Section 1
📘 One-Digit Division with a Remainder
New Concept
The amount left over is the remainder.
What’s next
Next, you'll apply this concept by solving division problems where a leftover amount, the remainder, is part of the answer.
In this Grade 4 lesson from Saxon Math Intermediate 4, students learn how to perform one-digit division with a remainder, using the standard division algorithm to find a quotient and identify the leftover amount written in R notation. The lesson walks through the steps of dividing, multiplying, and subtracting to calculate remainders, supported by dot sketches and real-world word problems involving equal groups.
Section 1
📘 One-Digit Division with a Remainder
The amount left over is the remainder.
Next, you'll apply this concept by solving division problems where a leftover amount, the remainder, is part of the answer.
Section 2
remainder
When a number cannot be perfectly divided into equal groups, the amount left over is the remainder. For instance, while 12 dots can be split into three perfect groups of four, 13 dots cannot. After making three groups of four, one dot remains. This leftover amount is the remainder, representing the part that does not fit evenly.
For , we can make 3 groups, with 1 left over. The answer is written as .
For , we can make 5 groups of three (), with 2 left over. The answer is .
For , we can make 4 groups of six (), with 1 left over. The answer is .
Think of it as sharing cookies! If you have 13 cookies for 4 friends, each gets 3, but 1 cookie is left. That lonely, extra cookie is the remainder!
Section 3
One-Digit Division with a Remainder
To solve a division problem like , first find how many full groups you can make. Since is close to 13 without going over, you write 3 as the quotient. Next, multiply your answer by the divisor () and write it below. Finally, subtract to find the remainder ().
To solve : Divide 16 by 3 to get 5. Multiply . Subtract . The answer is .
To solve : Divide 12 by 5 to get 2. Multiply . Subtract . The answer is .
To solve : Divide 23 by 4 to get 5. Multiply . Subtract . The answer is .
It’s a simple three-step dance: Divide, Multiply, and then Subtract! This helps you find the number of full groups and identify exactly what’s left over at the end.
Section 4
Interpreting Remainders in Word Problems
In real-world scenarios, the remainder holds a specific meaning that guides your final answer. If 20 people need rides in vans that hold 6 each, dividing gives 3 R 2. This means 3 vans are filled completely, and the remainder of 2 represents the people who need a separate car. The context determines how you use leftovers.
20 members need rides in vans that hold 6. . This means 3 vans are full and 2 members need a separate ride.
Lucius needs 18 quarts of cider, sold in 4-quart gallons. . He must buy 5 full gallons to have enough cider.
Nina threw a shot put 28 feet. To find the yards, . This is 9 full yards and 1 extra foot.
Don't just write 'R 2' and walk away! That remainder could be leftover pizza slices, people needing another car, or extra feet of ribbon. Always ask what it represents!
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Section 1
📘 One-Digit Division with a Remainder
The amount left over is the remainder.
Next, you'll apply this concept by solving division problems where a leftover amount, the remainder, is part of the answer.
Section 2
remainder
When a number cannot be perfectly divided into equal groups, the amount left over is the remainder. For instance, while 12 dots can be split into three perfect groups of four, 13 dots cannot. After making three groups of four, one dot remains. This leftover amount is the remainder, representing the part that does not fit evenly.
For , we can make 3 groups, with 1 left over. The answer is written as .
For , we can make 5 groups of three (), with 2 left over. The answer is .
For , we can make 4 groups of six (), with 1 left over. The answer is .
Think of it as sharing cookies! If you have 13 cookies for 4 friends, each gets 3, but 1 cookie is left. That lonely, extra cookie is the remainder!
Section 3
One-Digit Division with a Remainder
To solve a division problem like , first find how many full groups you can make. Since is close to 13 without going over, you write 3 as the quotient. Next, multiply your answer by the divisor () and write it below. Finally, subtract to find the remainder ().
To solve : Divide 16 by 3 to get 5. Multiply . Subtract . The answer is .
To solve : Divide 12 by 5 to get 2. Multiply . Subtract . The answer is .
To solve : Divide 23 by 4 to get 5. Multiply . Subtract . The answer is .
It’s a simple three-step dance: Divide, Multiply, and then Subtract! This helps you find the number of full groups and identify exactly what’s left over at the end.
Section 4
Interpreting Remainders in Word Problems
In real-world scenarios, the remainder holds a specific meaning that guides your final answer. If 20 people need rides in vans that hold 6 each, dividing gives 3 R 2. This means 3 vans are filled completely, and the remainder of 2 represents the people who need a separate car. The context determines how you use leftovers.
20 members need rides in vans that hold 6. . This means 3 vans are full and 2 members need a separate ride.
Lucius needs 18 quarts of cider, sold in 4-quart gallons. . He must buy 5 full gallons to have enough cider.
Nina threw a shot put 28 feet. To find the yards, . This is 9 full yards and 1 extra foot.
Don't just write 'R 2' and walk away! That remainder could be leftover pizza slices, people needing another car, or extra feet of ribbon. Always ask what it represents!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter