Mathematics notes, unit 2
Addition, Subtraction, Multiplication and Division
Textbook Mathematics Year 2 (DLP), Part 1 and Part 2 (one combined PDF), pages Part 1, 45–122
What this chapter covers
- You can add two numbers and three numbers within 1 000, with and without regrouping (2.1.1, 2.1.2)
- You can subtract two numbers within 1 000, with and without regrouping, and subtract one number after another (2.2.1, 2.2.2)
- You can show multiplication as equal groups and repeated addition, and say the 0 to 10 times tables (2.3.1, 2.3.2)
- You can share and group to divide, use the division tables, and divide by 1, by 10 and with a remainder (2.4.1, 2.4.2)
- You can complete or make up a story for a number sentence (2.5.1)
- You can solve one-step problems about adding, subtracting, multiplying and dividing (2.5.2)
2.1Adding
To add is to put numbers together. We can add numbers up to 1 000.
Add on a number line
Add in columns
Write the numbers in a column so that ones are under ones, tens under tens and hundreds under hundreds. Always start adding from the ones.
Worked example: 134 + 225
Step 1. Ones: 4 + 5 = 9.Step 2. Tens: 3 + 2 = 5.
Step 3. Hundreds: 1 + 2 = 3.
Step 4. 134 + 225 = 359.
Add with regrouping
When the ones make 10 or more, regroup. Keep the ones and carry the ten to the tens column.
Worked example: 267 + 358
Step 1. Ones: 7 + 8 = 15 ones = 1 ten + 5 ones. Write 5, carry 1 ten.Step 2. Tens: 1 + 6 + 5 = 12 tens = 1 hundred + 2 tens. Write 2, carry 1 hundred.
Step 3. Hundreds: 1 + 2 + 3 = 6.
Step 4. 267 + 358 = 625.
Do not forget the carried ten or hundred. Keep the digits in the right columns: in 82 + 145, the 8 of 82 goes under the tens.
Add three numbers
Add two numbers first, then add the answer to the third. You can also add the ones that make 10 first.
Worked example: 56 + 103 + 220
56 + 103 = 159. Then 159 + 220 = 379.Find 346 + 185.
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Ones: 6 + 5 = 11, write 1 carry 1. Tens: 1 + 4 + 8 = 13, write 3 carry 1. Hundreds: 1 + 3 + 1 = 5. The answer is 531.
Based on the Year 2 textbook, pages 46 to 61.
2.2Subtracting
To subtract is to take away, or to find the difference between two numbers.
Worked example: 349 − 216
Ones: 9 − 6 = 3. Tens: 4 − 1 = 3. Hundreds: 3 − 2 = 1. The answer is 133.Subtract with regrouping
If the top digit is too small, regroup: change 1 from the next place. 1 ten becomes 10 ones. 1 hundred becomes 10 tens.
Worked example: 346 − 185
Step 1. Ones: 6 − 5 = 1.Step 2. Tens: 4 is less than 8. Change 1 hundred to 10 tens: 14 tens − 8 tens = 6 tens. Hundreds left: 2.
Step 3. Hundreds: 2 − 1 = 1.
Step 4. 346 − 185 = 161.
When there is a 0, as in 200 − 153, regroup in two steps: 1 hundred to 10 tens, then 1 ten to 10 ones. Check your answer by adding: 47 + 153 = 200.
Subtract one number after another
Worked example: 289 − 60 − 105
289 − 60 = 229. Then 229 − 105 = 124.Check subtraction with addition. 124 + 105 + 60 = 289, so the answer is right.
Find 502 − 138.
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Regroup: 502 is 4 hundreds, 9 tens and 12 ones. 12 − 8 = 4, 9 − 3 = 6, 4 − 1 = 3. The answer is 364. Check: 364 + 138 = 502.
Based on the Year 2 textbook, pages 62 to 75.
2.3Multiplying
Multiplication is repeated addition of equal groups. The sign is ×. 3 × 2 means 3 groups of 2.
The order does not change the answer. 2 × 4 = 4 × 2 = 8.
Times tables
Build a times table by counting on. The 3 times table is 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
| Table | Counting on |
|---|---|
| 2 | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 |
| 5 | 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 |
| 9 | 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 |
| 10 | 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 |
Any number × 1 = the number itself (7 × 1 = 7). Any number × 0 = 0 (7 × 0 = 0).
In the 9 times table the digits of each answer add up to 9: 18 (1 + 8), 27 (2 + 7), 36 (3 + 6).
What is 6 × 4? Write it as an addition too.
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6 × 4 = 24. As addition: 4 + 4 + 4 + 4 + 4 + 4 = 24.
Based on the Year 2 textbook, pages 81 to 94.
2.4Dividing
Division is sharing equally or putting things into equal groups. The sign is ÷. 6 ÷ 3 = 2 means 6 shared among 3 gives 2 each.
Division is the opposite of multiplication. Because 6 × 3 = 18, we know 18 ÷ 3 = 6 and 18 ÷ 6 = 3. Use the times tables to divide.
Special cases
- Any number ÷ 1 = the number itself: 3 ÷ 1 = 3.
- A number ÷ 10: 30 ÷ 10 = 3 (3 groups of ten).
- 0 ÷ any number = 0: 0 ÷ 4 = 0. We cannot divide by 0.
Division with a remainder
Worked example: 20 ÷ 6
Step 1. From the 6 times table: 3 × 6 = 18 (4 × 6 = 24 is too big).Step 2. 20 − 18 = 2 left over.
Step 3. 20 ÷ 6 = 3 remainder 2.
The remainder must always be smaller than the number you divide by. If your remainder is 6 or more when dividing by 6, you can still make another group.
What is 47 ÷ 7?
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6 × 7 = 42 and 47 − 42 = 5. So 47 ÷ 7 = 6 remainder 5.
Based on the Year 2 textbook, pages 95 to 115.
2.5Stories and problems
Every number sentence can tell a story. 3 × 5 = 15 can be: "There are 3 vases and each has 5 flowers, so there are 15 flowers."
To solve a problem, follow four steps.
- Read and find the important numbers.
- Decide whether to add, subtract, multiply or divide.
- Write the number sentence and work it out.
- Write the answer with the unit, then check it.
Worked example
50 pupils go to a museum. A van carries 10 pupils. How many vans are needed?50 ÷ 10 = 5 vans.
Words that help: "altogether" and "total" mean add or multiply; "left" and "difference" mean subtract; "shared equally" and "put into equal groups" mean divide. "Each" tells you the size of one group, so read the whole question before you decide.
Arif buys 4 packets of biscuits. Each has 8 biscuits. How many biscuits?
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4 × 8 = 32 biscuits.
Based on the Year 2 textbook, pages 76 to 80 and 116 to 122.
Summary
- Add and subtract in columns, starting from the ones. Regroup when ones or tens are not enough or reach 10.
- Check subtraction with addition.
- 3 × 2 means 3 groups of 2. The order does not matter: 2 × 4 = 4 × 2.
- Any number × 1 is itself and any number × 0 is 0.
- Division is sharing equally and is the opposite of multiplication.
- The remainder is always smaller than the number you divide by.