Worksheet on Equivalent fractions - Free Printable

Let’s solve this step by step.

We are given a grid with numbers arranged in columns. The goal is to find the missing number at the bottom of the rightmost column (the one that ends with “?”).

Looking at the rightmost column, we see these numbers from top to bottom:

- 52
- 51
- 51
- 49
- 48
- 47
- 46
- 45
- 44
- 43
- 42
- 41
- 40
- 39
- 38
- 37
- 36
- 35
- 34
- ?

Wait — let’s list them carefully from top to bottom as they appear in the image (reading vertically down the last column):

Actually, looking again — the rightmost column has:

Top: 52
Then: 51
Then: 51
Then: 49
Then: 48
Then: 47
Then: 46
Then: 45
Then: 44
Then: 43
Then: 42
Then: 41
Then: 40
Then: 39
Then: 38
Then: 37
Then: 36
Then: 35
Then: 34
Then: ? ← this is what we need to find.

But wait — let’s count how many numbers are listed above the “?”.

From 52 down to 34, that’s:

52, 51, 51, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34 → that’s 19 numbers.

Now, look at the pattern. It seems like it’s mostly decreasing by 1 each time… but there’s a repeat: two 51s, and then jumps from 51 to 49 (skipping 50).

Let’s write the sequence with positions:

Position 1: 52
Position 2: 51
Position 3: 51 ← same as previous
Position 4: 49 ← skipped 50
Position 5: 48
Position 6: 47
Position 7: 46
Position 8: 45
Position 9: 44
Position 10: 43
Position 11: 42
Position 12: 41
Position 13: 40
Position 14: 39
Position 15: 38
Position 16: 37
Position 17: 36
Position 18: 35
Position 19: 34
Position 20: ? ← our answer

So from position 4 onward, it’s decreasing by 1 every time: 49, 48, 47, ..., down to 34.

That means from position 4 (value 49) to position 19 (value 34), how many steps?

From 49 to 34 is a drop of 15 over 15 steps? Let’s check:

Position 4: 49
Position 5: 48 → -1
Position 6: 47 → -1
...
Each step decreases by 1.

From position 4 to position 19 is 15 steps (19 - 4 = 15).

Starting at 49, after 15 steps of -1, we get: 49 - 15 = 34 → which matches position 19.

So the pattern from position 4 onward is consistent: decrease by 1 each row.

Therefore, position 20 should be 34 - 1 = 33.

But wait — let’s double-check the entire column for any other patterns or errors.

Alternatively, maybe the column is meant to be all consecutive integers from 52 down to something, but with some duplicates or skips.

List of values in order:

52, 51, 51, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, ?

If we ignore the duplicate 51 and the skip from 51 to 49, the rest is perfectly sequential downward.

Perhaps the intention is just to continue the downward trend from 34.

Since from 49 down to 34 it’s strictly decreasing by 1, and 34 is the last known value, the next should logically be 33.

Also, notice that in the bottom row, under the columns, there are labels:

Under first column: nothing visible? Wait — actually, at the very bottom, under the columns, we see:

Left to right:

First column: no label? Or maybe "Math" is under the whole thing? Actually, looking back — at the bottom left, there's an oval with "Math", and at the bottom right, under the last column, we have small boxes with numbers: 30, 45, 60, 55, 50 — but those might be distractors or part of another system.

Wait — perhaps I misread the structure.

Another approach: Maybe each column represents a separate sequence, and we’re to find the pattern within the last column only.

In the last column, starting from the top:

Row 1: 52
Row 2: 51
Row 3: 51
Row 4: 49
Row 5: 48
Row 6: 47
Row 7: 46
Row 8: 45
Row 9: 44
Row 10: 43
Row 11: 42
Row 12: 41
Row 13: 40
Row 14: 39
Row 15: 38
Row 16: 37
Row 17: 36
Row 18: 35
Row 19: 34
Row 20: ?

From row 4 to row 19: 49 down to 34 — that’s 16 numbers? Let’s count rows 4 through 19 inclusive: 19 - 4 + 1 = 16 numbers.

Values: 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34 → yes, 16 numbers, decreasing by 1 each time.

So row 20 should be 33.

Is there any reason to think otherwise? The earlier irregularities (two 51s, skip from 51 to 49) might be red herrings or errors, but since the long stretch is perfectly linear, we should follow that.

Moreover, if we consider the difference between row 1 and row 20: 52 to ? — if it were perfect countdown, 52 - 19 = 33 (since 20 rows total, subtract 19 steps). But because of the duplicate and skip, it’s not perfect, but from row 4 onward it is.

Actually, from row 1 to row 20 is 19 intervals.

If it were perfect countdown: 52, 51, 50, 49, ..., down to 52 - 19 = 33.

But in reality, we have:

Row 1: 52
Row 2: 51 → ok
Row 3: 51 → instead of 50 → so we’re “behind” by 1 here
Row 4: 49 → instead of 49? Wait, if row 3 was supposed to be 50, but it’s 51, then row 4 should be 49? That would mean it corrected itself.

Let’s simulate what it *should* be if counting down by 1 each row:

Ideal sequence for 20 rows starting at 52:

Row 1: 52
Row 2: 51
Row 3: 50
Row 4: 49
Row 5: 48
...
Row 20: 52 - 19 = 33

Actual sequence:

Row 1: 52 → matches
Row 2: 51 → matches
Row 3: 51 → should be 50 → so +1 error
Row 4: 49 → should be 49 → matches ideal
Row 5: 48 → matches
...
All subsequent match ideal.

So at row 3, it stayed at 51 instead of going to 50, but then at row 4 it went to 49, which is correct for row 4 in ideal sequence.

That means from row 4 onward, it’s back on track with the ideal countdown.

Therefore, row 20 should still be 33, as per ideal countdown.

The anomaly at row 3 didn’t throw off the rest; it just had a duplicate, but then resumed the correct decrement.

Thus, the missing number is 33.

Final Answer:
33