Multi-Digit Division

Understanding Division#

Division is the process of splitting a quantity into equal groups. It is the inverse (opposite) operation of multiplication. In Grade 4, you will divide large numbers — up to four-digit dividends — by one-digit divisors.

Division Vocabulary#

• Dividend — the number being divided (the total amount)
• Divisor — the number you are dividing by (the size or number of groups)
• Quotient — the answer to a division problem
• Remainder — the amount left over when a number cannot be divided evenly

In 84 ÷ 6 = 14:

• 84 is the dividend
• 6 is the divisor
• 14 is the quotient

Two Ways to Think About Division#

Sharing (partitive division): 24 cookies shared equally among 6 friends — how many dös each friend get? 24 ÷ 6 = 4 cookies each

Grouping (measurement division): 24 cookies placed in bags of 6 — how many bags? 24 ÷ 6 = 4 bags

Both situations use the same math, but the meaning is different. Reading word problems carefully helps you understand which type you are solving.

Division and Multiplication: The Inverse Relationship#

Division and multiplication undo each other. If you know that 6 × 4 = 24, you also know:

• 24 ÷ 6 = 4
• 24 ÷ 4 = 6

This relationship helps you check division answers: multiply the quotient by the divisor, and you should get the dividend. If 84 ÷ 6 = 14, then 14 × 6 = 84. ✓

Mental Math Division#

Use place value to divide mentally:

• 3,600 ÷ 4 → Think: 36 ÷ 4 = 9, then × 100 = 900
• 4,200 ÷ 7 → Think: 42 ÷ 7 = 6, then × 100 = 600

These mental math shortcuts build number sense and make formal division faster.