Multiplication Puzzles

Solve the multiplication puzzles mentally. Fill in the blank boxes.

Examples:

Question 1.

Explanation:
First multiply 8 with 70 and 400 and write in boxes in the first row and multiply 9 with 70 and 400 and write in boxes in the second row.

Question 2.

Explanation:
First multiply 80 with 5 and 7 and write in boxes in the first row and multiply 600 with 5 and 7 and write in boxes in the second row.

Question 3.

Explanation:
First multiply 50 with 9 and 4 and write in boxes in the first row and multiply 7000 with 9 and 4 and write in boxes in the second row.

Question 4.

Explanation:
First multiply 7 with 500 and 600 and write in boxes in the first row and multiply 4 with 500 and 600 and write in boxes in the second row.

Question 5.

Explanation:
First multiply 30 with 9 and 8 and write in boxes in the first row and multiply 700 with 9 and 8 and write in boxes in the second row.

Question 6.

Explanation:
First multiply 9 with 400 and 500 and write in boxes in the first row and multiply 20 with 400 and 500 and write in boxes in the second row.

Make up and solve some puzzles of your own.

Question 7.

Explanation:
First multiply 5 with 20 and 30 and write in boxes in the first row and multiply 7 with 20 and 30 and write in boxes in the second row.

Question 8.

Explanation:
First multiply 200 with 8 and 9 and write in boxes in the first row and multiply 400 with 8 and 9 and write in boxes in the second row.

Practice

Question 9.
321 + 869 = ___

Explanation:
The sum of 321 and 869 is 1190.

Question 10.
5,401 – 752 = ___

Explanation:
The difference of 5401 and 752 is 4649.

Question 11.
4,568 + 8,735 = ___

Explanation:
The sum of 4568 and 8735 is 13303.

Question 12.
9,156 – 4,584 = ___

Explanation:
The difference of 9156 and 4584 is 4572.

Write an estimate and show your thinking. Solve using a calculator. Check to see that your answer is reasonable.

Question 1.
Alice sleeps an average of 9 hours per night. A cat can sleep up to 20 hours per day. About how many more hours does a cat sleep in 1 month than Alice? ___________
Estimate: _________
Answer: Cat sleeps 420 hours than Alice in a month

Explanation:
Given:
Number of hours Alice sleeps per night = 9 hours
Number of hours Cat sleeps per night = 20 hours
Let
The total number of hours for which Alice Sleeps in one month be x
The total number of hours for which Cat sleeps in one month be y
Number of hours for which Alice Sleeps in one month
X = number of days in a month × Number of hours Alice sleeps per night
X = 30 × 9
X = 180 Hours
Number of hours for which Cat Sleeps in one month
y= number of days in a month × Number of hours cat sleeps per night
y = 30 × 20
y = 600 Hours
Now,
= y – x
=600 – 180
=420 hours

Question 2.
Koalas sleep about 22 hours a day. Pandas sleep about 10 hours a day. About how many more hours does a typical koala sleep in 1 year than a typical panda?
Estimate: ______
Given,
Koalas sleep about 22 hours a day. Pandas sleep about 10 hours a day.
Estimate: (20 × 400) – (10 × 400) = 8000 – 4000 = 4000
(22 × 365) – (10 × 365) = 8030- 3650= 4380 more hours per year

Question 3.
There are 30 Major League Baseball (MLB) teams and 32 National Football League (NFL) teams. The expanded roster for MLB teams is 40 players and it is 53 for NFL teams. How many more players are in the NFL than in the MLB?
Estimate: ______
Given that,
There are 30 Major League Baseball (MLB) teams and 32 National Football League (NFL) teams.
The expanded roster for MLB teams is 40 players and it is 53 for NFL teams.
30 × 50 = 1500
30 × 40 = 1200
1500 – 1200 = 300
32 × 53 = 1696 – 1200 = 496 more players

Practice

Round to the nearest thousand.

Question 4.
45,493 ________
45,000

Explanation:
Compare the last 3 digits.493 is less than 500.So, 45,493 is rounded to the previous thousand that is 45,000.

Question 5.
1,409,836 ________
1,410,000

Explanation:
Compare the last 3 digits.836 is more than 500. So, 1,409,836 is rounded to the next thousand that is 1,410,000.

Partitioning Rectangles

Solve the multiplication problems by partitioning a rectangle. Then add each part of the rectangle to get the product.

Question 1.
4 ∗ 35 = ___

Explanation:
I solved the multiplication problems by partitioning a rectangle. Then adding each part of the rectangle to get the product.

Question 2.
6 ∗ 83 = ___

Explanation:
I solved the multiplication problems by partitioning a rectangle. Then adding each part of the rectangle to get the product.

Question 3.
9 ∗ 49 = ___

Explanation:
I solved the multiplication problems by partitioning a rectangle. Then adding each part of the rectangle to get the product.

Practice

Question 4.
9,289 + 1,476 = ___

Explanation:
The sum of 9289 and 1476 is 10765.

Question 5.
6,503 – 3,547 = ___

Explanation:
The difference of 6503 and 3547 is 2956.

Question 6.
5,619 + 5,999 = ____

Explanation:
The sum of 5619 and 5999 is 11618.

Question 7.
5,005 – 2,446 = _____

Explanation:
The difference of 5005 and 2446 is 2559.

Converting Liquid Measures

Complete the table.

Question 1.

Explanation:
As we know 1 liter is equal to 1000 milliliters so 8l is 8000ml, 15l is 15000ml, 20l is 20000ml and 25l is 25000ml.

Question 2.
Mrs. Wong’s students kept track of how much water they used to water the classroom plants. The first week they used 24 liters, and the second week they used 17 liters. How many more milliliters did they use the first week than the second?

Explanation:
Mrs. Wong’s students kept track of how much water they used to water the classroom plants.
The first week they used 24 liters, and the second week they used 17 liters.
24 – 17 = 7 liters
Now convert from liters to milliliters
1 liter = 1000 ml
7 liters = 7 × 1000 = 7000ml

Question 3.
My fish tank holds 64 liters of water. My neighbor’s tank holds 58 liters of water. How many milliliters is that combined?

Explanation:
Given,
My fish tank holds 64 liters of water. My neighbor’s tank holds 58 liters of water.
64 + 58 = 122 liters
Now convert from liters to milliliters
1 liter = 1000 ml
122 liters = 122 × 1000 = 122000ml

Question 4.
Mrs. Reyes filled her kiddie pool with 83 liters of water. Her children added 2,000 mL of water to the pool. How many liters of water are in the pool now?

Explanation:
Given,
Mrs. Reyes filled her kiddie pool with 83 liters of water.
Her children added 2,000 mL of water to the pool.
Now convert from liters to milliliters
1 liter = 1000 ml
2 liters = 2 × 1000 = 2000ml
83 + 2 = 85 liters
Thus there are 85 liters of water are in the pool now.

Practice

Question 5.
4,638 + 9,807 = ___

Explanation:
The sum of 4638 and 9807 is 14445.

Question 6.
7,322 – 3,741 = ____

Explanation:
The difference of 7322 and 3741 is 3581.

Question 7.
55,812 + 6,529 = ___

Explanation:
The sum of 55812 and 6529 is 62341.

Question 8.
98,001 – 7,443 = ____

Explanation:
The difference of 98001 and 7443 is 90558.

Using Multiplication

Ms. Patel wants to keep her classroom calculators in a box that is 25 centimeters long, 15 centimeters wide, and 5 centimeters tall. The calculators measure 12 centimeters long, 7 centimeters wide, and 1 centimeter tall. How many calculators can Ms. Patel fit in the box?

Question 1.
Solve this problem. Show or explain how you solved the problem.

Four calculators fit in a layer.
The box is 5 cm tall, so there are 5 layers of calculators.
The box fits 4 containers × 5 = 20 calculators in all

Question 2.
I drew a picture of the bottom layer. I made sure that all of the numbers in the problem and the parts of the picture were labelled to show what is meant in the problem
The height of the box is 5 cm and there are 4 stacks
4 × 5 = 20

Practice

Sketch a rectangle or use partial products to solve.

Question 3.
27 ∗ 4 = ____

Explanation:
The product of 27 and 4 is 108.

Question 4.
48 ∗ 9 = ____

Explanation:
The product of 48 and 9 is 432.

Question 5.
43 ∗ 3 = ___

Explanation:
The product of 43 and 3 is 129.

Question 6.
81 ∗ 5 = ___

Explanation:
The product of 81 and 5 is 405.

Multiplying in Parts

In the example, a rectangle was drawn to represent the problem. Then partial-products multiplication was used to record the work in a simpler way. Use partial-products multiplication to solve Problems 1 and 2.

Example:

Question 1.

Explanation:
The product of 48 and 3 is 144.

Question 2.

Explanation:
The product of 653 and 8 is 5224.

Practice

Write the numbers in expanded form.

Question 3.
905,603 _____________
9(100,000s)+5(1000s)+6(100s)+3(1s).

Explanation:
I wrote the expanded form of the above number 905,603.

Question 4.
589,043 _________
5(100,000s)+8(10,000s)+9(1000s)+4(10s)+3(1s).

Explanation:
I wrote the expanded form of the above number 589,043.

Question 5.
2,599,002 ________
2(1,000,000s)+5(100,000s)+9(10,000s)+9(1,000s)+2(1s).

Explanation:
I wrote the expanded form of the above number 2,599,002.

Question 6.
8,003,952 _________
8(1,000,000s)+3(1,000s)+9(100s)+5(10s)+2(1s).

Explanation:
I wrote the expanded form of the above number 8,003,952.

Using a Measurement Scale

Question 1.
Fill in the blanks on the measurement scale.

Complete the two-column tables.

Explanation:
I filled the blanks on the measurement scale in kilograms and grams.
25kg is equals to 25000g, 50kg is 50000g, 75kg is 75000g and 100kg is 100000g.

Question 2.

Explanation:
I filled the blanks in the above table with their equal amounts of grams and kilograms.
k kg is 6000g, 14kg is 14000g, 27kg is 27000g and 101kg is 101000g.

Question 3.

Explanation:
I filled the blanks in the above table with their equal amounts of grams and kilograms.
237kg is 237000g, 98kg is 98000g, 485kg is 485000g and 920kg is 920000g.

Question 4.
Find three items in your home that have the mass listed in grams or kilograms. Be sure to tell whether the mass is kilograms or grams.

Explanation:
I selected three items which i see in my house they are sugar, bread and butter and i filled the table with the names of the items and their weights in grams and kilograms.

Question 5.
Among other foods, a giraffe in a zoo eats 4 kg of plant pellets and 5 kg of hay each day. How many grams of these foods does a giraffe eat in one week?

Explanation:
The giraffe in zoo eats 4 kg of plant pellets and 5 kg of hay each day.
1 kg is equal to 1000g.
It means 4000g of plant pellets and 5000g of hay in a day so multiply the number of grams with 7 that is number of days in a week.
4000×7=28000, 5000×7=35000
Add the products 28000 and 35000 = 63000
Therefore 63000 grams of these foods a giraffe eat in one week.

Practice

Question 6.
52 ∗ 7 = ___

Explanation:
The product of 52 and 7 is 364.

Question 7.
99 ∗ 4 = ___

Explanation:
The product of 99 and 4 is 396.

Question 8.
61 ∗ 8 = ___

Explanation:
The product of 61 and 8 is 488.

Question 9.
49 ∗ 6 = ____

Explanation:
The product of 49 and 6 is 294.

Money Number Stories

Family Note Today your child solved multistep number stories involving multiplication, addition, and subtraction of money amounts. Have your child explain a plan for solving each of the following problems and then solve it.

Mr. Russo is buying equipment for his baseball team. Use the table to the right to answer questions about his purchases.

Question 1.
Mr. Russo needs 9 helmets and 8 gloves. How much will they cost in all?
Answer: $____ Answer: Question 2. Mr. Russo wants to buy 6 bats for his team. How much more would it cost for him to buy 6 metal bats than 6 wooden bats? Answer: Mr. Russo wants to buy 6 bats for his team. The cost of wooden bat is$49
The cost of metal bat is $74 49 × 6 = 294 74 × 6 = 444 444 – 294 = 150 It would cost$150 for him to buy 6 metal bats than 6 wooden bats.

Question 3.
Mr. Russo buys 5 wooden bats and gives the cashier $300. How much change does he get? Answer:$55

Explanation:
The cost of wooden bat is $49 49 × 5 = 245 300 – 245 = 55 Question 4. If the cashier only has$10 and $1 bills, what are two ways he could make Mr. Russo’s change? Answer: 5$10 and 5 $1 or he can give$60 and take \$5 from Russo.

Practice

List the factors for the following numbers:

Question 5.
21 ___ ___ __ ___
1,3,7,21 are the factors of 21.

Question 6.
40 __ ___ __ ___
1,2,4,5,8,10,20,40 are the factors of 40.

Question 7.
36 __ __ __ ___
1,2.3,4,6,9,12,18,36 are the factors of 36.

Question 8.
45 __ __ __ __
1,5,9,45 are the factors of 45.

Practicing Partial-Products Multiplication

Solve using partial-products multiplication.

Question 1.
46 ∗ 38 = ____

Explanation:
The product of 46 and 38 is 1748.

Question 2.

Explanation:
The product of 65 and 32 is 2080.

Question 3.
Donnie and Raj went apple picking at an orchard that had 65 rows of trees. Each row had 22 trees in it. How many trees were in the orchard?
Number model with unknown: _____

Explanation:
Donnie and Raj went apple picking at an orchard that had 65 rows of trees. Each row had 22 trees in it, Multiply 65 and 22 to find the number of tress.
The product of 65 and 22 is 1430.
There are 1430 trees in the orchard.

Question 4.
A new apartment building has 33 floors, with 24 apartments on each floor. How many apartments are in the building?
Number model with unknown:

Explanation:
A new apartment building has 33 floors, with 24 apartments on each floor, Multiply 33 and 24 to find the number of apartments in the buliding.
The product of 33 and 24 is 792.
There are 792 apartments in the building.

Practice

Question 5.
37 ∗ 5 = ___

Explanation:
The product of 37 and 5 is 185.

Question 6.
27 ∗ 6 = ___

Explanation:
The product of 27 and 6 is 162.

Question 7.
332 ∗ 6 = ____

Explanation:
The product of 332 and 6 is 1992.

Question 8.
2,958 ∗ 7 = ____

Explanation:
The product of 2958 and 7 is 20706.

Extended Multiplication Facts

Solve mentally.

Question 1.
6 ∗ 7 = ___
6 * 7 = 42

Explanation:
The product of 6 and 7 is 42.

6 ∗ 70 = ___
6 * 70 = 420

Explanation:
The product of 6 and 70 is 420.

60 ∗ 7 = ___
60 * 7 = 420

Explanation:
The product of 60 and 7 is 420.

60 ∗ 70 = ___
60 * 70 = 4200

Explanation:
The product of 60 and 70 is 4200.

600 ∗ 7 = ___
600 * 7 = 4200

Explanation:
The product of 600 and 7 is 4200.

60 ∗ 700 = ___
60 * 700 = 42000

Explanation:
The product of 60 and 700 is 42000.

Question 2.
5 ∗ 6 = ___
5 * 6 = 30

Explanation:
The product of 5 and 6 is 30.

5 ∗ 60 = ___
5 * 60 = 300

Explanation:
The product of 5 and 60 is 300.

50 ∗ 6 = ___
50 * 6 = 300

Explanation:
The product of 50 and 6 is 300.

50 ∗ 60 = ___
50 * 60 = 3000

Explanation:
The product of 50 and 60 is 3000.

500 ∗ 6 = ___
500 * 6 = 3000

Explanation:
The product of 500 and 6 is 3000.

50 ∗ 600 = ___
50 * 600 = 30000

Explanation:
The product of 50 and 600 is 30000.

Question 3.
4 ∗ 8 = ___
4 * 8 = 32

Explanation:
The product of 4 and 8 is 32.

4 ∗ 80 = ___
4 * 80 = 320

Explanation:
The product of 4 and 80 is 320.

40 ∗ 8 = ___
40 * 8 = 32

Explanation:
The product of 40 and 8 is 320.

40 ∗ 80 = ___
40 * 80 = 3200

Explanation:
The product of 40 and 80 is 3200.

400 ∗ 8 = ___
400 * 8 = 3200

Explanation:
The product of 400 and 8 is 3200.

40 ∗ 800 = ___
40 * 800 = 32000

Explanation:
The product of 40 and 800 is 32000.

Question 4.
5 ∗ ___ = 15
5 * 3 = 15

Explanation:
The product of 5 and 3 is 15.

30 ∗ ___ = 150
30 * 5 = 150

Explanation:
The product of 30 and 5 is 150.

30 ∗ ___ = 1,500
30 * 50 = 1500

Explanation:
The product of 30 and 50 is 1500.

___ ∗ 50 = 150
3 * 50 = 150

Explanation:
The product of 3 and 50 is 150.

___ ∗ 500 = 1,500
3 * 500 = 1500

Explanation:
The product of 3 and 500 is 1500.

30 ∗ ___ = 15,000
30 * 500 = 15000

Explanation:
The product of 30 and 500 is 15000.

Question 5.
54 ___ is times as many as 9.
6

Explanation:
54 is 6 times as many as 9.

540 is ___ times as many as 90.
6

Explanation:
540 is 6 times as many as 90.

5,400 is ___ times as many as 90.
60

Explanation:
5400 is 60 times as many as 90.

540 is 60 times as many as ___.
9

Explanation:
540 is 60 times as many as 9.

5,400 is 6 times as many as ___.
900

Explanation:
5400 is 6 times as many as 900.

54,000 is 6 times as many as ___.
9000

Explanation:
54000 is 6 times as many as 9000.

Practice

Question 6.
6,419 + 7,809 = ___

Explanation:
The sum of 6419 and 7809 is 14228.

Question 7.
8,045 – 5,906 = ____

Explanation:
The difference of 8045 and 5906 is 2139.

Question 8.
76,543 + 84,086 = ___

Explanation:
The sum of 76543 and 84086 is 160629.

Question 9.
65,409 – 32,777 = ___

Explanation:
The difference of 65409 and 32777 is 32632.

Finding the Area

Question 1.
Find the area.
Equation: _____

Explanation:
Multiply 27 and 18 to find the area of the given rectangle
Equation:27 * 18 = 486

Question 2.
A tool bench is 35 inches long and 19 inches wide. How many square inches of the basement floor does it cover?
Equation: ___

Explanation:
Multiply 35 and 19 to find the number of square inches that the basement floor covers
Equation:35 * 19 = 665

Question 3.
Find the area.

Equations: _________

Explanation:
Multiply 30 and 100, 20 and 20 and both the products found to know the area of the given shape.
Equations:30 * 100 = 3000, 20 * 20 = 400, 3000+400=3400.

Practice

List all of the factors for the numbers below.

Question 4.
48 ________
1,2,4,6,8,12,24,48 are the factors of 48.

Question 5.
62 _________
1,2,31,62 are the factors of 62.

Question 6.
63 ______
1,7,9,63 are the factors of 63.

Question 7.
55 ______
1,5,11,55 are the factors of 55.

Multistep Multiplication Number Stories

Write estimates and number models for each problem. Then solve.

Question 1.
Rosalie is collecting stickers for a scrapbook. She collected 8 stickers per day for 2 weeks and then collected 5 stickers per day for 2 weeks.
How many stickers has Rosalie collected?
Estimate: _____
Number models with unknowns:

Estimate:
(10 × 7) × 2 = 140
(5 × 7) × 2 = 70
140 + 70 = 210 stickers
(8 × 7) × 2 = x
(5 × 7) × 2 = y
112 + 70 = s
s = 182

Question 2.
Rashaad’s sister gives him 2 packs of baseball cards per month. Each pack has 11 cards. She gives him 3 extra packs for his birthday. How many cards does Rashaad get in a year?
Estimate: ______
Number models with unknowns:

Estimate:
2 × 10 × 12 = 240
3 × 10 = 30
240 + 30 = 270 cards

2 × 11 × 12 = a
3 × 11 = b
264 + 33 = c
c = 297 cards

Answer: Yes, my estimate is less than my actual answer because I rounded down from 11 to 10 cards.

Practice

Name all the factor pairs.

Question 3.
50 ______
1 and 50, 2 and 25, 50 and 10 are the pair factors of 50.

Question 4.
72 ______
1 and 72, 2 and 36, 3 and 24, 4 and 18, 6 and 12, 8 and 9 are the pair factors of 72.

Question 5.
85 _____
1 and 85, 5 and 17 are the pair factors of 85.

Question 6.
90 ______
1 and 90, 2 and 45, 3 and 30, 5 and 18, 6 and 15, 9 and 10 are the pair factors of 90.

Lattice Multiplication

Use the lattice method to find the products.

Question 1.
8 ∗ 67 = ___

Explanation:
The product of 5 and 67 is 536.

Question 2.
7 ∗ 836 = __

Explanation:
The product of 836 and 7 is 5852.

Question 3.
6 ∗ 531 = __

Explanation:
The product of 531 and 6 is 3186.

Question 4.
44 ∗ 58 = ___

Explanation:
The product of 44 and 58 is 2552.

Question 5.
84 ∗ 78 = __

Explanation:
The product of 84 and 78 is 6552.

Practice

Question 6.
77 ∗ 8 = __

Explanation:
The product of 77 and 8 is 66.

Question 7.1
49 ∗ 2 = __

Explanation:
The product of 49 and 2 is 98.

Question 8.
89 ∗ 4 = __