Question 1
Tom has 3 pencils. Sarah has 4 times as many pencils as Tom. How many pencils does Sarah have?
Tom has 3 pencils. Sarah has 4 times as many pencils as Tom. How many pencils does Sarah have?
💡Explanation:
4 times as many means multiplication. 3 multiplied by 4 is 12.
4 times as many means multiplication. 3 multiplied by 4 is 12.
Question 2
An additive comparison uses addition or subtraction, while a multiplicative comparison uses or division.
An additive comparison uses addition or subtraction, while a multiplicative comparison uses or division.
💡Explanation:
Multiplicative comparisons are based on multiplying or dividing by a scale factor.
Multiplicative comparisons are based on multiplying or dividing by a scale factor.
Question 3
Mia has 5 stickers. Leo has 3 more stickers than Mia. How many stickers does Leo have?
Mia has 5 stickers. Leo has 3 more stickers than Mia. How many stickers does Leo have?
💡Explanation:
'3 more than' indicates an additive comparison. 5 plus 3 equals 8.
'3 more than' indicates an additive comparison. 5 plus 3 equals 8.
Question 4
The phrase 'times as many' is a clue for a comparison.
The phrase 'times as many' is a clue for a comparison.
💡Explanation:
'Times as many' means you are scaling a number, which requires multiplication.
'Times as many' means you are scaling a number, which requires multiplication.
Question 5
A book costs $4. A video game costs 5 times as much as the book. How much does the video game cost?
A book costs $4. A video game costs 5 times as much as the book. How much does the video game cost?
💡Explanation:
'5 times as much' means you multiply the cost of the book ($4) by 5, giving $20.
'5 times as much' means you multiply the cost of the book ($4) by 5, giving $20.
Question 6
If Ben has 6 marbles and Dan has 2 more marbles than Ben, Dan has marbles.
If Ben has 6 marbles and Dan has 2 more marbles than Ben, Dan has marbles.
💡Explanation:
Adding 2 to Ben's 6 marbles gives an additive comparison total of 8.
Adding 2 to Ben's 6 marbles gives an additive comparison total of 8.
Question 7
Which statement represents a multiplicative comparison?
Which statement represents a multiplicative comparison?
💡Explanation:
'3 times as many' shows multiplication, which is a multiplicative comparison.
'3 times as many' shows multiplication, which is a multiplicative comparison.
Question 8
The phrase '3 more than' is an example of an comparison.
The phrase '3 more than' is an example of an comparison.
💡Explanation:
'More than' without the word 'times' indicates addition.
'More than' without the word 'times' indicates addition.
Question 9
A small plant is 2 inches tall. A large plant is 4 times as tall. How tall is the large plant?
A small plant is 2 inches tall. A large plant is 4 times as tall. How tall is the large plant?
💡Explanation:
4 times as tall means 2 multiplied by 4, which is 8 inches.
4 times as tall means 2 multiplied by 4, which is 8 inches.
Question 10
To find a value that is '5 times as many' as 4, you calculate 4 times , which equals 20.
To find a value that is '5 times as many' as 4, you calculate 4 times , which equals 20.
💡Explanation:
Multiplying the base quantity by the scale factor 5 gives 20.
Multiplying the base quantity by the scale factor 5 gives 20.
Question 11
John has 10 dollars. Lily has 4 dollars less than John. How much money does Lily have?
John has 10 dollars. Lily has 4 dollars less than John. How much money does Lily have?
💡Explanation:
'4 dollars less than' is an additive comparison using subtraction: 10 - 4 = 6.
'4 dollars less than' is an additive comparison using subtraction: 10 - 4 = 6.
Question 12
An additive comparison tells us how much more or less one amount is by using or subtraction.
An additive comparison tells us how much more or less one amount is by using or subtraction.
💡Explanation:
Additive comparisons involve adding or subtracting a fixed amount.
Additive comparisons involve adding or subtracting a fixed amount.
Question 13
A toy car is 3 cm long. A train is 6 times as long as the toy car. How long is the train?
A toy car is 3 cm long. A train is 6 times as long as the toy car. How long is the train?
💡Explanation:
'6 times as long' means multiplying 3 by 6, which equals 18.
'6 times as long' means multiplying 3 by 6, which equals 18.
Question 14
Multiplicative comparisons use multiplication to show how many larger one quantity is than another.
Multiplicative comparisons use multiplication to show how many larger one quantity is than another.
💡Explanation:
The scale factor tells you how many times larger the new amount is.
The scale factor tells you how many times larger the new amount is.
Question 15
Which expression shows '6 times as many as 7'?
Which expression shows '6 times as many as 7'?
💡Explanation:
'Times as many' translates directly to multiplication (6 x 7).
'Times as many' translates directly to multiplication (6 x 7).
Question 16
If a dog weighs 10 pounds and a cat weighs 3 pounds less, the cat weighs pounds.
If a dog weighs 10 pounds and a cat weighs 3 pounds less, the cat weighs pounds.
💡Explanation:
Subtracting 3 from 10 gives 7, which is an additive comparison.
Subtracting 3 from 10 gives 7, which is an additive comparison.
Question 17
Which expression shows '5 more than 8'?
Which expression shows '5 more than 8'?
💡Explanation:
'5 more than' means you add 5 to 8.
'5 more than' means you add 5 to 8.
Question 18
To solve a multiplicative comparison problem, you multiply the given number by the factor.
To solve a multiplicative comparison problem, you multiply the given number by the factor.
💡Explanation:
The scale factor describes the multiplier in a comparison.
The scale factor describes the multiplier in a comparison.
Question 19
Rina read 4 pages. Zuri read 3 times as many pages as Rina. How many pages did Zuri read?
Rina read 4 pages. Zuri read 3 times as many pages as Rina. How many pages did Zuri read?
💡Explanation:
'3 times as many' means 4 x 3 = 12.
'3 times as many' means 4 x 3 = 12.
Question 20
If Tim has 9 cards and Pam has 9 more cards than Tim, Pam has cards.
If Tim has 9 cards and Pam has 9 more cards than Tim, Pam has cards.
💡Explanation:
9 plus 9 equals 18, representing an additive comparison.
9 plus 9 equals 18, representing an additive comparison.
Question 21
A blue ribbon is 5 inches long. A red ribbon is 2 times as long. What is the length of the red ribbon?
A blue ribbon is 5 inches long. A red ribbon is 2 times as long. What is the length of the red ribbon?
💡Explanation:
2 times as long means 5 x 2 = 10 inches.
2 times as long means 5 x 2 = 10 inches.
Question 22
The sentence 'Group A has 4 times as many points as Group B' describes a comparison.
The sentence 'Group A has 4 times as many points as Group B' describes a comparison.
💡Explanation:
Using 'times as many' creates a multiplicative relationship.
Using 'times as many' creates a multiplicative relationship.
Question 23
There are 8 dogs in the park. There are 2 fewer cats than dogs. How many cats are in the park?
There are 8 dogs in the park. There are 2 fewer cats than dogs. How many cats are in the park?
💡Explanation:
'2 fewer than' is additive (subtraction): 8 - 2 = 6.
'2 fewer than' is additive (subtraction): 8 - 2 = 6.
Question 24
If you multiply a number by , the value stays the same.
If you multiply a number by , the value stays the same.
💡Explanation:
Any number multiplied by 1 equals itself.
Any number multiplied by 1 equals itself.
Question 25
A box has 6 crayons. A big box has 4 times as many crayons. How many crayons are in the big box?
A box has 6 crayons. A big box has 4 times as many crayons. How many crayons are in the big box?
💡Explanation:
4 times as many means 6 x 4 = 24.
4 times as many means 6 x 4 = 24.
Question 26
An additive comparison answers the question 'How more?'
An additive comparison answers the question 'How more?'
💡Explanation:
Additive comparisons find the difference by adding or subtracting.
Additive comparisons find the difference by adding or subtracting.
Question 27
Dad is 30 years old. Son is 5 years old. Which statement is correct?
Dad is 30 years old. Son is 5 years old. Which statement is correct?
💡Explanation:
30 divided by 5 is 6, so Dad is 6 times as old (multiplicative comparison).
30 divided by 5 is 6, so Dad is 6 times as old (multiplicative comparison).
Question 28
A multiplicative comparison answers the question 'How many as many?'
A multiplicative comparison answers the question 'How many as many?'
💡Explanation:
The key phrase for multiplicative comparison is 'times as many' or 'times as much'.
The key phrase for multiplicative comparison is 'times as many' or 'times as much'.
Question 29
Jake collected 7 shells. Emma collected 3 times as many shells as Jake. How many shells did Emma collect?
Jake collected 7 shells. Emma collected 3 times as many shells as Jake. How many shells did Emma collect?
💡Explanation:
3 times as many means 7 x 3 = 21.
3 times as many means 7 x 3 = 21.
Question 30
To solve '4 times as many as 5', you multiply 4 by , which gives 20.
To solve '4 times as many as 5', you multiply 4 by , which gives 20.
💡Explanation:
The numbers 4 and 5 are multiplied to find the total of 20.
The numbers 4 and 5 are multiplied to find the total of 20.
Question 31
Mia has 120 stickers. She shares them equally among 3 friends. How many stickers does each friend get?
Mia has 120 stickers. She shares them equally among 3 friends. How many stickers does each friend get?
💡Explanation:
120 divided by 3 is 40 because 12 tens divided by 3 is 4 tens.
120 divided by 3 is 40 because 12 tens divided by 3 is 4 tens.
Question 32
A baker made 200 cookies and put them into 4 boxes equally. There are cookies in each box.
A baker made 200 cookies and put them into 4 boxes equally. There are cookies in each box.
💡Explanation:
200 divided by 4 equals 50 since 20 divided by 4 is 5, and you add one zero.
200 divided by 4 equals 50 since 20 divided by 4 is 5, and you add one zero.
Question 33
A farmer planted 240 seeds in 4 rows. Each row has the same number of seeds. How many seeds are in each row?
A farmer planted 240 seeds in 4 rows. Each row has the same number of seeds. How many seeds are in each row?
💡Explanation:
240 divided by 4 is 60 because 24 divided by 4 is 6.
240 divided by 4 is 60 because 24 divided by 4 is 6.
Question 34
Tom saved 180 dollars in 2 months. He saved the same amount each month. Tom saved dollars each month.
Tom saved 180 dollars in 2 months. He saved the same amount each month. Tom saved dollars each month.
💡Explanation:
180 divided by 2 is 90 because 18 divided by 2 is 9.
180 divided by 2 is 90 because 18 divided by 2 is 9.
Question 35
A library has 300 books on 5 shelves. Each shelf has an equal number of books. How many books are on each shelf?
A library has 300 books on 5 shelves. Each shelf has an equal number of books. How many books are on each shelf?
💡Explanation:
300 divided by 5 is 60 because 30 divided by 5 is 6.
300 divided by 5 is 60 because 30 divided by 5 is 6.
Question 36
A school bought 400 new pencils. They gave them to 4 classes equally. Each class got pencils.
A school bought 400 new pencils. They gave them to 4 classes equally. Each class got pencils.
💡Explanation:
400 divided by 4 equals 100.
400 divided by 4 equals 100.
Question 37
Leo has 80 toy cars. He puts them into 2 boxes equally. How many toy cars are in each box?
Leo has 80 toy cars. He puts them into 2 boxes equally. How many toy cars are in each box?
💡Explanation:
80 divided by 2 is 40 because 8 divided by 2 is 4.
80 divided by 2 is 40 because 8 divided by 2 is 4.
Question 38
Emma arranged 350 chairs into 7 equal rows. There are chairs in each row.
Emma arranged 350 chairs into 7 equal rows. There are chairs in each row.
💡Explanation:
350 divided by 7 is 50 because 35 divided by 7 is 5.
350 divided by 7 is 50 because 35 divided by 7 is 5.
Question 39
A toy factory made 450 teddy bears and packed them into 9 boxes equally. How many bears are in each box?
A toy factory made 450 teddy bears and packed them into 9 boxes equally. How many bears are in each box?
💡Explanation:
450 divided by 9 is 50 because 45 divided by 9 is 5.
450 divided by 9 is 50 because 45 divided by 9 is 5.
Question 40
Sam collected 270 shells and put them into 3 buckets equally. Each bucket has shells.
Sam collected 270 shells and put them into 3 buckets equally. Each bucket has shells.
💡Explanation:
270 divided by 3 is 90 because 27 divided by 3 is 9.
270 divided by 3 is 90 because 27 divided by 3 is 9.
Question 41
A teacher has 160 markers. She shares them equally among 4 groups of students. How many markers does each group get?
A teacher has 160 markers. She shares them equally among 4 groups of students. How many markers does each group get?
💡Explanation:
160 divided by 4 is 40 because 16 divided by 4 is 4.
160 divided by 4 is 40 because 16 divided by 4 is 4.
Question 42
A store has 490 apples in 7 baskets. Each basket has the same amount. There are apples in each basket.
A store has 490 apples in 7 baskets. Each basket has the same amount. There are apples in each basket.
💡Explanation:
490 divided by 7 is 70 because 49 divided by 7 is 7.
490 divided by 7 is 70 because 49 divided by 7 is 7.
Question 43
Lily baked 210 cupcakes for 3 parties. She gave the same number of cupcakes to each party. How many cupcakes did each party get?
Lily baked 210 cupcakes for 3 parties. She gave the same number of cupcakes to each party. How many cupcakes did each party get?
💡Explanation:
210 divided by 3 is 70 because 21 divided by 3 is 7.
210 divided by 3 is 70 because 21 divided by 3 is 7.
Question 44
A park has 600 trees planted in 6 equal rows. There are trees in each row.
A park has 600 trees planted in 6 equal rows. There are trees in each row.
💡Explanation:
600 divided by 6 is 100 because 6 divided by 6 is 1.
600 divided by 6 is 100 because 6 divided by 6 is 1.
Question 45
Max earned 560 points in a video game over 7 levels. He earned the same points each level. How many points did he earn per level?
Max earned 560 points in a video game over 7 levels. He earned the same points each level. How many points did he earn per level?
💡Explanation:
560 divided by 7 is 80 because 56 divided by 7 is 8.
560 divided by 7 is 80 because 56 divided by 7 is 8.
Question 46
A delivery driver drove 320 miles in 4 days. He drove the same distance every day. He drove miles each day.
A delivery driver drove 320 miles in 4 days. He drove the same distance every day. He drove miles each day.
💡Explanation:
320 divided by 4 is 80 because 32 divided by 4 is 8.
320 divided by 4 is 80 because 32 divided by 4 is 8.
Question 47
A school bus carried 640 students in 8 trips. The same number of students rode the bus each trip. How many students rode on each trip?
A school bus carried 640 students in 8 trips. The same number of students rode the bus each trip. How many students rode on each trip?
💡Explanation:
640 divided by 8 is 80 because 64 divided by 8 is 8.
640 divided by 8 is 80 because 64 divided by 8 is 8.
Question 48
A florist has 720 flowers and makes 9 bouquets. Each bouquet has the same number of flowers. There are flowers in each bouquet.
A florist has 720 flowers and makes 9 bouquets. Each bouquet has the same number of flowers. There are flowers in each bouquet.
💡Explanation:
720 divided by 9 is 80 because 72 divided by 9 is 8.
720 divided by 9 is 80 because 72 divided by 9 is 8.
Question 49
Lucy has 540 beads. She puts them into 6 boxes equally. How many beads are in each box?
Lucy has 540 beads. She puts them into 6 boxes equally. How many beads are in each box?
💡Explanation:
540 divided by 6 is 90 because 54 divided by 6 is 9.
540 divided by 6 is 90 because 54 divided by 6 is 9.
Question 50
An art teacher used 480 tubes of paint for 6 tables of students. Each table got tubes of paint.
An art teacher used 480 tubes of paint for 6 tables of students. Each table got tubes of paint.
💡Explanation:
480 divided by 6 is 80 because 48 divided by 6 is 8.
480 divided by 6 is 80 because 48 divided by 6 is 8.
Question 51
A philanthropic organization intends to distribute 420,000 promotional flyers equally among 7 regional community centers. How many flyers will each center receive?
A philanthropic organization intends to distribute 420,000 promotional flyers equally among 7 regional community centers. How many flyers will each center receive?
💡Explanation:
Utilizing place value, divide the non-zero leading digits: 42 ÷ 7 = 6. Since 420,000 is 42 ten-thousands (or by accounting for the remaining four zeros after adjusting), appending the appropriate place value yields 60,000.
Utilizing place value, divide the non-zero leading digits: 42 ÷ 7 = 6. Since 420,000 is 42 ten-thousands (or by accounting for the remaining four zeros after adjusting), appending the appropriate place value yields 60,000.
Question 52
An agricultural enterprise harvested 560 tons of grain and allocated them uniformly across 8 storage silos. By calculating the fundamental quotient of 56 divided by 8 and adjusting for the trailing zeros, each silo holds tons of grain.
An agricultural enterprise harvested 560 tons of grain and allocated them uniformly across 8 storage silos. By calculating the fundamental quotient of 56 divided by 8 and adjusting for the trailing zeros, each silo holds tons of grain.
💡Explanation:
By isolating the leading digits, 56 ÷ 8 = 7. Factoring in the place value of 560 (which is 56 tens), 56 tens ÷ 8 equals 7 tens, resulting in 70.
By isolating the leading digits, 56 ÷ 8 = 7. Factoring in the place value of 560 (which is 56 tens), 56 tens ÷ 8 equals 7 tens, resulting in 70.
Question 53
A municipal authority has budgeted $3,600,000 for 9 distinct urban development initiatives, funding each project with an identical monetary allocation. What is the exact budget assigned to each initiative?
A municipal authority has budgeted $3,600,000 for 9 distinct urban development initiatives, funding each project with an identical monetary allocation. What is the exact budget assigned to each initiative?
💡Explanation:
Divide the leading significant digits: 36 ÷ 9 = 4. Accounting for the five trailing zeros in 3,600,000, the quotient is 400,000.
Divide the leading significant digits: 36 ÷ 9 = 4. Accounting for the five trailing zeros in 3,600,000, the quotient is 400,000.
Question 54
A logistics corporation needs to transport 2,400 crates of electronics utilizing 4 heavy-duty freight trucks with equal load capacities. Each truck will carry crates.
A logistics corporation needs to transport 2,400 crates of electronics utilizing 4 heavy-duty freight trucks with equal load capacities. Each truck will carry crates.
💡Explanation:
Isolate the non-zero digits: 24 ÷ 4 = 6. Incorporating the remaining two zeros from 2,400 gives 600.
Isolate the non-zero digits: 24 ÷ 4 = 6. Incorporating the remaining two zeros from 2,400 gives 600.
Question 55
During a massive archival reorganization, an institution sorted 81,000 manuscripts into 9 specialized chronological vaults, ensuring an equal distribution. How many manuscripts were housed in each vault?
During a massive archival reorganization, an institution sorted 81,000 manuscripts into 9 specialized chronological vaults, ensuring an equal distribution. How many manuscripts were housed in each vault?
💡Explanation:
Divide 81 by 9 to get 9, and apply the three zeros from 81,000 to yield 9,000 manuscripts per vault.
Divide 81 by 9 to get 9, and apply the three zeros from 81,000 to yield 9,000 manuscripts per vault.
Question 56
A pharmaceutical manufacturing plant produced 48,000 doses of a vaccine, which were then packed equally into 6 secure distribution crates. Each crate contains doses.
A pharmaceutical manufacturing plant produced 48,000 doses of a vaccine, which were then packed equally into 6 secure distribution crates. Each crate contains doses.
💡Explanation:
Compute the basic division 48 ÷ 6 = 8, and retain the three trailing zeros to determine the final quantity of 8,000.
Compute the basic division 48 ÷ 6 = 8, and retain the three trailing zeros to determine the final quantity of 8,000.
Question 57
An astronomical observatory cataloged 630,000 stellar formations, dispersing the data evenly across 7 supercomputing arrays for analysis. How many formations were processed by each array?
An astronomical observatory cataloged 630,000 stellar formations, dispersing the data evenly across 7 supercomputing arrays for analysis. How many formations were processed by each array?
💡Explanation:
Evaluate 63 ÷ 7 = 9. Appending the four zeros corresponding to 630,000 results in 90,000 formations per array.
Evaluate 63 ÷ 7 = 9. Appending the four zeros corresponding to 630,000 results in 90,000 formations per array.
Question 58
An excavation team meticulously cataloged 35,000 artifacts over a season, dividing the total quantity evenly among 5 university research departments. Each department received artifacts.
An excavation team meticulously cataloged 35,000 artifacts over a season, dividing the total quantity evenly among 5 university research departments. Each department received artifacts.
💡Explanation:
Divide 35 by 5 to obtain 7, and affix the three zeros from 35,000 to arrive at 7,000.
Divide 35 by 5 to obtain 7, and affix the three zeros from 35,000 to arrive at 7,000.
Question 59
A telecommunications enterprise transmitted a total of 5,400,000 data packets across 6 primary fiber-optic nodes, distributing the volume uniformly. How many packets passed through each node?
A telecommunications enterprise transmitted a total of 5,400,000 data packets across 6 primary fiber-optic nodes, distributing the volume uniformly. How many packets passed through each node?
💡Explanation:
Divide 54 by 6 to yield 9. Accounting for the five trailing zeros in 5,400,000 produces 900,000 packets.
Divide 54 by 6 to yield 9. Accounting for the five trailing zeros in 5,400,000 produces 900,000 packets.
Question 60
A botanical garden cultivated 24,000 rare orchid specimens, arranging them symmetrically within 3 expansive greenhouses. Each greenhouse accommodates specimens.
A botanical garden cultivated 24,000 rare orchid specimens, arranging them symmetrically within 3 expansive greenhouses. Each greenhouse accommodates specimens.
💡Explanation:
Isolate the leading digits: 24 ÷ 3 = 8. Adding the three zeros from 24,000 gives 8,000.
Isolate the leading digits: 24 ÷ 3 = 8. Adding the three zeros from 24,000 gives 8,000.
Question 61
An industrial milling plant produced 320,000 metric tons of steel, dispatching the output equally to 4 major fabrication hubs. What metric tonnage did each hub receive?
An industrial milling plant produced 320,000 metric tons of steel, dispatching the output equally to 4 major fabrication hubs. What metric tonnage did each hub receive?
💡Explanation:
Compute 32 ÷ 4 = 8. Since there are four zeros in 320,000, the calculated distribution is 80,000 metric tons.
Compute 32 ÷ 4 = 8. Since there are four zeros in 320,000, the calculated distribution is 80,000 metric tons.
Question 62
A publishing house printed 72,000 volumes of an encyclopedia set, apportioning them equally among 9 international distribution centers. Each center obtained volumes.
A publishing house printed 72,000 volumes of an encyclopedia set, apportioning them equally among 9 international distribution centers. Each center obtained volumes.
💡Explanation:
Perform the core division 72 ÷ 9 = 8, and preserve the three trailing zeros to determine the total of 8,000.
Perform the core division 72 ÷ 9 = 8, and preserve the three trailing zeros to determine the total of 8,000.
Question 63
A renewable energy conglomerate generated 490,000 megawatt-hours of electricity, funneling the power through 7 regional substations in equal measure. How many megawatt-hours were routed through each substation?
A renewable energy conglomerate generated 490,000 megawatt-hours of electricity, funneling the power through 7 regional substations in equal measure. How many megawatt-hours were routed through each substation?
💡Explanation:
Divide the significant digits: 49 ÷ 7 = 7. Factoring in the four zeros of 490,000 yields 70,000 megawatt-hours.
Divide the significant digits: 49 ÷ 7 = 7. Factoring in the four zeros of 490,000 yields 70,000 megawatt-hours.
Question 64
A maritime fleet transported 1,800 shipping containers, offloading them evenly across 3 docking terminals. Each terminal processed containers.
A maritime fleet transported 1,800 shipping containers, offloading them evenly across 3 docking terminals. Each terminal processed containers.
💡Explanation:
Using basic math facts, 18 ÷ 3 = 6. Retaining the two trailing zeros from 1,800 results in 600.
Using basic math facts, 18 ÷ 3 = 6. Retaining the two trailing zeros from 1,800 results in 600.
Question 65
An aerospace facility manufactured 2,700,000 specialized components, parceling them out equally to 9 assembly plants. How many components were delivered to each plant?
An aerospace facility manufactured 2,700,000 specialized components, parceling them out equally to 9 assembly plants. How many components were delivered to each plant?
💡Explanation:
Simplify by dividing 27 by 9, which equals 3. Appending the five zeros from 2,700,000 leads to 300,000 components.
Simplify by dividing 27 by 9, which equals 3. Appending the five zeros from 2,700,000 leads to 300,000 components.
Question 66
A high-capacity data center archived 450,000 digital files, distributing the load uniformly across 5 secure servers. Each server holds files.
A high-capacity data center archived 450,000 digital files, distributing the load uniformly across 5 secure servers. Each server holds files.
💡Explanation:
Calculate 45 ÷ 5 = 9, and apply the four trailing zeros from 450,000 to get 90,000.
Calculate 45 ÷ 5 = 9, and apply the four trailing zeros from 450,000 to get 90,000.
Question 67
A municipal water authority pumped 6,300,000 gallons of treated water into 7 municipal reservoirs, ensuring a balanced distribution. How many gallons did each reservoir store?
A municipal water authority pumped 6,300,000 gallons of treated water into 7 municipal reservoirs, ensuring a balanced distribution. How many gallons did each reservoir store?
💡Explanation:
Divide 63 by 7 to achieve 9. Incorporating the five zeros from 6,300,000 calculates out to 900,000 gallons.
Divide 63 by 7 to achieve 9. Incorporating the five zeros from 6,300,000 calculates out to 900,000 gallons.
Question 68
A state park management team planted 12,000 native saplings across 4 ecological zones in equal proportions. Each zone received saplings.
A state park management team planted 12,000 native saplings across 4 ecological zones in equal proportions. Each zone received saplings.
💡Explanation:
Isolate the leading digits: 12 ÷ 4 = 3. Attaching the three zeros from 12,000 gives 3,000.
Isolate the leading digits: 12 ÷ 4 = 3. Attaching the three zeros from 12,000 gives 3,000.
Question 69
A global courier service sorted 2,100,000 parcels, channeling them equally into 3 primary sorting hubs. How many parcels were handled by each hub?
A global courier service sorted 2,100,000 parcels, channeling them equally into 3 primary sorting hubs. How many parcels were handled by each hub?
💡Explanation:
Divide 21 by 3 to get 7. Accounting for the five trailing zeros in 2,100,000 results in 700,000 parcels.
Divide 21 by 3 to get 7. Accounting for the five trailing zeros in 2,100,000 results in 700,000 parcels.
Question 70
A nationwide retail chain distributed 40,000 promotional catalogs equally among 8 flagship department stores. Each store was allotted catalogs.
A nationwide retail chain distributed 40,000 promotional catalogs equally among 8 flagship department stores. Each store was allotted catalogs.
💡Explanation:
Evaluate 40 ÷ 8 = 5, and retain the three zeros of 40,000 to determine the exact total of 5,000.
Evaluate 40 ÷ 8 = 5, and retain the three zeros of 40,000 to determine the exact total of 5,000.
Welcome to our interactive 4th-grade math test on Multiplicative Comparisons vs. Additive Comparisons! Mastering the difference between additive and multiplicative comparisons is a crucial milestone in elementary math, helping students transition from basic addition to advanced proportional reasoning. Ready to see how well you can tell these comparison types apart? Take the quiz below to test your skills!
Click to Read Detailed Information
Understanding Multiplicative vs. Additive Comparisons in 4th Grade Math
In 4th-grade mathematics, students learn to interpret multiplication equations as comparisons. Understanding how comparison statements work is essential for solving multi-step word problems and building a strong foundation for algebra and ratios in later grades. The core curriculum distinguishes between two main types of comparisons: additive comparisons and multiplicative comparisons.
What is an Additive Comparison?
An additive comparison focuses on the difference between two quantities. It answers the question, “How much more?” or “How much less?” You use addition or subtraction to solve additive comparisons.
- Keyword clues: “more than,” “less than,” “taller than,” “heavier by,” “older than.”
- Example: Sarah has 7 stickers. John has 12 stickers. How many more stickers does John have than Sarah?
- Equation: 12 – 7 = 5. (John has 5 more stickers than Sarah. This is an additive comparison because we found the sum/difference by adding or subtracting.)
What is a Multiplicative Comparison?
A multiplicative comparison focuses on scaling—how many times larger or smaller one quantity is compared to another. It answers the question, “How many times as many?” You use multiplication or division to solve multiplicative comparisons.
- Keyword clues: “times as many,” “times as much,” “twice as old,” “half as many.”
- Example: Sarah has 7 stickers. John has 3 times as many stickers as Sarah. How many stickers does John have?
- Equation: 7 × 3 = 21. (John has 21 stickers. This is a multiplicative comparison because John’s amount is scaled up by a factor of 3.)
Key Differences at a Glance
| Feature | Additive Comparison | Multiplicative Comparison |
|---|---|---|
| Core Question | How much more or less? | How many times as many/much? |
| Operation Used | Addition (+) or Subtraction (-) | Multiplication (×) or Division (÷) |
| Example Statement | “Tom has 4 more books than Mia.” | “Tom has 4 times as many books as Mia.” |
Tips for Mastering Math Word Problems
- Read carefully: Look closely at phrases like “4 more than” versus “4 times as many.” A single word completely changes the operation!
- Visualize the problem: Draw bar models or tape diagrams. For additive comparisons, show one quantity being added to another. For multiplicative comparisons, show equal groups repeating.
- Ask yourself the guiding question: Are we combining or finding a difference (additive), or are we scaling up or sharing equally into groups (multiplicative)?
Use this interactive test to practice identifying and solving both types of comparison problems, and watch your math confidence grow!