Number Operations

Whole-number operations help us combine, compare, group, and share quantities. Addition and subtraction are inverse operations, and multiplication and division are also inverse operations. When you solve a problem, ask yourself what the situation is asking you to do: combine, remove, group, or share.nnAddition example: 347 + 286 = 633. Start in the ones place: 7 + 6 = 13, write 3 and regroup 1 ten. Next, 4 + 8 + 1 = 13 tens, write 3 and regroup 1 hundred. Then 3 + 2 + 1 = 6 hundreds. The answer is 633.nnSubtraction example: 825 - 367 = 458. Start in the ones place: 5 - 7 needs regrouping, so rename 2 tens as 20 ones and add to 5 to make 25. Then 25 - 7 = 18, write 8 and regroup 1 ten. Next, 1 ten becomes 11 tens after regrouping from the hundreds place. 11 - 6 = 5, and 7 - 3 = 4. The answer is 458.nnMultiplication example: 24 x 3 = 72. Think of 24 as 20 + 4. Three groups of 20 is 60 and three groups of 4 is 12. 60 + 12 = 72.nnDivision example without a remainder: 24 ÷ 6 = 4. This means 24 shared into 6 equal groups gives 4 in each group.nnDivision example with a remainder: 25 ÷ 6 = 4 remainder 1. This means 25 shared into 6 equal groups gives 4 in each group and 1 is left over.nnCommon misconceptions and corrections: Students may line up digits incorrectly, forget to regroup, or treat division as repeated subtraction without checking the remainder. A helpful correction is to ask whether the problem is asking for a total, a difference, a product, or a quotient, and then model the action with a simple drawing or place-value chart.