Award in Mathematics -
Number and Measure (Level 1)
Topic 4: Calculating with integers
The following questions are typical at Level 1. The written methods shown here are recommended, but you may know and use other methods. What is important is that you always show all of your working out.
Addition with regrouping
Example: 838 + 714
Method:
Arrange the two numbers in columns.
Find the total of the units column. 8 + 4 = 12, which is 1 ten and 2 units. Regroup the ten into the tens column.
Find the total of the tens column. 3 tens +1 ten + 1 ten = 5 tens.
Find the total of the hundreds column. 8 hundreds + 7 hundreds = 15 hundreds, which is 1 thousand and 5 hundreds. Regroup the 1 thousand into the thousands column.
838 + 714 = 1552
Addition of three integers
Example: 695 + 881 + 62
Method:
Arrange the three numbers in columns.
Find the total of the units column. 5 + 1 + 2 = 8 .
Find the total of the tens column. 9 tens + 8 tens + 6 tens = 23 tens, which is 2 hundreds and 3 tens. Regroup the 2 hundreds into the hundreds column.
Find the total of the hundreds column. 6 hundreds + 8 hundreds + 2 hundreds = 16 hundreds, which is 1 thousand and 6 hundreds. Regroup the 1 thousand into the thousands column.
695 + 881 + 62 = 1638
Subtraction with regrouping
Example: 432 – 268
Method:
Arrange the two numbers in columns.
Complete the units column first. You can't take 8 from 2. Regroup 1 ten into the units column, leaving 2 tens in the tens column.
Now the units column can be completed. 12 – 8 = 4.
Complete the tens column next. You can't take 6 tens from 2 tens. Regroup 1 hundred into the tens column, leaving 3 hundreds in the hundreds column.
Now the tens column can be completed. 12 tens – 6 tens = 6 tens.
Finally, complete the hundreds column. 3 hundreds – 2 hundreds = 1 hundred.
432 – 268 = 164
Subtraction with the 'zero problem' (or the 'empty column problem')
Example: 704 – 459
Method:
Arrange the two numbers in columns.
Complete the units column first. You can't take 9 from 4 so you need to regroup a ten into the units column. However, the tens column is empty.
Regroup 1 hundred into the tens column, leaving 6 hundreds in the hundreds column. Now you can regroup 1 ten into the units column, leaving 9 tens in the tens column.
Now the units column can be completed. 14 – 9 = 5.
Next the tens column can be completed. 9 tens – 5 tens = 4 tens.
Finally the hundreds column can be completed. 6 hundreds – 4 hundreds = 2 hundreds.
704 – 459 = 245
Multiplication with regrouping
Example: 187 × 5
Method:
Arrange the number to be multiplied in columns, with an answer box below, as you would for an addition.
Complete the units column first. 7 × 5 = 35, which is 3 tens and 5 units. Regroup the 3 tens into the tens column.
Next complete the tens column. 8 tens × 5 = 40 tens. Add the 5 regrouped tens to make 45 tens, which is 4 hundreds and 5 tens. Regroup the 4 hundreds into the hundreds column.
Finally complete the hundreds column. 1 hundred × 5 = 5 hundreds. Add the 4 regrouped hundreds to make 9 hundreds.
187 × 5 = 985
Division with regrouping
Example: 1 300 ÷ 4
Method:
Most people regroup for division differently than for the other operations, by beginning with the furthest column to the left. The calculation is usually laid out differently too (see below).
In the thousands column, 4 thousands will not go into 1 thousand, so the 1 thousand is regrouped into the hundreds column.
In the hundreds column, 4 hundreds will go into 13 hundreds 3 times, with 1 hundred remaining. This hundred is regrouped into the tens column.
In the tens column, 4 tens will go into 10 tens 2 times,
with 2 tens remaining. These tens are regrouped into the units column.
Finally, in the units column, 4 will go into 20 5 times.
1 300 ÷ 4 = 325
