Working with Whole Numbers

Mastering addition, subtraction, multiplication, and division.

What are Whole Numbers & Basic Operations?

Whole numbers are the basic counting numbers starting from 0. They are 0, 1, 2, 3, 4, and so on, without any fractions or decimals.

In mathematics, we perform several basic operations with whole numbers:

Whole Number Operations: Examples

Addition (+)

Problem: Add 187 and 56.

We can use the column method, aligning numbers by place value:

187 + 56 ----- 243
  1. Start from the rightmost column (units): 7 + 6 = 13. Write down 3, carry over 1 to the tens column.
  2. Tens column: 8 + 5 + 1 (carried) = 14. Write down 4, carry over 1 to the hundreds column.
  3. Hundreds column: 1 + 1 (carried) = 2. Write down 2.

Answer: 243

Subtraction (-)

Problem: Subtract 67 from 245.

Using the column method with borrowing (regrouping):

245 (becomes 2 3 ¹5) - 67 (becomes 6 7) ----- 178
  1. Units column: 5 - 7. We can't do this, so borrow 1 ten from the 4 tens (making it 3 tens). The 5 units become 15 units. Now, 15 - 7 = 8.
  2. Tens column: We have 3 tens left. 3 - 6. Again, borrow 1 hundred from the 2 hundreds (making it 1 hundred). The 3 tens become 13 tens. Now, 13 - 6 = 7.
  3. Hundreds column: We have 1 hundred left. 1 - 0 = 1.

Answer: 178

Multiplication (×)

Problem: Multiply 56 by 23.

Using long multiplication:

56 × 23 ----- 168 (56 × 3) 1120 (56 × 20) ----- 1288
  1. Multiply 56 by the units digit of 23 (which is 3): 56 × 3 = 168.
  2. Multiply 56 by the tens digit of 23 (which is 2, representing 20): 56 × 20 = 1120. (Write a 0 in the units place as a placeholder).
  3. Add the results: 168 + 1120 = 1288.

Answer: 1288

Division (÷)

Problem: Divide 137 by 5.

Using long division (bus stop method):

27 r 2 _______ 5 | 137 -10 ↓ (5 × 2 = 10) --- 37 -35 (5 × 7 = 35) --- 2 (Remainder)
  1. How many times does 5 go into 1? 0. So, look at 13.
  2. How many times does 5 go into 13? It goes 2 times (5 × 2 = 10). Write 2 above the 3.
  3. Subtract 10 from 13: 13 - 10 = 3.
  4. Bring down the next digit (7) to make 37.
  5. How many times does 5 go into 37? It goes 7 times (5 × 7 = 35). Write 7 above the 7.
  6. Subtract 35 from 37: 37 - 35 = 2. This is the remainder.

Answer: 27 with a remainder of 2 (or 27 r 2)

Test Your Whole Number Skills!

1. Add: 348 + 175 = ?

Answer: 523

Explanation: Use column addition with carrying.

2. Subtract: 503 - 267 = ?

Answer: 236

Explanation: Use column subtraction with borrowing.

3. Multiply: 64 × 7 = ?

Answer: 448

Explanation: (4×7=28, write 8 carry 2. 6×7=42, +2=44).

4. Divide: 96 ÷ 8 = ?

Answer: 12

Explanation: 8 goes into 9 once (remainder 1). 8 goes into 16 twice.

Exam-Style Whole Number Problems

1. A builder is ordering materials. He needs 1500 bricks. Bricks are sold in pallets of 500. Each pallet costs £250. He also needs 12 bags of cement, and each bag costs £5. What is the total cost of the bricks and cement?

Answer: £810

Explanation:

  1. Calculate the number of pallets of bricks needed: 1500 bricks ÷ 500 bricks/pallet = 3 pallets. (Division)
  2. Calculate the total cost of the bricks: 3 pallets × £250/pallet = £750. (Multiplication)
  3. Calculate the total cost of the cement: 12 bags × £5/bag = £60. (Multiplication)
  4. Calculate the total cost of materials: £750 (bricks) + £60 (cement) = £810. (Addition)

2. A school is taking 125 students on a trip. Each bus can hold 48 students.
a) How many buses are needed for the trip?
b) If each bus costs £180 to hire, what is the total cost of hiring the buses?
c) If the school has a budget of £600 for transport, how much money will be left over or how much more money is needed?

Answers:

a) 3 buses

b) £540

c) £60 left over

Explanation:

a) Number of buses needed:

  1. Divide the total number of students by the bus capacity: 125 students ÷ 48 students/bus = 2.604.... (Division)
  2. Since you can't have a fraction of a bus and all students must go, round up to the next whole number. So, 3 buses are needed.

b) Total cost of hiring buses:

  1. Multiply the number of buses by the cost per bus: 3 buses × £180/bus = £540. (Multiplication)

c) Money left over or needed:

  1. Subtract the total bus cost from the budget: £600 (budget) - £540 (cost) = £60. (Subtraction)
  2. Since the result is positive, there is £60 left over.

3. Jane earns £12 per hour and works 35 hours a week. Her weekly deductions for tax and national insurance total £85.
a) How much does Jane earn in a week before deductions?
b) How much is her take-home pay per week after deductions?
c) If she saves £50 each week from her take-home pay, how much will she have saved after 4 weeks?

Answers:

a) £420

b) £335

c) £200

Explanation:

a) Earnings before deductions:

  1. Multiply hourly rate by hours worked: £12/hour × 35 hours = £420. (Multiplication)

b) Take-home pay after deductions:

  1. Subtract total deductions from gross earnings: £420 - £85 = £335. (Subtraction)

c) Savings after 4 weeks:

  1. Multiply weekly savings by the number of weeks: £50/week × 4 weeks = £200. (Multiplication)

Interactive Tool: Solve the Sum!

Calculate the answer to the problem shown below.

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Key Whole Number Facts