples, and there are others not visible.

But given the information, I cannot match the shown cut-outs to any number in the grid.

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✔ Conclusion:

The correct reciprocals for the numbers in the grid are:

| Number | Reciprocal |
|--------|------------|
| $ \frac{8}{33} $ | $ \frac{33}{8} $ |
| $ \frac{33}{8} $ | $ \frac{8}{33} $ |
| $ 5\frac{3}{5} $ | $ \frac{5}{28} $ |
| $ \frac{1}{16} $ | $ 16 $ |
| $ \frac{16}{1} $ | $ \frac{1}{16} $ |
| $ 16 $ | $ \frac{1}{16} $ |
| $ \frac{11}{15} $ | $ \frac{15}{11} $ |
| $ 15 $ | $ \frac{1}{15} $ |
| $ \frac{14}{17} $ | $ \frac{17}{14} $ |
| $ 4\frac{1}{8} $ | $ \frac{8}{33} $ |
| $ \frac{2}{7} $ | $ \frac{7}{2} $ |
| $ \frac{7}{16} $ | $ \frac{16}{7} $ |
| $ \frac{4}{7} $ | $ \frac{7}{4} $ |

The cut-outs shown ($ \frac{3}{4}, \frac{4}{3}, \frac{5}{8}, \frac{8}{5} $) do not match any of these reciprocals.

Therefore, either:
- The image is incomplete,
- Or there is a mistake in the problem,
- Or the cut-outs are for a different version of the worksheet.

But if we assume the cut-outs are correct, then they must be matched to numbers not in the visible grid.

Alternatively, perhaps the task is to identify which cut-out is the reciprocal of which number, but based on the current data, no match exists.

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🟩 Final Answer:

Based on the visible numbers in the grid, none of the shown cut-outs ($ \frac{3}{4}, \frac{4}{3}, \frac{5}{8}, \frac{8}{5} $) are reciprocals of any number in the grid.

Therefore, these cut-outs do not belong to any of the given numbers.

Possible explanation: The image may be cropped, or additional cut-outs are missing. The actual reciprocals needed are:
- $ \frac{33}{8} $, $ \frac{8}{33} $, $ \frac{5}{28} $, $ 16 $, $ \frac{1}{16} $, $ \frac{15}{11} $, $ \frac{1}{15} $, $ \frac{17}{14} $, $ \frac{8}{33} $, $ \frac{7}{2} $, $ \frac{16}{7} $, $ \frac{7}{4} $

So the correct cut-outs should include these, not $ \frac{3}{4}, \frac{4}{3}, \frac{5}{8}, \frac{8}{5} $.

Thus, the shown cut-outs are incorrect or for a different problem.

If you have access to the full set of cut-outs, please check for $ \frac{33}{8} $, $ \frac{8}{33} $, $ 16 $, $ \frac{1}{16} $, etc.

Otherwise, the solution cannot be completed with the given cut-outs.