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Dividing Orally

The student divides by 10, 100 and 1000 in the head by splitting the numeral rather than working the long division.

5 micro-lessons

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Splitting the Numeral

Dividing by 10, 100 or 1000 just cuts digits off the right-hand end.

Splitting the Numeral

When a number is divided by $10$ , the quotient is obtained by removing the first digit from the right. The single digit removed is the remainder, and the rest of the number is the quotient.

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Three Splits From Page 45

The book's own three examples, and one from the worksheet.

Problem. Divide the following numbers orally by applying the digit-splitting rule:

$459 \div 10$
$6,926 \div 100$
$98,217 \div 1000$
$4,324 \div 100$

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How Many Digits to Cut

The three rules on one card, with an example of each.

Divide by 10

Cut 1 digit from right

459 \div 10

Q: 45 | R: 9

Divide by 100

Cut 2 digits from right

6, 926 \div 100

Q: 69 | R: 26

Divide by 1000

Cut 3 digits from right

98, 217 \div 1000

Q: 98 | R: 217

The Rule of Splitting

What is left on the left is the quotient. What was cut off on the right is the remainder. The counting always starts from the right-hand end.

Connection: Multiplying by these numbers adds that many zeros on the right; dividing cuts that many digits off!

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Complete the Table

Five rows from the Worksheet 5 table.

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Let's complete the table by dividing orally using the splitting method. As a model, when solving $7,321 \div 10$ , the quotient is $732$ and remainder is $1$ . For row (b), dividing $213 \div 10$ , we split the number to get a quotient of and a remainder of . Moving to row (d), $4,324 \div 100$ means removing two digits, which gives a quotient of and a remainder of . In row (g), calculating $47,321 \div 1000$ yields a quotient of and a remainder of . For row (k), evaluating $98,271 \div 10$ by cutting one digit results in a quotient of and a remainder of . Finally, for row (l), $73,219 \div 100$ leaves us with a quotient of and a remainder of .

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The Rest of the Table

The remaining six rows from Worksheet 5.

Review the remaining divisions from Worksheet 5 and explain the reasoning for row (h).

Here are the remaining oral divisions from the worksheet:

(c) $19,827 \div 10 \rightarrow$ Quotient: $1982$ , Remainder: $7$
(e) $98,276 \div 100 \rightarrow$ Quotient: $982$ , Remainder: $76$
(f) $62,731 \div 100 \rightarrow$ Quotient: $627$ , Remainder: $31$
(h) $9,827 \div 1000 \rightarrow$ Quotient: $9$ , Remainder: $827$
(i) $62,578 \div 1000 \rightarrow$ Quotient: $62$ , Remainder: $578$
(j) $12,345 \div 1000 \rightarrow$ Quotient: $12$ , Remainder: $345$

Look closely at row (h). Often, students think that getting a single-digit quotient means they have done something wrong.

Quotient for 9,827 ÷ 1000*

What is the single-digit quotient for row (h)?

Why is a single digit correct?*

Justify why getting a 1-digit quotient is entirely correct here based on the mathematical rule for dividing by 1000.

Real-World Connection (Optional)

When might you divide a 4-digit number by 1000 in daily life?

← previousFive-Digit Dividends next →Division Word Problems

Splitting the Numeral

Dividing by 10, 100 or 1000 just cuts digits off the right-hand end.

Splitting the Numeral

When a number is divided by $10$ , the quotient is obtained by removing the first digit from the right. The single digit removed is the remainder, and the rest of the number is the quotient.

1 / 3

Three Splits From Page 45

The book's own three examples, and one from the worksheet.

Problem. Divide the following numbers orally by applying the digit-splitting rule:

$459 \div 10$
$6,926 \div 100$
$98,217 \div 1000$
$4,324 \div 100$

1 / 5

Complete the Table

Five rows from the Worksheet 5 table.

0 of 10 blanks filled

The Rest of the Table

The remaining six rows from Worksheet 5.

Review the remaining divisions from Worksheet 5 and explain the reasoning for row (h).

Here are the remaining oral divisions from the worksheet:

(c) $19,827 \div 10 \rightarrow$ Quotient: $1982$ , Remainder: $7$
(e) $98,276 \div 100 \rightarrow$ Quotient: $982$ , Remainder: $76$
(f) $62,731 \div 100 \rightarrow$ Quotient: $627$ , Remainder: $31$
(h) $9,827 \div 1000 \rightarrow$ Quotient: $9$ , Remainder: $827$
(i) $62,578 \div 1000 \rightarrow$ Quotient: $62$ , Remainder: $578$
(j) $12,345 \div 1000 \rightarrow$ Quotient: $12$ , Remainder: $345$

Look closely at row (h). Often, students think that getting a single-digit quotient means they have done something wrong.

Quotient for 9,827 ÷ 1000*

What is the single-digit quotient for row (h)?

Why is a single digit correct?*

Justify why getting a 1-digit quotient is entirely correct here based on the mathematical rule for dividing by 1000.

Real-World Connection (Optional)

When might you divide a 4-digit number by 1000 in daily life?