Basic 7 · Mathematics · Number Operations
Adding, Subtracting, Multiplying and Dividing Multi-Digit Numbers
In this topic you will add and subtract numbers of up to four digits and beyond with regrouping, check answers by estimation and inverse operations, and multiply and divide multi-digit numbers by one- and two-digit numbers.
By the end of these notes you should be able to:
- Add multi-digit numbers with regrouping and check by estimation
- Subtract multi-digit numbers with regrouping and check using addition
- Multiply and divide multi-digit numbers by 1- and 2-digit numbers
What you already know
- Place value and mental strategies
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
- Number Operations
- Indicator
- B7.1.2.2.1 – Add and subtract up to four-digit numbers
Introduction
Adding prices at the market, totalling school fees or counting votes all need accurate addition. With larger numbers, we line up digits by place value and regroup when necessary.
1. Column Addition
Write the numbers one below the other so that ones are under ones, tens under tens and so on. Add from the right (the ones column). If a column adds up to 10 or more, write the ones digit and carry the tens digit to the next column. This is called regrouping.
Add with regrouping
Calculate 4,786 + 3,659.
- Ones: 6 + 9 = 15; write 5, carry 1.
- Tens: 8 + 5 + 1 = 14; write 4, carry 1.
- Hundreds: 7 + 6 + 1 = 14; write 4, carry 1.
- Thousands: 4 + 3 + 1 = 8.
Answer: 8,445
2. Checking by Estimation
Round each number to the nearest thousand: 5,000 + 4,000 = 9,000. The answer 8,445 is close to 9,000, so it is reasonable. If you had got 84,450 or 845, the estimate would show that something was wrong.
3. Adding Three or More Numbers
Add three numbers
A school collected GH₵2,465 in Term 1, GH₵3,078 in Term 2 and GH₵1,987 in Term 3. Find the total.
- 2,465 + 3,078 = 5,543.
- 5,543 + 1,987 = 7,530.
- Estimate: 2,000 + 3,000 + 2,000 = 7,000; the answer is reasonable.
Answer: GH₵7,530
4. Common Mistakes
The most common errors are forgetting to carry and misaligning digits. Write neatly in columns, and write small carried digits clearly above the next column. When adding decimals, line up the decimal points.
New words
- regrouping
- Exchanging 10 ones for 1 ten, and so on, when adding or subtracting.
- carry
- To move a tens digit to the next column in addition.
- column
- A vertical line of digits with the same place value.
- sum
- The answer to an addition.
Summary
- Line up digits by place value and add from the ones column, carrying when a column total is 10 or more.
- Estimate first to check whether the answer is reasonable.
- Keep columns neat and line up decimal points when adding decimals.
Class activity: Market Totals
- Use cedi play notes to model the cost of four items from a market price list.
- Add the prices using column addition.
- Check the total by estimation.
You need: Bottle tops, Ghana cedi play notes, Number cards
Exercises
Answer in your exercise book first, then check your answers.
1. 2,345 + 1,234 =
- A. 3,579
- B. 3,569
- C. 3,479
- D. 4,579
Show answer
Answer: 3,579No regrouping.2. 5,678 + 2,945 =
- A. 8,623
- B. 8,523
- C. 7,623
- D. 8,613
Show answer
Answer: 8,623With regrouping.3. Addition starts from the ones column.
- A. True
- B. False
Show answer
Answer: TrueRight to left.4. The answer to an addition is the ______.
Show answer
Answer: sumTotal.5. Estimate and then calculate 3,987 + 4,026.
Show answer
Answer: Estimate 4,000 + 4,000 = 8,000; exact 8,013.Estimate then add.6. Explain why lining up digits by place value is important.
Show answer
Answer: Only digits of the same place value can be added together; misaligning gives wrong answers.Place value.
Lesson 2
- Strand
- Number
- Sub-strand
- Number Operations
- Indicator
- B7.1.2.2.1 – Add and subtract up to four-digit numbers
Introduction
Finding change, working out a difference in population or calculating how much is left all need subtraction. When a digit on top is smaller, we regroup by borrowing from the next place.
1. Column Subtraction with Regrouping
Subtract with regrouping
Calculate 7,302 − 4,568.
- Ones: 2 − 8 cannot be done; tens is 0, so regroup from hundreds: 3 hundreds become 2 hundreds and 10 tens.
- Now regroup 1 ten: 9 tens and 12 ones. 12 − 8 = 4.
- Tens: 9 − 6 = 3.
- Hundreds: 2 − 5 cannot be done; regroup 1 thousand: 12 − 5 = 7, leaving 6 thousands.
- Thousands: 6 − 4 = 2.
Answer: 2,734
2. Checking by Addition
Subtraction and addition are inverse operations. To check 7,302 − 4,568 = 2,734, add 2,734 + 4,568. If you get 7,302, the answer is correct.
3. Subtracting from Numbers with Zeros
Subtract from a round number
Calculate 5,000 − 2,763.
- Regroup: 5,000 = 4 thousands, 9 hundreds, 9 tens and 10 ones.
- Ones: 10 − 3 = 7; tens: 9 − 6 = 3; hundreds: 9 − 7 = 2; thousands: 4 − 2 = 2.
Answer: 2,237
4. Word Problems
Population difference
Town A has 8,450 people and Town B has 5,875 people. How many more people live in Town A?
- 8,450 − 5,875.
- Ones: 0 − 5, regroup: 10 − 5 = 5. Tens: 4 − 1 = 3, 3 − 7, regroup: 13 − 7 = 6. Hundreds: 4 − 1 = 3, 3 − 8, regroup: 13 − 8 = 5. Thousands: 8 − 1 = 7, 7 − 5 = 2.
Answer: 2,575 more people
New words
- difference
- The answer to a subtraction.
- inverse operation
- An operation that undoes another, such as addition and subtraction.
- regroup (borrow)
- Exchange 1 from a higher place for 10 in the next lower place.
- minuend
- The number you subtract from.
Summary
- Subtract from the ones column, regrouping when the top digit is smaller.
- Check subtraction by adding the answer to the number subtracted.
- Numbers with zeros may need regrouping across several places.
Class activity: Subtraction Check
- Each partner writes three subtraction problems with four-digit numbers.
- Swap and solve.
- Check each answer by addition.
You need: Bottle tops, Ghana cedi play notes, Number cards
Exercises
Answer in your exercise book first, then check your answers.
1. 6,875 − 2,431 =
- A. 4,444
- B. 4,344
- C. 4,454
- D. 3,444
Show answer
Answer: 4,444No regrouping.2. 4,000 − 1,357 =
- A. 2,643
- B. 2,743
- C. 3,643
- D. 2,653
Show answer
Answer: 2,643Regroup across zeros.3. Subtraction can be checked by addition.
- A. True
- B. False
Show answer
Answer: TrueInverse operations.4. The answer to a subtraction is the ______.
Show answer
Answer: differenceWhat is left.5. Calculate 9,213 − 5,678 and check by addition.
Show answer
Answer: 3,535; 3,535 + 5,678 = 9,213.Check.6. Esi had GH₵2,500. She paid GH₵1,345 for fees and GH₵387 for books. How much is left?
Show answer
Answer: GH₵768 (2,500 − 1,345 = 1,155; 1,155 − 387 = 768).Two steps.
Lesson 3
- Strand
- Number
- Sub-strand
- Number Operations
- Indicator
- B7.1.2.2.2 – Multiply or divide multi-digit numbers by 1- and 2-digit numbers
Introduction
A farmer packs 1,248 oranges into bags of 24. How many bags? A trader buys 36 sacks of rice at GH₵485 each. What is the cost? Long multiplication and division solve such problems.
1. Multiplying by a 2-Digit Number
Long multiplication
Calculate 485 × 36.
- 485 × 6 = 2,910.
- 485 × 30 = 14,550.
- Add: 2,910 + 14,550 = 17,460.
Answer: 17,460
2. Short Division by a 1-Digit Number
Short division
Calculate 5,736 ÷ 8.
- 57 ÷ 8 = 7 remainder 1.
- 13 ÷ 8 = 1 remainder 5.
- 56 ÷ 8 = 7.
Answer: 717
3. Long Division by a 2-Digit Number
Long division
Calculate 1,248 ÷ 24.
- 24 into 124: 24 × 5 = 120, remainder 4.
- Bring down 8: 48.
- 24 into 48: 2.
Answer: 52 bags
4. Remainders in Real Life
Sometimes division leaves a remainder. If 1,250 oranges are packed into bags of 24, then 1,250 ÷ 24 = 52 remainder 2. There are 52 full bags and 2 oranges left over. Depending on the question, we may give the remainder, round up (if every orange must be packed, 53 bags are needed), or ignore it.
5. Checking Multiplication and Division
Multiplication and division are inverse operations. Check 1,248 ÷ 24 = 52 by multiplying 52 × 24 = 1,248. Estimation also helps: 485 × 36 is about 500 × 40 = 20,000, so 17,460 is reasonable.
New words
- product
- The answer to a multiplication.
- quotient
- The answer to a division.
- remainder
- The amount left over after division.
- long division
- A method of dividing by larger numbers in steps.
Summary
- Multiply by a 2-digit number by multiplying by the ones and the tens separately and adding.
- Divide using short division for 1-digit divisors and long division for 2-digit divisors.
- Interpret remainders sensibly and check by the inverse operation.
Class activity: Packing Problems
- Use bottle tops to model sharing 156 items into groups of 12.
- Solve three packing and buying problems using long multiplication and division.
- Check answers using 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. 234 × 3 =
- A. 702
- B. 692
- C. 712
- D. 602
Show answer
Answer: 702Short multiplication.2. 2,436 ÷ 12 =
- A. 203
- B. 213
- C. 230
- D. 302
Show answer
Answer: 203Long division.3. The answer to a division is called the quotient.
- A. True
- B. False
Show answer
Answer: TrueDivision result.4. The amount left over after division is the ______.
Show answer
Answer: remainderLeftover.5. Calculate 367 × 24.
Show answer
Answer: 8,808 (367 × 4 = 1,468; 367 × 20 = 7,340).Long multiplication.6. 500 learners are to be seated at tables of 12. How many tables are needed? Explain.
Show answer
Answer: 42 tables; 500 ÷ 12 = 41 remainder 8, so one more table is needed for the 8 learners.Round up.
Homework
- Solve three addition, three subtraction and three multiplication or division problems from your daily life.