Addition, Subtraction, Multiplication and Division:
- Using a variety of methods for addition and subtraction, including column methods
- Multiplying and dividing with two-digit numbers by a one-digit number
- Solving problems involving multiplication and division
Using a Variety of
Methods for Addition and Subtraction
1. Q: Solve: 345 + 278 (without regrouping)
A: 623
2. Q: Solve: 521 - 187 (borrowing from the tens place)
A: 334
3. Q: Add 732 and 459 using the place value table method. (Break down the numbers by place value and add each place value column)
A: Ones: 2 + 9 = 11 (write down 1, carry over 1) Tens: 3 + 5 + 1 (carry over) = 9 (write down 9) Hundreds: 7 + 4 = 11 (write down 1) Total: 1191
4. Q: Estimate the sum of 872 and 431 by rounding each number to the nearest hundred.
A: 900 + 400 = 1300 (estimate)
5. Q: John has 23 red marbles and Sarah has 47 blue marbles. How many marbles do they have in total? (Can be solved using counting on strategy or addition)
A: 23 + 47 = 70 marbles
Multiplication and Division with Two-Digit Numbers by a One-Digit Number
6. Q: Multiply 42 x 7.
A: 294
7. Q: Divide 638 by 4.
A: 159 (remainder 2)
8. Q: Lisa buys 3 notebooks at $5 each. How much does she pay in total?
A: Total cost = Price per notebook * Number of notebooks Total cost = $5/notebook * 3 notebooks = $15
9. Q: A rectangular garden bed is 12 meters long and 7 meters wide. What is the area (total space covered) of the garden bed? (Area = length x width)
A: Area = 12 meters x 7 meters = 84 square meters
10. Q: There are 48 cookies shared equally among 8 friends. How many cookies does each friend receive?
A: Cookies per friend = Total cookies / Number of friends Cookies per friend = 48 cookies / 8 friends = 6 cookies/friend
Solving Problems Involving Multiplication and Division
11. Q: A baker needs 3 cups of flour for every cake. If he wants to make 6 cakes, how much flour does he need in total?
A: Total flour = Flour per cake * Number of cakes Total flour = 3 cups/cake * 6 cakes = 18 cups
12. Q: A train travels 567 kilometers on the first day and 234 kilometers on the second day. What is the total distance traveled in the two days? (Involves both addition and multiplication)
A: Total distance = Distance on day 1 + Distance on day 2 Total distance = 567 km + 234 km = 801 km
13. Q: A rectangular pizza measures 30 centimeters long and 25 centimeters wide. What is the perimeter of the pizza? (Perimeter is the total length of all sides added together)
A: Perimeter = 2 (length + width) since there are 2 lengths and 2 widths to consider Perimeter = 2 (30 cm + 25 cm) = 110 centimeters
14. Q: A shelf can hold a maximum weight of 10,000 kilograms. Boxes weighing a total of 2,135 kilograms are placed on the shelf. How much weight can still be added without exceeding the limit? (Involves subtraction)
A: Remaining capacity = Maximum weight - Weight of boxes on shelf Remaining capacity = 10,000 kg - 2,135 kg = 7,865 kg
15. Q: Sarah has collected 234 stickers. Lisa has 17 fewer stickers than Sarah. How many stickers does Lisa have? (Involves subtraction)
A: Lisa's stickers = Sarah's stickers - Difference Lisa's stickers = 234 stickers - 17 stickers = 217 stickers
16. Q: A rectangular box has a length of 12 centimeters, a width of 5 centimeters, and a height of 8 centimeters. What is the volume of the box? (Volume = length x width x height)
A: Volume = 12 cm x 5 cm x 8 cm = 480 cubic centimeters
17. Q: Mary has $25. She spends $7 on a book and $4 on a pencil case. How much money does she have left? (Involves subtraction)
A: Money left = Starting amount - Money spent Money left = $25 - $7 - $4 = $14
18. Q: A square piece of paper measures 18 centimeters on each side. What is the area of the square? (Area = side length x side length)
A: Area = 18 cm x 18 cm = 324 square centimeters
19. Q: A recipe requires 1/4 cup of sugar for every 1 cup of flour. If David uses 2 cups of flour, how much sugar does he need?
A: Sugar needed = Flour used x Sugar per cup of flour Sugar needed = 2 cups * 1/4 cup/cup = 1/2 cup (can be written as 0.5 cup)
20. Q: Estimate the difference between 1,234 and 789 by rounding each number to the nearest hundred.
A: 1,200 - 800 = 400 (estimate)
Challenge Questions (applying multiple operations):
21. Q: A bus travels 723 kilometers on the first day, 456 kilometers on the second day, and 387 kilometers on the third day. What is the total distance traveled in the three days? (Involves addition)
A: Total distance = Day 1 distance + Day 2 distance + Day 3 distance Total distance = 723 km + 456 km + 387 km = 1,566 km
22. Q: A rectangular garden is 15 meters long and 8 meters wide. If John wants to build a fence around the entire garden, how much fencing does he need? (Involves perimeter and multiplication)
A: Perimeter = 2 (length + width) Perimeter = 2 (15 meters + 8 meters) = 46 meters Fence needed: Since the fence goes around the whole garden, multiply the perimeter by 2 (to account for two lengths and two widths) Fence needed = Perimeter x 2 Fence needed = 46 meters x 2 = 92 meters
23. Q: A bag of rice weighs 5 kilograms. There are 3 bags of rice. What is the total weight of the rice? (Involves multiplication)
A: Total weight = Weight per bag x Number of bags Total weight = 5 kg/bag * 3 bags = 15 kilograms
24. Q: A movie ticket costs $12.50 for adults and $7.80 for children. How much more expensive is an adult ticket compared to a child's ticket? (Involves subtraction)
A: Price difference = Adult price - Child price Price difference = $12.50 - $7.80 = $4.70
25. Q: A farmer harvests 4,231 apples on Monday and 1,879 on Tuesday. What is the total number of apples harvested in the two days? (Involves addition
)
A: Total apples = Apples on Monday + Apples on Tuesday Total apples = 4,231 + 1,879 = 6,110
Mental Math Practice:
26. Q: Solve: 45 + 23 (without regrouping)
A: 68
27. Q: Solve: 78 - 35 (borrowing from the tens place)
A: 43
28. Q: Double 17.
A: 17 x 2 = 34
29. Q: Triple 21.
A: 21 x 3 = 63
30. Q: Halve 48.
A: 48 / 2 = 24
31. Q: If 1 apple costs $0.50, how much do 4 apples cost?
A: Total cost = Price per apple * Number of apples Total cost = $0.50/apple * 4 apples = $2.00
32. Q: John has 12 marbles and Sarah has 3 times as many. How many marbles does Sarah have?
A: Sarah's marbles = John's marbles * 3 Sarah's marbles = 12 marbles * 3 = 36 marbles
33. Q: A recipe requires 2 eggs for every cake. If Mary bakes 5 cakes, how many eggs does she need in total?
A: Eggs needed = Cakes baked * Eggs per cake Eggs needed = 5 cakes * 2 eggs/cake = 10 eggs
34. Q: Estimate the product of 32 x 7 by rounding each number to the nearest ten.
A: 30 x 10 = 300 (estimate)
35. Q: A square plot of land measures 20 meters on each side. What is the area of the land? (Area = side length x side length)
A: Area = 20 meters x 20 meters = 400 square meters
Word Problems (applying a mix of operations):
36. Q: A shelf can hold a maximum weight of 12,000 kilograms. Boxes weighing a total of 3,456 kilograms are already on the shelf. If additional boxes each weigh 215 kilograms, how many more boxes can be added without exceeding the weight limit? (Involves subtraction and division)
A: Remaining capacity = Maximum weight - Weight of existing boxes Remaining capacity = 12,000 kg - 3,456 kg = 8,544 kg Number of additional boxes: Divide the remaining capacity by the weight of each new box Number of boxes = Remaining capacity / Weight per box Number of boxes = 8,544 kg / 215 kg/box = 40 boxes (round down to nearest whole box)
37. Q: A train travels 678 kilometers on the first day and 1.5 times the distance on the second day. What is the total distance traveled in the two days? (Involves multiplication and addition)
A: Distance on day 2 = Distance on day 1 x 1.5 Distance on day 2 = 678 km * 1.5 = 1,017 km Total distance = Day 1 distance + Day 2 distance Total distance = 678 km + 1,017 km = 1,695 km
38. Q: A rectangular table is 1.2 meters long and 0.75 meters wide. What is the area of the table? (Involves multiplication)
A: Area = length x width (remember to consider the decimal places when multiplying) Area = 1.2 meters x 0.75 meters = 0.9 square meters
39. Q: A baker needs 2.5 cups of flour for every cake. If he wants to make 4.5 cakes, how much flour does he need in total? (Involves multiplication)
A: Total flour = Flour per cake * Number of cakes (consider decimals) Total flour = 2.5 cups/cake * 4.5 cakes = 11.25 cups
40. Q: A rectangular garden is 8 meters long and 5 meters wide. If Mary wants to plant a border of flowers around the entire garden using 2 meters of fencing for each side, how much fencing does she need in total? (Involves perimeter and multiplication)
A: Perimeter = 2 (length + width) Perimeter = 2 (8 meters + 5 meters) = 26 meters Fencing needed: Since the fence goes around the whole garden, multiply the perimeter by the fencing needed per side (2 meters) Fence needed = Perimeter x Fencing needed per side Fence needed = 26 meters * 2 meters/side = 52 meters
41. Q: There are 7 days in a week. If John goes for a 30-minute jog every other day, how many minutes does he jog in a week?
A: He jogs every other day, so jogs for 7 days / 2 days/jog = 3.5 jogs (round down to 3 whole jogs) Total jog time = Number of jogs * Minutes per jog Total jog time = 3 jogs * 30 minutes/jog = 90 minutes
42. Q: A box of cookies costs $4.25. If Sarah buys 3 boxes, how much does she pay in total?
A: Total cost = Price per box * Number of boxes Total cost = $4.25/box * 3 boxes = $12.75
43. Q: A rectangular pizza measures 35 centimeters long and 20 centimeters wide. What is the area of the pizza? (Area = length x width)
A: Area = 35 cm x 20 cm = 700 square centimeters
44. Q: A recipe requires 1/3 cup of milk for every 1 cup of flour. If Lisa uses 4 cups of flour, how much milk does she need?
A: Milk needed = Flour used x Milk per cup of flour Milk needed = 4 cups * 1/3 cup/cup = 1.33 cups (round down to 1.3 cups)
45. Q: A bag of rice weighs 10 kilograms. How many grams does it weigh? (1 kilogram = 1000 grams)
A: Weight in grams = Weight in kilograms x Conversion rate Weight in grams = 10 kg * 1000 g/kg = 10,000 grams
46. Q: There are 12 months in a year. How many days are there in 3 years? (Consider if it's a leap year or not)
A: Assuming a regular year (not a leap year) with 365 days each: Total days = Days per year x Number of years Total days = 365 days/year * 3 years = 1,095 days
47. Q: A square sheet of paper measures 15 centimeters on each side. What is the perimeter of the square? (Perimeter is the total length of all sides added together)
A: Perimeter of square = Side length x 4 (since all sides contribute to the total distance around the shape) Perimeter = 15 cm x 4 = 60 centimeters
48. Q: Mary has collected 423 stickers. She gives 17 stickers to each of her 5 friends. How many stickers does she have left? (Involves subtraction and multiplication)
A: Stickers
given away = Number of friends * Stickers per friend Stickers given away = 5 friends * 17 stickers/friend = 85 stickers Stickers left = Starting number - Stickers given away Stickers left = 423 stickers - 85 stickers = 338 stickers
49. Q: A rectangular picture frame is 25 centimeters long and 18 centimeters wide. What is the perimeter of the picture frame? (Perimeter is the total length of all sides added together)
A: Perimeter = 2 (length + width) since there are 2 lengths and 2 widths to consider Perimeter = 2 (25 cm + 18 cm) = 86 centimeters
50. Q: A bus can travel 95 kilometers per hour. If it travels for 4 hours, how far does it travel in total?
A: Distance traveled = Speed x Time Distance traveled = 95 kilometers/hour * 4 hours = 380 kilometers
