Multiplication and Division - ISEE Lower Level Mathematics Achievement

1. A baker makes 12 dozen muffins. He then sells 135 of the muffins. How many muffins does the baker have left?
   Answer: 9 muffins First, calculate the total number of muffins made. Since a dozen is 12, the baker makes $12 \times 12 = 144$ muffins. Next, subtract the number of muffins sold from the total: $144 - 135 = 9$. The baker has 9 muffins left.
2. A movie theater has 14 rows of seats, and each row has 22 seats. For a particular show, 250 seats were sold. How many seats were empty?
   Answer: 58 seats First, calculate the total number of seats in the theater by multiplying the number of rows by the seats per row: $14 \times 22 = 308$ seats. Then, subtract the number of sold seats from the total to find the number of empty seats: $308 - 250 = 58$ seats.
3. A library has 392 new books to put on shelves. Each shelf can hold exactly 28 books. How many shelves will be completely filled by these new books?
   Answer: 14 shelves To find the number of shelves needed, divide the total number of books by the number of books each shelf can hold: $392 \div 28$. Performing the division: $392 \div 28 = 14$. Since there is no remainder, exactly 14 shelves will be completely filled.
4. A stationery store sells pens in packs of 6 for $3. A teacher needs to buy exactly 54 pens for her students. How much will it cost to buy the required number of pens?
   Answer: $27 This is a two-step problem. First, find the number of packs the teacher needs to buy by dividing the total number of pens by the number of pens per pack: $54 \div 6 = 9$ packs. Second, calculate the total cost by multiplying the number of packs by the cost per pack: $9 \times \$3 = \$27$.
5. A school needs to transport 115 students on a field trip. Each bus can hold a maximum of 25 students. What is the minimum number of buses required to transport all the students?
   Answer: 5 buses To find the number of buses, divide the total number of students by the capacity of one bus: $115 \div 25 = 4$ with a remainder of 15. This means 4 buses will be completely full, but there will be 15 students left over. To transport these remaining students, one more bus is needed. Therefore, a total of $4 + 1 = 5$ buses are required.
6. A factory produces 45 toys every hour. The factory operates for 8 hours a day. If the toys are packed into boxes that hold 15 toys each, how many boxes are filled in one day?
   Answer: 24 boxes First, calculate the total number of toys produced in one day: $45 \text{ toys/hour} \times 8 \text{ hours} = 360 \text{ toys}$. Next, divide the total number of toys by the number of toys per box to find how many boxes are filled: $360 \div 15 = 24$ boxes.
7. A rectangular community garden measures 12 meters by 18 meters. A special type of fertilizer needs to be spread along the entire border of the garden. If one bag of fertilizer covers 6 meters of the border, how many bags are needed?
   Answer: 10 bags The border of the garden is its perimeter. The perimeter of a rectangle is calculated as $2 \times (\text{length} + \text{width})$. The perimeter is $2 \times (18 + 12) = 2 \times 30 = 60$ meters. To find the number of bags needed, divide the total perimeter by the coverage per bag: $60 \div 6 = 10$ bags.
8. There are 7 days in a week and 24 hours in a day. How many hours are there in 3 full weeks?
   Answer: 504 hours First, find the total number of days in 3 weeks: $3 \text{ weeks} \times 7 \text{ days/week} = 21 \text{ days}$. Then, multiply the total number of days by the number of hours in a day: $21 \text{ days} \times 24 \text{ hours/day} = 504 \text{ hours}$.
9. The total cost for 6 identical hats was $72. At the same price per hat, what would be the cost for 4 of these hats?
   Answer: $48 First, find the cost of a single hat by dividing the total cost by the number of hats: $\$72 \div 6 = \$12$ per hat. Next, multiply the cost per hat by the new quantity of hats: $\$12 \times 4 = \$48$.
10. A fundraising event sold 150 tickets at $5 each. The cost to rent the hall was $200, and the cost for food was $3 for each ticket sold. What was the total profit from the event?
    Answer: $100 First, calculate the total revenue from ticket sales: $150 \times \$5 = \$750$. Next, calculate the total costs. The food cost is $150 \times \$3 = \$450$. The total cost is the hall rental plus the food cost: $\$200 + \$450 = \$650$. Finally, calculate the profit by subtracting total costs from total revenue: $\$750 - \$650 = \$100$.
11. A candy maker has 250 pieces of candy. He wants to put them into bags with 12 pieces in each bag. What is the greatest number of full bags he can make?
    Answer: 20 bags This is a division word problem that tests your understanding of remainders and what "full bags" means in a real-world context. To find how many full bags the candy maker can create, you need to divide the total pieces by pieces per bag: $250 \div 12$. When you perform this division, you get $20.833...$ or $20\frac{10}{12}$. This means you can make 20 complete bags with 10 pieces left over. The key insight is that the question asks for "full bags" — partial bags don't count. Even though you have 10 extra pieces, that's not enough to make another complete bag of 12, so you can only make 20 full bags. Looking at the wrong answers: Choice A (10 bags) is far too low and likely comes from miscalculating the division entirely. Choice B (22 bags) incorrectly rounds $20.833$ up to the nearest whole number, but you can't round up when dealing with physical objects — you simply don't have enough candy for 22 complete bags. Choice C (21 bags) makes the same rounding error but is closer to the actual quotient. When you see division word problems involving "complete" or "full" groups, always round down to the nearest whole number, even if the decimal portion is large. The remainder tells you how many items are left over, not how many additional complete groups you can make. This type of problem appears frequently on standardized tests, so practice recognizing when to ignore remainders versus when they matter.
12. A farmer has 18 rows of apple trees with 15 trees in each row. He also has 12 rows of pear trees with 10 trees in each row. How many more apple trees than pear trees does the farmer have?
    Answer: 150 trees First, calculate the total number of apple trees: $18 \times 15 = 270$ apple trees. Next, calculate the total number of pear trees: $12 \times 10 = 120$ pear trees. Finally, find the difference between the number of apple trees and pear trees: $270 - 120 = 150$.
13. A water tank holds 600 gallons of water. A pump removes water at a rate of 15 gallons per minute. If the pump runs for 30 minutes, how many gallons of water are left in the tank?
    Answer: 150 gallons First, calculate the total amount of water removed by the pump. The pump removes $15 \text{ gallons/minute} \times 30 \text{ minutes} = 450 \text{ gallons}$. Then, subtract the amount removed from the initial amount in the tank: $600 - 450 = 150$ gallons remaining.
14. A pizza is cut into 8 slices. A soccer team buys 5 identical pizzas for 10 players to share equally. If all the slices are eaten, how many slices does each player eat?
    Answer: 4 slices First, find the total number of slices. There are 5 pizzas with 8 slices each, so there are $5 \times 8 = 40$ slices in total. Then, divide the total number of slices by the number of players: $40 \div 10 = 4$ slices per player.
15. The area of a rectangular field is 432 square yards. If the length of the field is 24 yards, what is its width in yards?
    Answer: 18 yards When you encounter a rectangular area problem, remember that area equals length times width: $A = l \times w$. Since you know the area and one dimension, you can find the missing dimension by rearranging this formula. Given that the area is 432 square yards and the length is 24 yards, you need to solve for width: $432 = 24 \times w$. To isolate the width, divide both sides by 24: $w = \frac{432}{24} = 18$ yards. Let's examine why the other answers are incorrect. Choice A (16 yards) gives you $24 \times 16 = 384$ square yards, which is too small. Choice B (10,368 yards) represents a common error where students multiply 432 by 24 instead of dividing—this would give you an impossibly large width that makes no geometric sense. Choice C (20 yards) yields $24 \times 20 = 480$ square yards, which exceeds the given area. You can verify that D is correct: $24 \times 18 = 432$ square yards, matching exactly. Study tip: Always check your work by substituting your answer back into the original formula. Also, watch out for the multiplication trap—when you have area and need to find a missing dimension, you divide, not multiply. If your calculated width seems unreasonably large compared to the length, you've likely made this error.
16. Four friends collected a total of 96 seashells. They decided to share them equally. If one of the friends, Sarah, then gives away 7 of her shells, how many shells does she have left?
    Answer: 17 shells First, find out how many shells each friend received. Divide the total number of shells by the number of friends: $96 \div 4 = 24$ shells per friend. Sarah starts with 24 shells. Then, she gives away 7, so she has $24 - 7 = 17$ shells left.
17. Leo can pack 15 boxes in an hour. Mia can pack 12 boxes in an hour. If they both work for 4 hours, how many more boxes will Leo have packed than Mia?
    Answer: 12 boxes This is a multi-step work rate problem where you need to calculate how much each person accomplishes over time, then find the difference. Start by finding how many boxes each person packs in 4 hours. Leo packs 15 boxes per hour, so in 4 hours he packs $15 \times 4 = 60$ boxes. Mia packs 12 boxes per hour, so in 4 hours she packs $12 \times 4 = 48$ boxes. The difference is $60 - 48 = 12$ boxes, making D correct. Let's examine why the other answers are wrong. Choice A (3 boxes) represents the difference in their hourly rates (15 - 12 = 3), but this ignores that they worked for 4 hours. Choice B (108 boxes) is the total number of boxes both workers packed combined (60 + 48 = 108). This is a common trap where students add instead of finding the difference. Choice C (27 boxes) appears to be a calculation error, possibly from incorrectly multiplying the rate difference by hours and adding extra (3 × 4 = 12, then somehow getting to 27). When you see work rate problems asking "how many more," always follow this pattern: calculate each person's total output over the given time period, then subtract to find the difference. Don't just look at the difference in rates per hour—you must account for the total time worked. The key is recognizing that rate differences get magnified over longer work periods.
18. David can solve 16 math problems in 8 minutes. Working at the same constant rate, how many math problems can he solve in 20 minutes?
    Answer: 40 problems First, find David's rate of solving problems. He solves $16 \div 8 = 2$ problems per minute. To find how many he can solve in 20 minutes, multiply his rate by the new time: $2 \times 20 = 40$ problems.

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