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Basic 8 · Mathematics · Addition and Subtraction

Adding, Subtracting, Multiplying and Dividing Large Numbers

In this topic you will add and subtract numbers with more than four digits and multiply and divide multi-digit numbers by 2- and 3-digit numbers.

By the end of these notes you should be able to:

  • Add numbers with more than four digits
  • Subtract numbers with more than four digits
  • Multiply and divide multi-digit numbers by 2- and 3-digit numbers

What you already know

  • Operations on multi-digit numbers (Basic 7)

Copy everything that has a blue line on its left into your notebook. The other parts are for reading.

Lesson 1

Strand
Number
Sub-strand
Addition and Subtraction
Indicator
B8.1.2.2.1 – Add and subtract more than four-digit numbers

Introduction

A company adds up monthly sales. A district adds up votes. Adding large numbers accurately is a basic but vital skill.

1. Column Addition

Add

Calculate 3,478,926 + 1,852,387.

  1. Ones: 6 + 7 = 13; write 3, carry 1.
  2. Tens: 2 + 8 + 1 = 11; write 1, carry 1.
  3. Hundreds: 9 + 3 + 1 = 13; write 3, carry 1.
  4. Thousands: 8 + 2 + 1 = 11; write 1, carry 1.
  5. Ten thousands: 7 + 5 + 1 = 13; write 3, carry 1.
  6. Hundred thousands: 4 + 8 + 1 = 13; write 3, carry 1.
  7. Millions: 3 + 1 + 1 = 5.

Answer: 5,331,313

2. Estimating First

Estimate 3,500,000 + 1,900,000 = 5,400,000. The exact answer, 5,331,313, is close, so it is reasonable. If you had 53,313,130, the estimate would show a mistake.

Ballot boxes being counted at an election
Figure 1: Counting votes Add the votes for three candidates in a made-up election.

3. Adding in Context

Votes

In an election, three candidates received 1,245,673, 987,450 and 342,108 votes. Find the total votes.

  1. 1,245,673 + 987,450 = 2,233,123.
  2. 2,233,123 + 342,108 = 2,575,231.

Answer: 2,575,231 votes

4. Properties for Checking

Addition is commutative, so you can check by adding in a different order: 342,108 + 987,450 + 1,245,673 should give the same total. Writing digits neatly in columns prevents most mistakes. Use graph paper if your columns tend to slip.

5. Why Large Numbers Matter

National budgets, population figures and company accounts all use numbers in the millions and billions. A small slip in one column can mean thousands of cedis, so accountants check their totals more than once.

New words

sum
The answer to an addition.
carry
To move a digit to the next column.
column
A vertical line of digits.
estimate
An approximate answer.

Summary

  • Line up digits by place value and add from the right, carrying as needed.
  • Estimate first and check by adding in a different order.
  • Neat columns prevent errors.

Class activity: Votes Addition

  1. Use made-up election results for four constituencies.
  2. Add the votes for each candidate.
  3. Check by estimating and by adding in another order.

You need: Bottle tops, Ghana cedi play notes, Number cards

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. 1,200,000 + 3,400,000 =

    • A. 4,600,000
    • B. 4,500,000
    • C. 2,200,000
    • D. 46,000,000
    Show answer
    Answer: 4,600,000Add.

  2. 2. 456,789 + 123,456 =

    • A. 580,245
    • B. 570,245
    • C. 580,135
    • D. 579,245
    Show answer
    Answer: 580,245Carrying.

  3. 3. Addition can be checked by adding in another order.

    • A. True
    • B. False
    Show answer
    Answer: TrueCommutative.

  4. 4. The answer to an addition is the ______.

    Show answer
    Answer: sumTotal.

  5. 5. Calculate 2,345,678 + 4,567,890.

    Show answer
    Answer: 6,913,568Column addition.

  6. 6. Estimate and then calculate 7,895,432 + 2,104,568.

    Show answer
    Answer: Estimate 10,000,000; exact 10,000,000.Estimate.

Lesson 2

Strand
Number
Sub-strand
Addition and Subtraction
Indicator
B8.1.2.2.1 – Add and subtract more than four-digit numbers

Introduction

Subtraction tells us how much is left, how far apart two numbers are or how much more one thing is than another.

1. Column Subtraction

Subtract

Calculate 6,000,450 − 2,873,186.

  1. Ones: 0 − 6; regroup from tens: 10 − 6 = 4.
  2. Tens: 5 tens lent one, leaving 4; 4 − 8 needs regrouping from the hundreds: 14 − 8 = 6.
  3. Hundreds: 4 lent one, leaving 3; 3 − 1 = 2.
  4. Thousands: 0 − 3; regroup across the zeros from the millions: 10 − 3 = 7.
  5. Ten thousands: 9 − 7 = 2.
  6. Hundred thousands: 9 − 8 = 1.
  7. Millions: 6 lent one, leaving 5; 5 − 2 = 3.

Answer: 3,127,264

2. Checking with Addition

Check by adding: 3,127,264 + 2,873,186 = 6,000,450. This matches the original number, so the answer is correct.

A bank teller counting money at a counter
Figure 2: At the bank Write a subtraction problem about a bank balance.

3. Subtraction in Context

Balance

A company had GH₵9,250,000 in its account and paid out GH₵3,475,500 in salaries and GH₵1,280,750 for materials. Find the balance.

  1. Total paid: 3,475,500 + 1,280,750 = 4,756,250.
  2. Balance: 9,250,000 − 4,756,250 = 4,493,750.

Answer: GH₵4,493,750

4. Adding on as Another Method

To find 5,000,000 − 3,764,500 mentally, add on from the smaller number: 3,764,500 + 235,500 = 4,000,000, and 4,000,000 + 1,000,000 = 5,000,000. So the difference is 235,500 + 1,000,000 = 1,235,500. This is how traders often give change.

5. Finding the Missing Number

Subtraction also finds missing numbers. If a school needs 2,500,000 bricks and has 1,750,000, the shortage is 750,000. Writing the problem as 1,750,000 + ? = 2,500,000 shows why adding on and subtracting give the same result.

New words

difference
The answer to a subtraction.
regroup
To exchange one in a higher place for ten in the next.
balance
The amount left in an account.
adding on
Finding a difference by counting up.

Summary

  • Subtract from the right, regrouping across zeros where needed.
  • Check by adding the answer to the number subtracted.
  • Adding on is a useful mental method.

Class activity: Bank Balance

  1. Start with a balance of GH₵5,000,000.
  2. Make five withdrawals and deposits.
  3. Calculate the final balance and check.

You need: Bottle tops, Ghana cedi play notes, Number cards

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. 5,000,000 − 2,000,000 =

    • A. 3,000,000
    • B. 7,000,000
    • C. 2,000,000
    • D. 300,000
    Show answer
    Answer: 3,000,000Subtract.

  2. 2. 8,300,000 − 4,750,000 =

    • A. 3,550,000
    • B. 4,550,000
    • C. 3,450,000
    • D. 3,650,000
    Show answer
    Answer: 3,550,000Regrouping.

  3. 3. Subtraction can be checked by addition.

    • A. True
    • B. False
    Show answer
    Answer: TrueInverse.

  4. 4. The answer to a subtraction is the ______.

    Show answer
    Answer: differenceResult.

  5. 5. Calculate 7,200,500 − 3,450,750.

    Show answer
    Answer: 3,749,750Regroup.

  6. 6. A school had 12,500 books and gave away 3,275 and bought 1,840. How many now?

    Show answer
    Answer: 11,065Two steps.

Lesson 3

Strand
Number
Sub-strand
Multiplication and Division
Indicator
B8.1.2.2.2 – Multiply or divide multi-digit numbers by 2- and 3-digit numbers

Introduction

A farmer sells 4,250 bags at GH₵385 each. A company shares GH₵7,560,000 among 125 workers. These are jobs for long multiplication and long division.

1. Long Multiplication

Multiply

Calculate 4,250 × 385.

  1. 4,250 × 5 = 21,250.
  2. 4,250 × 80 = 340,000.
  3. 4,250 × 300 = 1,275,000.
  4. Add: 21,250 + 340,000 + 1,275,000.

Answer: 1,636,250

2. Long Division

Divide

Calculate 7,560 ÷ 36.

  1. 36 into 75: 2, remainder 3.
  2. Bring down 6: 36 into 36 is 1.
  3. Bring down 0: 36 into 0 is 0.

Answer: 210

Divide by a 3-digit number

Calculate 45,756 ÷ 123.

  1. 123 into 457: 3 (369), remainder 88.
  2. Bring down 5: 885; 123 × 7 = 861, remainder 24.
  3. Bring down 6: 246; 123 × 2 = 246, remainder 0.

Answer: 372

Workers loading bags onto a truck
Figure 3: Loading bags Write a multiplication problem about bags of produce.

3. Estimating to Check

4,250 × 385 is about 4,000 × 400 = 1,600,000, close to the exact answer. 45,756 ÷ 123 is about 45,000 ÷ 100 = 450 or 48,000 ÷ 120 = 400, so an answer near 372 is reasonable. Estimation catches errors in place value.

4. Remainders

In real problems, think about what the remainder means. If 1,000 learners travel in buses with 45 seats, 1,000 ÷ 45 = 22 remainder 10. So 23 buses are needed, because the 10 learners must also travel.

5. Choosing an Efficient Method

Look for shortcuts before starting. 4,250 × 400 is 1,700,000, so 4,250 × 385 is that amount less 4,250 × 15. Dividing both numbers by a common factor also helps: 7,560 ÷ 36 is the same as 1,260 ÷ 6, which is 210.

New words

product
The answer to a multiplication.
quotient
The answer to a division.
remainder
What is left after dividing.
long division
A step-by-step way to divide.

Summary

  • Multiply by each digit in turn and add the results.
  • Divide step by step, bringing down digits.
  • Estimate to check and interpret remainders sensibly.

Class activity: Long Calculations

  1. Each partner writes two multiplications and two divisions.
  2. Swap and solve them.
  3. Check by the inverse operation.

You need: Bottle tops, Ghana cedi play notes, Number cards

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. 325 × 12 =

    • A. 3,900
    • B. 3,250
    • C. 390
    • D. 4,000
    Show answer
    Answer: 3,900Long multiplication.

  2. 2. 8,640 ÷ 72 =

    • A. 120
    • B. 12
    • C. 1,200
    • D. 80
    Show answer
    Answer: 120Long division.

  3. 3. The answer to a division is the quotient.

    • A. True
    • B. False
    Show answer
    Answer: TrueDivision.

  4. 4. What is left after dividing is the ______.

    Show answer
    Answer: remainderLeftover.

  5. 5. Calculate 2,345 × 67.

    Show answer
    Answer: 157,1152,345 × 60 + 2,345 × 7.

  6. 6. 2,000 learners are to travel in buses with 48 seats. How many buses are needed?

    Show answer
    Answer: 42 buses; 2,000 ÷ 48 = 41 remainder 32.Round up.

Homework

  1. Solve five addition, subtraction, multiplication and division problems with large numbers.
Adding, Subtracting, Multiplying and Dividing Large Numbers – Basic 8 Mathematics Notes | sirbus