Problem 450 - Prealgebra

Question

Oswaldo divided 300 by 8 and said his answer was 37 with a remainder of 4. How can you check to make sure he is correct?

Step-by-Step Solution

Answer

Oswaldo's answer is correct because \(8 \times 37 + 4 = 300\).

Step 1: Understand Oswaldo's Answer

Oswaldo divided 300 by 8 and said the quotient is 37 with a remainder of 4. This means that 300 should be equal to \(8 \times 37 + 4\). Let's verify this.

Step 2: Compute the Product

Calculate the product of the divisor and quotient: \(8 \times 37\).

Step 3: Perform the Multiplication

Multiply 8 by 37: \(8 \times 37 = 296\).

Step 4: Add the Remainder

Add the remainder to the product we just calculated: \(296 + 4\).

Step 5: Verify the Result

Check if the sum of 296 and 4 equals 300: \(296 + 4 = 300\).

Step 6: Conclusion

Since \(8 \times 37 + 4 = 300\), Oswaldo's answer is correct.

Key Concepts

Division with Remainders

Division is a way of splitting a number into equal parts. When a number doesn’t divide evenly, we get a quotient and a remainder. For example, when Oswaldo divided 300 by 8, he got a quotient of 37 and a remainder of 4. In simple terms, 300 can be broken down into 37 parts of 8, and a leftover part, which is 4. So, we write this as:
300 = 8 × 37 + 4
When learning division with remainders, it's important to know that the remainder is always smaller than the divisor. In this case, the remainder 4 is less than the divisor 8. Checking if the division is correct involves multiplying the quotient by the divisor and adding the remainder. If this equation equals the original number, the division is correct. In Oswaldo's case:
8 × 37 + 4 = 296 + 4 = 300
This confirms that Oswaldo's division is correct.

Multiplication

Multiplication is one of the fundamental arithmetic operations. It’s essentially repeated addition. When we multiply two numbers, we are adding one number to itself a certain number of times. For instance, multiplying 8 by 37 means adding 8 to itself 37 times:
8 × 37 = 8 + 8 + 8 ... (37 times)
In our problem, to check Oswaldo's division, we calculate:
8 × 37 = 296
This step helps us verify the product before moving to the final step of adding the remainder.

Addition

Addition is the process of calculating the total of two or more numbers or amounts. In the case of Oswaldo's problem, after performing the multiplication, we need to add the remainder to the product. This step ensures that our original value is restored. Here’s how it works:
296 + 4 = 300
Adding 296 (the product of 8 and 37) and 4 (the remainder) results in 300. This confirms the accuracy of Oswaldo's division and proves his answer is correct.