How to Solve Word Problems with Four-digit Dividends and Two-digit Divisors

Dividing Four-digit Numbers by Two-digit Numbers in Word Problems

Example 1:

A city marathon had (8,640) participants and wanted to divide them equally into groups of (36) for a warm-up session. How many groups will be formed?

Solution Process:

Divide (8,640) by (36).

Answer:

There will be (240) groups.

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Example 2:

A factory produced (9,216) toys in a month. If they pack these toys in boxes of (48) each, how many boxes will they need?

Solution Process:

Divide (9,216) by (48).

Answer:

They will need (192) boxes.

Tackling word problems that involve dividing four-digit numbers by two-digit numbers requires a clear understanding of the problem’s context and careful calculations. By breaking down the problem, identifying the numbers involved, and performing the division, you can find the solution and apply this knowledge to various real-world scenarios. Practice regularly with different word problems to hone your skills and become adept at handling large-scale division challenges!

Practice Questions:

1. A school has (6,372) students and wants to distribute them equally in classes of (53). How many classes will be formed?

2. A library acquired (7,808) new books and plans to place them on shelves, with (56) books per shelf. How many shelves will they need?

3. A charity event had (8,294) attendees and wants to divide them into teams of (47) for various activities. How many teams can they form?

4. A company sold (9,576) products and wants to ship them in cartons of (84) each. How many cartons will they prepare?

5. A music festival sold (5,460) tickets and plans to divide the attendees into sections of (91) each for seating. How many sections will there be?

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Answers:

1. (120) classes with a remainder of (12)

2. (140) shelves ((139) full shelves and (24) books on the last one)

3. (176) teams with a remainder of (22)

4. (114) cartons

5. (60) sections

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A Trick for Dividing by Two-Digit Numbers

The hard part is guessing each digit of the quotient. Round the divisor to the nearest ten and use your times tables.

1. To find 7,808 ÷ 56, think of 56 as about 60.
2. 78 ÷ 60 is about 1, so the first digit is 1. 78 − 56 = 22. Bring down 0 to get 220.
3. 220 ÷ 60 is about 3. Try 3: 56 × 3 = 168, and 220 − 168 = 52, which is less than 56, so 3 works. Bring down 8 to get 528.
4. 528 ÷ 60 is about 8, but 56 × 9 = 504 is still less than 528, so use 9. 528 − 504 = 24.
5. Answer: 139 remainder 24. Check: 56 × 139 + 24 = 7,784 + 24 = 7,808.

If a guess is too big, the product will be larger than the number you are dividing; go down by 1. If the remainder is bigger than the divisor, go up by 1.

What to Do with the Remainder

In a word problem, the question tells you what the remainder means.

• Round up when everyone or everything must fit. 1,250 students ride buses with 48 seats each: 1,250 ÷ 48 = 26 R 2, so you need 27 buses.
• Drop it when only full groups count. 3,010 cookies go into boxes of 24: 3,010 ÷ 24 = 125 R 10, so you can fill 125 boxes.
• Use the remainder when the question asks what is left over. In the cookie problem, 10 cookies are left.
• Write it as a fraction or decimal when the amount can be split. 1,950 cm of ribbon cut into 12 equal pieces: 1,950 ÷ 12 = 162 R 6, so each piece is 162½ cm, or 162.5 cm.

Frequently Asked Questions

How do you do 4-digit by 2-digit division?

Use long division. Look at the first two digits and see how many times the divisor fits; if it does not fit, use the first three digits. Write that digit in the quotient, multiply, subtract and bring down the next digit. Repeat until all digits are used. Whatever is left is the remainder.

What is a trick for dividing by two-digit numbers?

Round the divisor to the nearest ten to estimate each quotient digit. For 56, think 60, so 220 ÷ 56 is about 220 ÷ 60, or 3. Then multiply the real divisor to check. If the product is too big, lower the digit by 1; if the remainder is bigger than the divisor, raise it by 1.

How do I check a division answer?

Multiply the quotient by the divisor and add the remainder. You should get the original dividend. For 6,372 ÷ 53 = 120 R 12, check 53 × 120 = 6,360, and 6,360 + 12 = 6,372. Also make sure the remainder is smaller than the divisor.

How is this different from 4-digit by 1-digit division?

The steps are the same: divide, multiply, subtract, bring down. With a one-digit divisor you can usually use times tables directly. With a two-digit divisor you often need to estimate each digit, and the first digit of the quotient usually comes from the first two or three digits of the dividend.