Mathematics
Grade 6
15 min
Divide multi-digit numbers by 1-digit numbers: word problems
Divide multi-digit numbers by 1-digit numbers: word problems
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Introduction & Learning Objectives
Learning Objectives
Identify the division operation required in word problems involving multi-digit numbers.
Translate real-world scenarios into mathematical division problems.
Accurately divide multi-digit numbers by 1-digit numbers using the standard algorithm.
Interpret remainders correctly in the context of word problems (e.g., rounding up, ignoring, or using as a fraction).
Formulate a clear, complete answer to word problems, including appropriate units.
Check the reasonableness of their answers using estimation or inverse operations.
Ever wonder how many cookies each friend gets if you bake a big batch? 🍪 Division helps us share things fairly and solve everyday puzzles!
In this lesson, we'll master how to solve word problems that require dividing large numbers b...
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Key Concepts & Vocabulary
TermDefinitionExample
DividendThe total number or amount that is being divided into smaller, equal parts.In the problem '456 marbles shared among 4 friends,' 456 is the dividend.
DivisorThe number by which the dividend is divided; it tells us how many equal groups to make or the size of each group.In the problem '456 marbles shared among 4 friends,' 4 is the divisor.
QuotientThe result of a division problem; it tells us how many are in each group or how many groups there are.If 456 marbles are shared among 4 friends, the quotient is 114 (marbles per friend).
RemainderThe amount left over after dividing when one number does not divide another exactly.If you divide 10 cookies among 3 friends, each gets 3 cookies, and there is 1 cookie left over. 1 is the remainder.
Word...
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Core Formulas
Division Algorithm (Checking Your Work)
$Dividend = Divisor \times Quotient + Remainder$
This rule helps you verify if your division is correct. If you multiply your quotient by the divisor and then add any remainder, the result should be equal to your original dividend.
Interpreting Remainders (Rounding Up)
If a word problem asks for 'how many full containers are needed' or 'how many trips are required,' you must round the quotient up to the next whole number if there is any remainder.
Even a small remainder means you need an additional full unit. For example, if you need 3.2 buses, you must get 4 buses to transport everyone.
Interpreting Remainders (Ignoring)
If a word problem asks for 'how many complete sets can be made' or 'how ma...
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Challenging
A secret code is a whole number between 610 and 620. When this number is divided by 9, it leaves a remainder of 5. What is the secret code?
A.615
B.617
C.613
D.619
Challenging
A student is solving this problem: 'An artist has 470 paintbrushes to put into containers. Each container holds 8 brushes. How many containers are needed?' The student reasons, '470 divided by 8 is 58 with a remainder of 6. Since the remainder is more than half of the divisor (6 is more than half of 8), I must round up. So, 59 containers are needed.' Evaluate the student's reasoning.
A.The reasoning is correct; rounding up is necessary because the remainder is large.
B.The reasoning is flawed; the decision to round up depends on the context (needing a place for the leftover items), not the size of the remainder.
C.The reasoning is flawed; the calculation is wrong, and the answer should be 58.
D.The reasoning is correct, but only because the problem involves physical objects.
Challenging
A tech company has 3,670 feet of cable. It needs to be cut into 7-foot sections. Each complete section can be sold for $4. What is the total value of all the complete 7-foot sections that can be cut?
A.$2,092
B.$14,680
C.$2,100
D.$2,096
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