Math Worksheets (Set of 5 Books) - Free Printable

Let's solve the problems in Worksheet - 17 step by step, focusing on the properties of multiplication, especially with 10, 100, and 1000.

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Part 1: Fill in the blanks

We’ll use properties like:
- Commutative Property: $ a \times b = b \times a $
- Associative Property: $ (a \times b) \times c = a \times (b \times c) $
- Distributive Property: $ a \times (b + c) = a \times b + a \times c $
- Multiplying by 10, 100, 1000: Add zeros accordingly
- Multiplying by 1: $ a \times 1 = a $
- Multiplying by 0: $ a \times 0 = 0 $

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#### 1. a) $ 4312 \times 4119 = 4119 \times \boxed{?} $

Using commutative property:
$$
4312 \times 4119 = 4119 \times 4312
$$
✔ Answer: 4312

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#### b) $ ? \times 7136 = 7136 \times 2108 $

Again, commutative property:
$$
2108 \times 7136 = 7136 \times 2108
$$
So the missing number is 2108

✔ Answer: 2108

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#### c) $ ? \times 3131 = 3232 \times 2482 $

This is not about commutativity unless both sides are equal. But here we need to find what number multiplied by 3131 gives the same result as $ 3232 \times 2482 $. That would be:

$$
\text{Let } x \times 3131 = 3232 \times 2482
\Rightarrow x = \frac{3232 \times 2482}{3131}
$$

But this seems messy. Wait — perhaps it's testing associative or distributive? Let’s look at other parts.

Wait — maybe it's just asking for commutative again?

But $ x \times 3131 = 3232 \times 2482 $ → This implies $ x = 3232 \times 2482 / 3131 $

But that’s not an integer likely. Maybe it's a typo or meant to be symmetric?

Wait — let’s check if 3232 × 2482 = 2482 × 3232, which is true, but not helpful.

Alternatively, could it be distributive?

Wait — no clear pattern. Perhaps the blank is just 3232, but then:

$ 3232 \times 3131 = 3232 \times 2482 $? Only if $ 3131 = 2482 $, which is false.

So this must be a mistake — or perhaps it's supposed to be:

Maybe the equation is meant to be:

$ a \times b = c \times d $, and we're to fill one blank.

But unless there's a specific property, we can't assume equality without calculation.

Wait — perhaps it's asking us to apply distributive property?

But no — it's written as:

$ ? \times 3131 = 3232 \times 2482 $

So unless the two products are equal, we can’t proceed.

But they are not equal.

Let me compute approximate values:

- $ 3232 \times 2482 \approx 3200 \times 2500 = 8,000,000 $
- $ 3131 \times x = 8,000,000 \Rightarrow x \approx 2555 $

But not nice number.

Wait — perhaps it's a typo? Or maybe it's meant to be:

Is it possible that the question is asking to use commutative property?

But no — left side has 3131, right side has 2482.

Unless it's:

$ 3232 \times 3131 = 3131 \times 3232 $ — but that’s not what it says.

Wait — maybe it's not about commutativity.

Alternatively, perhaps it's distributive?

But no structure.

Wait — maybe the problem is miswritten.

But let’s move on and come back.

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#### d) $ 3427 \times 5162 = 5862 \times [3427 \times 5162] $

This doesn't make sense.

Left: $ 3427 \times 5162 $

Right: $ 5862 \times (3427 \times 5162) $

So unless $ 5862 = 1 $, this is not equal.

So this can't be correct.

Wait — perhaps it's:

$ 3427 \times 5162 = 5862 \times [?] $

Then $ ? = \frac{3427 \times 5162}{5862} $

Still messy.

Wait — maybe it's associative?

But the format is strange.

Wait — perhaps it's:

$ (a \times b) = c \times (a \times b) $ — only if $ c=1 $

No.

Wait — maybe the bracketed part is a product?

Look:
$ 3427 \times 5162 = 5862 \times [3427 \times 5162] $

That would mean:

$ A = 5862 \times A $ → only if $ A = 0 $, which it isn't.

So this is incorrect.

Wait — perhaps it's a typo and should be:

$ 3427 \times 5162 = [3427 \times 5862] \times ? $

But still unclear.

Wait — perhaps the right-hand side is $ 5862 \times (3427 \times 5162) $, but that’s way bigger.

So something is wrong.

Wait — maybe it's:

$ 3427 \times 5162 = [3427 \times 5862] \times ? $

But no.

Alternatively, maybe it's distributive?

Wait — let's skip and go to next.

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#### e) $ [7672 \times 5868] \times 3213 = [5868 \times 3213] \times ? $

Use associative property:

Left: $ (7672 \times 5868) \times 3213 $

Right: $ (5868 \times 3213) \times ? $

We want to match the left side.

Note: $ (a \times b) \times c = a \times (b \times c) $

So:

$ (7672 \times 5868) \times 3213 = 7672 \times (5868 \times 3213) $

So compare to $ (5868 \times 3213) \times ? $

So $ (5868 \times 3213) \times ? = 7672 \times (5868 \times 3213) $

Therefore, $ ? = 7672 $

✔ Answer: 7672

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#### f) $ [1528 + 4642] \times 1628 = 1528 \times ? + 5991 \times ? $

First, simplify left side:

$ (1528 + 4642) \times 1628 = 6170 \times 1628 $

Now right side: $ 1528 \times ? + 5991 \times ? $

Wait — but 5991 ≠ 4642, so something’s off.

Wait — maybe typo?

Wait — perhaps it's:

$ (1528 + 4642) \times 1628 = 1528 \times 1628 + 4642 \times 1628 $

But the second term is written as $ 5991 \times ? $

But 5991 ≠ 4642.

Wait — unless it's distributive with different numbers.

Wait — maybe the bracket is wrong.

Wait — let's read carefully:

> $ [1528 + 4642] \times 1628 = 1528 \times ? + 5991 \times ? $

But 1528 + 4642 = 6170

So LHS = 6170 × 1628

RHS = 1528×? + 5991×?

But unless ? is same, and 1528 + 5991 = 7519 ≠ 6170, so no.

Wait — perhaps it's a typo and should be 4642 instead of 5991?

Because:

$ (1528 + 4642) \times 1628 = 1528 \times 1628 + 4642 \times 1628 $

So both blanks should be 1628

But here it says: $ 1528 \times ? + 5991 \times ? $

So unless 5991 is a typo for 4642, it’s invalid.

But maybe it's not distributive?

Wait — another possibility: maybe the second term is $ 5991 \times ? $, but that doesn’t help.

Wait — perhaps the expression is:

$ (1528 + 4642) \times 1628 = 1528 \times 1628 + 4642 \times 1628 $

But in the question, it's written as $ 1528 \times ? + 5991 \times ? $

So unless 5991 is a typo, it’s incorrect.

Wait — perhaps it's $ 1528 \times ? + 4642 \times ? $, and 5991 is a typo?

But 5991 is close to 6170? No.

Wait — 1528 + 4642 = 6170

And 5991 is less than that.

Alternatively, maybe it's:

$ (1528 + 4642) \times 1628 = 1528 \times 1628 + 4642 \times 1628 $

So both blanks are 1628

But in the question, it's written as $ 5991 \times ? $, which is confusing.

Wait — maybe it's not 5991, but 4642? Typo?

But let's suppose it's a typo and should be 4642.

Then answer is: both blanks = 1628

But as written, it’s 5991, which makes no sense.

Wait — maybe the left side is $ (1528 + 4642) \times 1628 $, and right is $ 1528 \times 1628 + 5991 \times ? $

Then:

LHS = 6170 × 1628

RHS = 1528 × 1628 + 5991 × ?

Set equal:

$ 6170 \times 1628 = 1528 \times 1628 + 5991 \times ? $

→ $ (6170 - 1528) \times 1628 = 5991 \times ? $

→ $ 4642 \times 1628 = 5991 \times ? $

→ $ ? = \frac{4642 \times 1628}{5991} $

Not nice.

So probably typo — likely should be 4642 instead of 5991

So assuming typo, and it's:

$ (1528 + 4642) \times 1628 = 1528 \times ? + 4642 \times ? $

Then by distributive property, both blanks are 1628

✔ Answer: 1628, 1628

But since it says 5991, maybe it's different.

Wait — perhaps the expression is:

$ [1528 + 4642] \times 1628 = 1528 \times ? + 5991 \times ? $

But 1528 + 4642 = 6170

So unless the right side is $ 1528 \times 1628 + 4642 \times 1628 $, it won't work.

So unless 5991 is a typo for 4642, it's invalid.

But let's assume typo, and proceed.

So both blanks = 1628

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#### g) $ ? \times 4126] + 2563 = 3139 \times [? \times 5991] $

This is very messy.

Left: $ ? \times 4126 + 2563 $

Right: $ 3139 \times (? \times 5991) $

So unless ? is zero, not equal.

Wait — perhaps it's:

$ [? \times 4126] + 2563 = 3139 \times [? \times 5991] $

Still hard.

But maybe it's distributive?

Unlikely.

Perhaps it's a typo.

Let’s skip and come back.

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#### h) $ 4616 \times 1 = \boxed{?} $

Any number × 1 = itself

✔ Answer: 4616

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#### i) $ ? \times 2725 = 2725 $

So $ x \times 2725 = 2725 $ → $ x = 1 $

✔ Answer: 1

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#### j) $ 6192 \times 0 = \boxed{?} $

Any number × 0 = 0

✔ Answer: 0

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#### k) $ 2396 \times 0 = \boxed{?} $

Same → 0

✔ Answer: 0

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#### l) $ 1 \times 4116 = \boxed{?} $

$ 1 \times a = a $

✔ Answer: 4116

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#### m) $ ? \times 734 = 0 $

Only if multiplier is 0 → $ ? = 0 $

✔ Answer: 0

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#### n) $ ? \times 4619 = 0 $

Same → $ ? = 0 $

✔ Answer: 0

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#### o) $ 2796 \times 0 = \boxed{?} $

→ 0

✔ Answer: 0

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#### p) $ 3538 \times \boxed{?} = 0 $

→ ? = 0

✔ Answer: 0

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#### q) $ 23 \times 126 = \boxed{?} $

Compute:
$ 23 \times 126 $

Break down:

$ 23 \times 100 = 2300 $
$ 23 \times 20 = 460 $
$ 23 \times 6 = 138 $

Total: $ 2300 + 460 = 2760 + 138 = 2898 $

✔ Answer: 2898

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#### r) $ 143 \times 82 + 1 \times 0 = \boxed{?} $

First, $ 1 \times 0 = 0 $

So $ 143 \times 82 + 0 = 143 \times 82 $

Compute:

$ 143 \times 80 = 11,440 $
$ 143 \times 2 = 286 $
Total: $ 11,440 + 286 = 11,726 $

✔ Answer: 11,726

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Part 2: Word Problems

#### a) Abha has 627 pouches. Each pouch has 10 pens. How many pens in all does she have?

$ 627 \times 10 = 6270 $

✔ Answer: 6270 pens

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#### b) $ 17 \times 100 = \boxed{?} $

$ 17 \times 100 = 1700 $

✔ Answer: 1700

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#### c) $ 22 \times 100 = \boxed{?} $

$ 22 \times 100 = 2200 $

✔ Answer: 2200

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#### d) A packet has 100 pins. How many pins will 29 such packets have?

$ 29 \times 100 = 2900 $

✔ Answer: 2900 pins

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#### e) $ 6 \times 1000 = \boxed{?} $

$ 6 \times 1000 = 6000 $

✔ Answer: 6000

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#### f) $ 3 \times 1000 = \boxed{?} $

$ 3 \times 1000 = 3000 $

✔ Answer: 3000

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#### g) A train can carry 1000 passengers in a trip. How many passengers can it carry in 5 trips?

$ 5 \times 1000 = 5000 $

✔ Answer: 5000 passengers

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Now Revisit Problem 1c and 1d — Likely Typos

Let’s re-express:

#### 1c) $ ? \times 3131 = 3232 \times 2482 $

If we assume commutative property, then:

$ 3232 \times 2482 = 2482 \times 3232 $

But that doesn’t help.

Unless the equation is:

$ 3232 \times 3131 = 3131 \times 3232 $ — but not what’s written.

Wait — maybe it’s meant to be:

$ 3232 \times 2482 = 2482 \times 3232 $ — but that’s trivial.

But the blank is on left: $ ? \times 3131 = 3232 \times 2482 $

So $ ? = \frac{3232 \times 2482}{3131} $

Let’s compute:

First, approximate:

- $ 3232 \times 2482 \approx 3200 \times 2500 = 8,000,000 $
- $ 3131 \approx 3100 $
- $ ? \approx 8,000,000 / 3100 \approx 2580 $

Not nice.

Wait — perhaps it’s distributive?

Or maybe it’s a typo and should be:

$ 3232 \times 3131 = 3131 \times ? $ → then ? = 3232

Yes! That makes sense.

So likely, the equation is:

$ 3232 \times 3131 = 3131 \times ? $

Then $ ? = 3232 $

But it’s written as $ ? \times 3131 = 3232 \times 2482 $

So unless 2482 is typo for 3232, it’s invalid.

Wait — maybe it’s:

$ ? \times 3131 = 3232 \times 3131 $ → then ? = 3232

Ah! So likely 2482 is a typo, should be 3131

So corrected: $ ? \times 3131 = 3232 \times 3131 $ → ? = 3232

✔ Answer: 3232

Similarly, 1d) $ 3427 \times 5162 = 5862 \times [3427 \times 5162] $

This would imply $ A = 5862 \times A $ → only if A=0, impossible.

So likely typo.

Maybe it's:

$ 3427 \times 5162 = [3427 \times 5862] \times ? $

Then $ ? = \frac{5162}{5862} $ — not integer.

Alternatively, maybe it's:

$ 3427 \times 5162 = 5162 \times 3427 $ — commutative → then the blank is 3427

But it says $ 5862 \times [3427 \times 5162] $ — no.

Wait — perhaps it's:

$ 3427 \times 5162 = 5862 \times ? $

Then $ ? = \frac{3427 \times 5162}{5862} $

Still messy.

Alternatively, maybe it's associative:

$ (a \times b) = c \times (a \times b) $ — only if c=1

No.

So likely typo.

But given the context, most likely 1c and 1d have typos.

But based on common patterns, let’s assume:

- 1c) $ ? \times 3131 = 3232 \times 3131 $ → ? = 3232
- 1d) $ 3427 \times 5162 = 5162 \times 3427 $ → but written as $ 5862 \times [3427 \times 5162] $ — not matching.

Wait — maybe it's:

$ 3427 \times 5162 = [3427 \times 5862] \times ? $

No.

Another idea: maybe it's:

$ 3427 \times 5162 = 5862 \times [3427 \times 5162] $ → divide both sides:

$ 1 = 5862 $ → false.

So definitely typo.

Given time, and based on standard worksheets, likely intended:

- 1c) $ ? \times 3131 = 3232 \times 3131 $ → ? = 3232
- 1d) $ 3427 \times 5162 = 5162 \times 3427 $ → but blank is not needed

But as written, it's unclear.

But since 1e and others work, we'll go with best guesses.

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✔ Final Answers:

#### 1. Fill in the blanks

a) 4312
b) 2108
c) 3232 *(assuming typo: 3232 × 3131 = 3131 × ?)*
d) 3427 *(if it's 3427 × 5162 = 5162 × 3427, but written poorly)*
e) 7672
f) 1628, 1628 *(assuming 5991 is typo for 4642)*
g) ??? *(too ambiguous — skip or assume typo)*
h) 4616
i) 1
j) 0
k) 0
l) 4116
m) 0
n) 0
o) 0
p) 0
q) 2898
r) 11,726

#### 2. Word Problems

a) 6270 pens
b) 1700
c) 2200
d) 2900 pins
e) 6000
f) 3000
g) 5000 passengers

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✔ Summary of Key Concepts Used:

- Commutative Property: $ a \times b = b \times a $
- Multiplying by 1: $ a \times 1 = a $
- Multiplying by 0: $ a \times 0 = 0 $
- Distributive Property: $ a \times (b + c) = a \times b + a \times c $
- Multiplying by 10, 100, 1000: Add 1, 2, or 3 zeros respectively

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Let me know if you'd like a cleaned-up version of the worksheet with corrections!