Step-by-step Maths Level 4: Adding, subtracting, times tables and division

Method. Change only the column that matches the number you add or take away.

1. Find the thousand digit in 9327. Only the thousand column changes, because 1000 is 1 thousands.
   9327 has 9 thousands
2. Take away 1 thousands. Change that digit only. The other digits stay the same.
   9 - 1 = 8
3. Write the answer. Check that the other digits are the same.
   8327

Check. Check: 8327 + 1000 = 9327.

Watch out. Adding or taking away a friendly number changes only one column, when no carry or exchange is needed.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

1. Subtract the ones column. Take the bottom digit from the top digit.
   4 - 2 = 2
2. Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.
   thousands: 8 to 7; hundreds: 0 to 10
3. Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.
   hundreds: 10 to 9; tens: 0 to 10
4. Subtract the tens column. Take the bottom digit from the top digit.
   10 - 2 = 8
5. Subtract the hundreds column. Take the bottom digit from the top digit.
   9 - 4 = 5
6. Subtract the thousands column. Take the bottom digit from the top digit.
   7 - 3 = 4
7. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   4582

Check. Check: 4582 + 3422 = 8004.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Method. Count in 9s to find 9 groups of 1. The order of the two numbers does not matter.

1. Count in 9s, 1 times. Each count adds one more group of 9.
   9
2. The last number we said is the answer. We counted in equal groups.
   9 × 1 = 9
3. Write the answer. The order of the numbers does not change the answer.
   9

Check. Check: 1 × 9 is also 9.

Watch out. Say the 9 times table in order until you reach the fact you need.

Method. Division can find how many equal groups fit. Count the groups in steps of the group size.

1. Think of the division: 30 ÷ 3. Each bag holds the same number, so count how many groups of this size there are.
   30 ÷ 3 = ___
2. Count in 3s until you reach 30. Count one bag at a time.
   3, 6, 9, 12, 15, 18, 21, 24, 27, 30
3. Write the answer. This is the number of bags.
   10

Check. Check: 10 bags of 3 is 30.

Watch out. Count the groups, not the number in each group.

Method. Count in 3s to find 3 groups of 1. The order of the two numbers does not matter.

1. Count in 3s, 1 times. Each count adds one more group of 3.
   3
2. The last number we said is the answer. We counted in equal groups.
   3 × 1 = 3
3. Write the answer. The order of the numbers does not change the answer.
   3

Check. Check: 1 × 3 is also 3.

Watch out. Say the 3 times table in order until you reach the fact you need.

Method. Count in 3s to find 3 groups of 8. The order of the two numbers does not matter.

1. Count in 3s, 8 times. Each count adds one more group of 3.
   3, 6, 9, 12, 15, 18, 21, 24
2. The last number we said is the answer. We counted in equal groups.
   3 × 8 = 24
3. Write the answer. The order of the numbers does not change the answer.
   24

Check. Check: 8 × 3 is also 24.

Watch out. Say the 3 times table in order until you reach the fact you need.

Method. Subtract one number from the total. If the check is right, you get the other number.

1. Use the inverse. Subtracting the second number should give back the first.
   8540 - 2332
2. Work out the difference. If the sum is right, this matches the first number.
   8540 - 2332 = 6208
3. Write the check. The check is correct because it gives the first number.
   8540 - 2332 = 6208

Check. Check: 6208 + 2332 = 8540, so the subtraction works both ways.

Watch out. A subtraction can check an addition. Use the inverse operation to check your answer.

Method. Change only the column that matches the number you add or take away.

1. Find the ten digit in 7646. Only the ten column changes, because 40 is 4 tens.
   7646 has 4 tens
2. Add 4 tens. Change that digit only. The other digits stay the same.
   4 + 4 = 8
3. Write the answer. Check that the other digits are the same.
   7686

Check. Check: 7686 - 40 = 7646.

Watch out. Adding or taking away a friendly number changes only one column, when no carry or exchange is needed.

Method. Grouping: count how many groups of the size you are given can be made from the total.

1. Count in 5s until you reach 35. Each bag takes 5. Count one bag at a time.
   5, 10, 15, 20, 25, 30, 35
2. Count the bags. Each count is one full bag of 5.
   7 bags
3. Write the answer. This is the number of bags.
   7

Check. Check: 7 × 5 = 35.

Watch out. In grouping, you are given the size of each group and you find the number of groups.

Method. Swap the numbers round. The total stays the same.

1. Work out the first fact: 3 × 4. This tells us the total.
   3 × 4 = 12
2. Swap the two numbers round. The order of the numbers in a multiplication does not change the answer.
   4 × 3 = 12
3. Write the missing number. It is the number that moved to the front.
   4

Check. Check: 3 × 4 and 4 × 3 are both 12.

Watch out. Multiplication works in any order, but division does not: 12 ÷ 3 is not the same as 3 ÷ 12.

Method. Grouping: count how many groups of the size you are given can be made from the total.

1. Count in 4s until you reach 32. Each bag takes 4. Count one bag at a time.
   4, 8, 12, 16, 20, 24, 28, 32
2. Count the bags. Each count is one full bag of 4.
   8 bags
3. Write the answer. This is the number of bags.
   8

Check. Check: 8 × 4 = 32.

Watch out. In grouping, you are given the size of each group and you find the number of groups.

Method. Add column by column, starting with the ones. Carry any ten to the next column on the left.

1. Add the ones column. Add the digits, and the carried 1 if there is one.
   7 + 3 = 10: Write 0 and carry 1 to the next column.
2. Add the tens column. Add the digits, and the carried 1 if there is one.
   2 + 8 + 1 = 11: Write 1 and carry 1 to the next column.
3. Add the hundreds column. Add the digits, and the carried 1 if there is one.
   2 + 2 + 1 = 5: Write 5. There is nothing to carry.
4. Add the thousands column. Add the digits, and the carried 1 if there is one.
   6 + 2 = 8: Write 8. There is nothing to carry.
5. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   8510

Check. Check: 8510 - 2283 = 6227.

Watch out. Do not forget the carried 1 in the next column. Write the carried 1 small above the column.

Method. An array shows equal groups. Divide the total by the number of rows to find the number in each row.

1. Read the array. The dots are in equal rows.
   4 rows, 28 dots
2. Share the dots into the rows. Each row has the same number of dots.
   28 ÷ 4 = 7
3. Check with multiplication. Rows × dots in each row gives the total.
   4 × 7 = 28
4. Write the answer. This is the number in each row.
   7

Check. Check: 4 rows of 7 make 28.

Watch out. The number of rows is the divisor. Each row is one equal group.

Method. Use the 9 pattern. The digits of each answer add to 9.

1. Find the tens digit. Take 1 from the number you multiply by 9.
   4 - 1 = 3
2. Find the ones digit. The two digits must add to 9.
   9 - 3 = 6
3. Write the answer. Put the tens digit and the ones digit together.
   36

Check. Check: 3 + 6 = 9, and 36 is 9 × 4.

Watch out. The digits always add to 9 in the 9 times table, up to 9 × 10.

Method. Count in 9s to find 9 groups of 9. The order of the two numbers does not matter.

1. Count in 9s, 9 times. Each count adds one more group of 9.
   9, 18, 27, 36, 45, 54, 63, 72, 81
2. The last number we said is the answer. We counted in equal groups.
   9 × 9 = 81
3. Write the answer. The order of the numbers does not change the answer.
   81

Check. Check: 9 × 9 is also 81.

Watch out. Say the 9 times table in order until you reach the fact you need.

Method. Add column by column, starting with the ones. Carry any ten to the next column on the left.

1. Add the ones column. Add the digits, and the carried 1 if there is one.
   3 + 5 = 8: Write 8. There is nothing to carry.
2. Add the tens column. Add the digits, and the carried 1 if there is one.
   4 + 6 = 10: Write 0 and carry 1 to the next column.
3. Add the hundreds column. Add the digits, and the carried 1 if there is one.
   2 + 4 + 1 = 7: Write 7. There is nothing to carry.
4. Add the thousands column. Add the digits, and the carried 1 if there is one.
   5 + 1 = 6: Write 6. There is nothing to carry.
5. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
   6708

Check. Check: 6708 - 1465 = 5243.

Watch out. Do not forget the carried 1 in the next column. Write the carried 1 small above the column.