Math practice worksheet with exercises on patterns, decimals, and equations.

Let's solve each problem step by step based on the image you described. I'll go through each question carefully.

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8. Write an equation to show the relationship between the input and output.

We are given two tables:

#### Table 1:
| Input (x) | Output (y) |
|-----------|------------|
| 7 | 28 |
| 3 | 12 |
| 1 | 4 |
| 5 | 20 |

Let’s look for a pattern:
- 7 → 28: 7 × 4 = 28
- 3 → 12: 3 × 4 = 12
- 1 → 4: 1 × 4 = 4
- 5 → 20: 5 × 4 = 20

So, y = 4x

✔ Answer: $ y = 4x $

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#### Table 2:
| Input (x) | Output (y) |
|-----------|------------|
| 25 | 5 |
| 50 | 10 |
| 5 | 1 |
| 10 | 2 |

Look at the pattern:
- 25 → 5: 25 ÷ 5 = 5
- 50 → 10: 50 ÷ 5 = 10
- 5 → 1: 5 ÷ 5 = 1
- 10 → 2: 10 ÷ 5 = 2

So, y = x ÷ 5 or $ y = \frac{x}{5} $

✔ Answer: $ y = \frac{x}{5} $

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9. Find the value of the underlined digit.

Assuming the underlined digits are as follows (based on typical problems):

#### 10. 37
If the underlined digit is 3, it's in the tens place → value = 30
If it's 7, it's in the ones place → value = 7

But since it says "underlined", and no underline shown here, let’s assume it's asking for place value.

But likely, we need to interpret from context.

Wait — looking at the list:

> 10. 37
> 11. 5,735.24
> 12. 22.8

Let’s assume one digit in each is underlined. Since not visible, we’ll assume common types.

But maybe the problem is asking to find the value of a specific digit (e.g., underlined). Let's suppose:

#### 10. 37 — if 3 is underlined → value = 30
→ ✔ 30

#### 11. 5,735.24 — if 3 is underlined (in tens place? Let's see):
Digits:
5 (thousands), 7 (hundreds), 3 (tens), 5 (ones), .2 (tenths), 4 (hundredths)

So if 3 is underlined → it's in the tens place → value = 30

But wait — maybe it's 7? Or 5?

Alternatively, perhaps 3 is in the tens place → 30

But let’s suppose 3 is underlined → 30

But without seeing underline, this is ambiguous.

Wait — perhaps the question is asking us to identify the value of a digit in a number.

Let me recheck the structure.

Actually, maybe the "Find the value of the underlined digit" applies to all three:

#### 10. 37
Suppose 3 is underlined → value = 30
(3 is in tens place)

#### 11. 5,735.24
Suppose 3 is underlined → it's in the tens place → value = 30

But wait — 5,735.24:
- 5: thousands
- 7: hundreds
- 3: tens
- 5: ones
- 2: tenths
- 4: hundredths

So 3 = 30

#### 12. 22.8
Suppose 8 is underlined → it's in the tenths place → value = 0.8

Or if 2 is underlined → could be 20 or 2

But since both 2s are same, but first 2 is tens, second is ones.

Let’s suppose:

- 10. 37 → 3 underlined → 30
- 11. 5,735.24 → 3 underlined → 30
- 12. 22.8 → 8 underlined → 0.8

But again, without visual, we must assume.

Alternatively, perhaps only one digit is underlined per number, but since not shown, let's move on.

But perhaps the question is just to state the value of the underlined digit, so we can’t answer definitively without knowing which digit is underlined.

But maybe the numbers are listed with implied underlining?

Wait — maybe it's a typo or formatting issue.

Let’s skip and come back.

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13. 7,445.6

> The 4 in the tens place is ___ the value of the 4 in the hundreds place.

Break down:

- 7,445.6
- 7: thousands
- 4: hundreds
- 4: tens
- 5: ones
- 6: tenths

So:
- 4 in hundreds place = 400
- 4 in tens place = 40

So, 40 is 1/10 of 400

So: “The 4 in the tens place is 1/10 the value of the 4 in the hundreds place.”

✔ Answer: $ \frac{1}{10} $

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14. 7,518.763

> The 8 in the ones place is ___ the value of the 8 in the hundredths place.

Wait — is there an 8 in the ones place?

7,518.763

Digits:
- 7: thousands
- 5: hundreds
- 1: tens
- 8: ones
- 7: tenths
- 6: hundredths
- 3: thousandths

So:
- 8 in ones place = 8
- But is there an 8 in the hundredths place? No — it's 6

Wait — the number is 7,518.763 → hundredths digit is 6, not 8

But the question says: “the 8 in the ones place” and “the 8 in the hundredths place”

But there is no 8 in the hundredths place!

That suggests a mistake.

Wait — maybe the number is different?

Wait — could it be 7,581.763?

But original says: 7,518.763

So digits:
- Ones: 8
- Tenths: 7
- Hundredths: 6
- Thousandths: 3

So no 8 in hundredths.

Unless it's a typo.

Alternatively, maybe it's 7,518.783? Then hundredths would be 8.

But assuming the number is correct: 7,518.763

Then there is no 8 in the hundredths place, so the question doesn't make sense.

But maybe it's a trick.

Wait — perhaps it's asking about the value of the 8 in ones vs. the 8 in hundredths, but there is no 8 in hundredths.

Wait — unless the number is 7,518.863? Then yes.

But as written: 7,518.763

So unless it's a typo, this is invalid.

But perhaps the intended number has an 8 in the hundredths place.

Let’s suppose it's 7,518.783 → then:
- 8 in ones place = 8
- 8 in hundredths place = 0.08

So: 8 ÷ 0.08 = 100 → so 8 in ones is 100 times the value of 8 in hundredths.

So: “The 8 in the ones place is 100 times the value of the 8 in the hundredths place.”

✔ Answer: 100 times

But since the number is written as 7,518.763, this may be a typo.

Alternatively, maybe it's 7,518.783 — that makes sense.

We’ll proceed with that assumption.

✔ Answer: 100 times

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Solve the equations:

#### 15. ____ + 100 = 850.32

Subtract 100 from both sides:

850.32 − 100 = 750.32

✔ Answer: 750.32

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#### 16. 3 × 800 = 3000 ÷ a

First, compute left side: 3 × 800 = 2400

So: 2400 = 3000 ÷ a

Now solve for a:

Multiply both sides by a: 2400a = 3000

Divide both sides by 2400: a = 3000 / 2400 = 30/24 = 5/4 = 1.25

✔ Answer: $ a = 1.25 $

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#### 17. 687.33 + _____ = 687.320

Wait — 687.33 + something = 687.320?

But 687.33 = 687.330

So: 687.330 + x = 687.320

Then x = 687.320 − 687.330 = −0.01

So: −0.01

But that seems odd.

Wait — maybe it's a typo?

Perhaps it should be: 687.33 + _____ = 687.330

Then x = 0

But as written: 687.33 + x = 687.320 → x = −0.01

But 687.320 is less than 687.33

So unless it's a subtraction, it's negative.

But possible.

✔ Answer: −0.01

But let’s check:

687.33 = 687.330

687.330 + (−0.01) = 687.320 → yes

So correct.

✔ Answer: −0.01

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#### 18. 54,000 − 90 = _____

54,000 − 90 = 53,910

✔ Answer: 53,910

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#### 19. If 30 ÷ 3 = 10, then 300 ÷ a = ?

We know: 30 ÷ 3 = 10

Now: 300 ÷ a = ?

Note: 300 is 10 times 30

So: 300 ÷ a = ?

But we want the result to be similar.

But the statement says: “if 30 ÷ 3 = 10, then 300 ÷ a = ?”

But what is the expected result?

It might be implying that the quotient remains the same?

But 300 ÷ a = 10 → then a = 30

So: a = 30

But maybe it’s asking for the value of the expression.

Wait — probably: if 30 ÷ 3 = 10, then 300 ÷ a = ?

And since 300 is 10× larger than 30, to keep quotient same, divisor must be 10× larger.

So: 300 ÷ 30 = 10

So a = 30

✔ Answer: 10

But the blank is after “then 300 ÷ a = ” → so likely the answer is 10

But we don’t know a.

Wait — perhaps the question is: if 30 ÷ 3 = 10, then 300 ÷ a = ? (and a is such that it's proportional)

But unless specified, we can't know.

Wait — perhaps it's a pattern: 30 ÷ 3 = 10 → 300 ÷ 30 = 10

So a = 30 → then 300 ÷ 30 = 10

So the answer is 10

✔ Answer: 10

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#### 20. If 30 ÷ 3 = 10, then 1 ÷ 0.03 = ?

We know: 30 ÷ 3 = 10

Now: 1 ÷ 0.03

Convert: 1 ÷ 0.03 = 1 ÷ (3/100) = 1 × (100/3) = 100/3 ≈ 33.333...

But how does it relate?

Note: 30 ÷ 3 = 10

Now: 1 ÷ 0.03 = ?

But 0.03 = 3/100

So 1 ÷ (3/100) = 100/3 ≈ 33.33

But let’s see if we can relate.

Note: 30 ÷ 3 = 10

Now: 1 ÷ 0.03 = ?

But 1 is 1/30 of 30, and 0.03 is 1/100 of 3

So: (1/30) ÷ (1/100 × 3) = (1/30) ÷ (3/100) = (1/30) × (100/3) = 100 / 90 = 10/9 ≈ 1.11

No — better:

1 ÷ 0.03 = 100 / 3 ≈ 33.33

But let’s compute directly:

0.03 × 33.333... = 1

So: 1 ÷ 0.03 = 33.333... = $ \frac{100}{3} $

But is there a relation?

Note: 30 ÷ 3 = 10

Now: 1 ÷ 0.03 = ?

But 0.03 = 3 × 0.01

So 1 ÷ (3 × 0.01) = (1 ÷ 0.01) ÷ 3 = 100 ÷ 3 = 33.333...

So: 100/3 or 33⅓

✔ Answer: $ \frac{100}{3} $ or 33.333...

But perhaps they want exact fraction.

✔ Answer: $ \frac{100}{3} $

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Summary of Answers:

8.
- Table 1: $ y = 4x $
- Table 2: $ y = \frac{x}{5} $

9.
- 10. 37 → if 3 is underlined: 30
- 11. 5,735.24 → if 3 is underlined: 30
- 12. 22.8 → if 8 is underlined: 0.8

13. The 4 in the tens place is 1/10 the value of the 4 in the hundreds place.

14. The 8 in the ones place is 100 times the value of the 8 in the hundredths place. *(assuming number is 7,518.783)*

15. 750.32

16. 1.25

17. −0.01

18. 53,910

19. 10

20. $ \frac{100}{3} $ or 33.333...

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⚠️ Note: Some answers depend on assumptions due to missing visual cues (like underlined digits). If you can provide clarification on which digits are underlined, I can adjust accordingly.

Let me know if you'd like these formatted differently!