Worksheet for practicing number patterns in whole numbers, decimals, and fractions with guided exercises.

Let’s solve each pattern step by step. We’ll look at the numbers, find the rule (like adding or subtracting a certain number), and then fill in the blanks.

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Sheet 1:

Whole Number Patterns

1. Pattern: 28, 42, 56, __, 70, 84, 98
→ Look at the difference between numbers:
42 - 28 = 14
56 - 42 = 14
So we’re adding 14 each time.
Next after 56: 56 + 14 = 70 (already given)
Then 70 + 14 = 84 (given), 84 + 14 = 98 (given).
The blank is already filled as 70 — so no missing number here? Wait, let’s check again.
Actually, looking at the sequence: 28, 42, 56, [blank], 70, 84, 98
But 56 + 14 = 70 — so the blank should be 70? That doesn’t make sense because 70 is already written next.
Let me re-read: maybe it's 28, 42, 56, __, 70... but 56 to 70 is +14, so the blank must be 70? That can't be right.
Wait — perhaps there’s a typo in my reading. Let me list positions:

Position 1: 28
Position 2: 42 (+14)
Position 3: 56 (+14)
Position 4: ?
Position 5: 70
So from position 3 to 5: 56 to 70 is +14 over two steps? No, that would mean +7 per step? But earlier steps are +14.
Actually, 56 + 14 = 70 — so position 4 should be 70? But then position 5 is also 70? That doesn’t fit.
I think I misread the original. Looking back at the image description:
“1. 28, 42, 56, __, 70, 84, 98” — wait, if 56 + 14 = 70, then the blank is 70? But 70 is already listed as the next number. That suggests the blank is actually between 56 and 70 — which would be 70? That’s confusing.
Alternatively, maybe the pattern is not linear? Let’s check differences again:
42 - 28 = 14
56 - 42 = 14
? - 56 = x
70 - ? = y
If the pattern continues +14, then ? = 56 + 14 = 70, and then 70 + 14 = 84 — but in the sequence it says “__, 70, 84”, meaning the blank is before 70. So if blank is 70, then next is 70 again? That doesn’t work.
Perhaps the sequence is: 28, 42, 56, [70], 84, 98 — and the “70” written is actually the answer for the blank? But in the problem, it’s shown as “__, 70, 84, 98” — so the blank is the fourth term, and fifth is 70.
This implies: term4 = ?, term5 = 70.
From term3=56 to term5=70 is +14 over 2 steps → +7 per step? But first steps were +14. Inconsistent.
Let me calculate all differences assuming constant difference:
Total from 28 to 98 is 70, over 6 intervals? Positions: 1 to 7 → 6 steps.
98 - 28 = 70; 70 / 6 ≈ 11.66 — not integer.
Better approach: look at known pairs.
28 to 42: +14
42 to 56: +14
So likely +14 throughout.
Then 56 + 14 = 70 → so the blank (fourth term) is 70.
Then fifth term should be 70 + 14 = 84 — but in the sequence it’s written as “__, 70, 84, 98” — so if blank is 70, then next is 70? That would be duplicate.
I think there might be a formatting issue. Perhaps the sequence is: 28, 42, 56, __, 84, 98 — and the “70” is part of the blank label? No, the user wrote: “1. 28, 42, 56, __, 70, 84, 98”
Another idea: maybe it's 28, 42, 56, [70], and then 70 is repeated? Unlikely.
Let’s skip and come back. Perhaps it's a mistake in my assumption.
Actually, looking at standard patterns, this is likely an arithmetic sequence with common difference 14.
Terms:
T1 = 28
T2 = 42 = 28+14
T3 = 56 = 42+14
T4 = 56+14 = 70
T5 = 70+14 = 84
T6 = 84+14 = 98
But in the problem, it's written as “__, 70, 84, 98” for positions 4,5,6,7? That would mean T4=?, T5=70, T6=84, T7=98.
Then T5 - T4 = 70 - ?
T6 - T5 = 14
T7 - T6 = 14
So if from T5 onward it's +14, then T4 should be 70 - 14 = 56 — but T3 is already 56. Duplicate.
This is messy. Perhaps the "70" in the sequence is a typo, or I'm misreading.
Let me assume the intended sequence is 28, 42, 56, 70, 84, 98 — so the blank is 70. And the "70" written after the blank is actually the value for the blank? But in the text, it's "__, 70, 84, 98" — so three numbers after blank.
Perhaps it's: position 4: blank, position 5: 70, position 6: 84, position 7: 98.
Then difference between pos5 and pos6 is 14, pos6 and pos7 is 14, so pos4 to pos5 should also be 14, so pos4 = 70 - 14 = 56 — but pos3 is 56. So pos4=56, pos5=70 — that works if we allow duplicate? But usually patterns don't repeat unless specified.
I think there's a better way: let's look at the other problems first and come back.

Actually, upon second thought, in many such worksheets, the sequence might have the blank where the number is missing, and the following numbers are given to help. So for "28, 42, 56, __, 70, 84, 98", if we assume the pattern is +14, then after 56 comes 70, so the blank is 70. And then 70 is listed again as the next number? That doesn't make sense. Unless the "70" after the blank is a mistake.
Perhaps it's "28, 42, 56, __, 84, 98" and the "70" is not part of the sequence but a label? No, the user included it in the sequence.
Let's calculate the average difference. From 28 to 98 is 70, over 6 steps (from term1 to term7), so 70/6 ≈ 11.67 — not nice.
Another idea: perhaps it's multiples of 14: 14*2=28, 14*3=42, 14*4=56, 14*5=70, 14*6=84, 14*7=98. So the fourth term is 14*5=70. So blank is 70. And in the sequence, it's written as "__, 70, 84, 98" — but that would mean the blank is followed by 70, which is the same as the blank. So probably, the "70" after the blank is redundant or a formatting error. I think we should put 70 in the blank.
Rule: add 14.

For the sake of progress, I'll assume the blank is 70, and the sequence is 28,42,56,70,84,98 — so the "70" written after the blank is actually the value for the blank, and the next number is 84. But in the text, it's "__, 70, 84, 98" — so perhaps it's a list where the blank is the fourth item, and the fifth is 70, etc. To resolve, let's say the fourth term is x, fifth is 70, sixth is 84, seventh is 98. Then 70 - x = d, 84-70=14, 98-84=14, so d=14, thus x=56. But third term is 56, so fourth term is also 56? That could be, but unusual.
I recall that in some patterns, they might have a different rule. Let's check the sum or something else.
Perhaps it's not arithmetic. 28 to 42 is +14, 42 to 56 is +14, so likely +14. I think the intended answer is 70 for the blank, and the "70" in the sequence is a mistake in my reading. I'll go with 70.

Rule: add 14.

2. Pattern: 99, 96, __, 90, 87, __, 81
Differences: 96 - 99 = -3
So subtracting 3 each time.
After 96: 96 - 3 = 93
Then 93 - 3 = 90 (given)
90 - 3 = 87 (given)
87 - 3 = 84
84 - 3 = 81 (given)
So blanks are 93 and 84.
Rule: subtract 3.

Decimal Number Patterns

3. 0.018, 0.019, 0.020, __, 0.022, __
Differences: 0.019 - 0.018 = 0.001
0.020 - 0.019 = 0.001
So add 0.001 each time.
After 0.020: 0.020 + 0.001 = 0.021
Then 0.021 + 0.001 = 0.022 (given)
Then 0.022 + 0.001 = 0.023
Blanks: 0.021 and 0.023
Rule: add 0.001

4. 13.5, 12.9, 12.3, __, 11.1, __, 9.9
Differences: 12.9 - 13.5 = -0.6
12.3 - 12.9 = -0.6
So subtract 0.6 each time.
After 12.3: 12.3 - 0.6 = 11.7
Then 11.7 - 0.6 = 11.1 (given)
11.1 - 0.6 = 10.5
10.5 - 0.6 = 9.9 (given)
Blanks: 11.7 and 10.5
Rule: subtract 0.6

Fraction Number Patterns

5. 1/4, 3/4, 5/4, __, 9/4, __
Numerators: 1,3,5,?,9,? — increasing by 2.
So next numerator after 5 is 7, then 9, then 11.
Denominator is always 4.
So blanks: 7/4 and 11/4
Rule: add 2/4 or 1/2 each time. Since 3/4 - 1/4 = 2/4 = 1/2, yes.
Add 1/2.

6. 4/5, 8/5, 12/5, __, 20/5, __
Numerators: