6.NS.B.2+B.3 6th Grade The Number System

Multi-Digit Operations

Fluently divide multi-digit numbers and add, subtract, multiply, and divide multi-digit decimals using the standard algorithm.

How to explain it

At this standard, students apply the standard algorithm for long division of multi-digit whole numbers and all four operations with multi-digit decimals, emphasizing place-value reasoning and decimal-point placement.

The anchor students hold onto: Whole-number division: Divide → Multiply → Subtract → Bring Down. Decimals: align points to add/subtract; count total decimal places to multiply; shift the decimal to make a whole divisor before dividing.

Multi-digit computation fluency (6.NS.B.2+B.3) extends directly to operations with rational numbers involving negatives in 7.NS.A, and supports decimal reasoning in 6.RP.A proportional problems.

Worked examples

Example 1 Whole-Number Long Division

Divide 3,276 ÷ 7.

Step 17 into 32 = 4 R 4; write 4 above tens digit

Step 2Bring down 7 → 47; 7 into 47 = 6 R 5; write 6

Step 3Bring down 6 → 56; 7 into 56 = 8; write 8

Step 43,276 ÷ 7 = 468

Answer468

Example 2 Multiplying Decimals

Multiply 3.6 × 2.4.

Step 1Ignore decimals: 36 × 24 = 864

Step 2Count decimal places: 1 + 1 = 2

Step 3Place decimal 2 from right: 8.64

Answer8.64

Common mistakes

What students write Counted decimal places in only one factor when multiplying — 4.5 × 2.8: moved 1 decimal place and got 126 instead of 12.6.

The fix Count decimal places in BOTH factors and ADD them — 4.5 (1 place) × 2.8 (1 place) = 2 total places → 12.6.

What students write Did not align decimal points when subtracting — computed 14.3 − 9.75 as 14.30 − 9.75 but borrowed incorrectly, getting 5.45 instead of 4.55.

The fix Line up the decimal points, write 14.30 − 9.75, then borrow column by column from right to left — answer is 4.55.

Teacher tip

Head off the two predictable errors before they happen. First: Count decimal places in BOTH factors and ADD them — 4.5 (1 place) × 2.8 (1 place) = 2 total places → 12.6. Second: Line up the decimal points, write 14.30 − 9.75, then borrow column by column from right to left — answer is 4.55.