Question

73×5+4 573×5 3,442÷6 = 573 remainder 4

Explanation:

Step1: Recall division formula

In division, \( \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \). Here, dividend is \( 3442 \), divisor is \( 6 \), quotient is \( 573 \), remainder is \( 4 \).

Step2: Verify using formula

Calculate \( 6\times573 + 4 \). First, \( 573\times5 = 2865 \)? Wait, no, \( 573\times6=573\times(5 + 1)=573\times5+573\times1 \). Wait, let's compute \( 573\times6 \): \( 500\times6 = 3000 \), \( 70\times6 = 420 \), \( 3\times6 = 18 \), so \( 3000+420 + 18=3438 \). Then \( 3438+4 = 3442 \), which matches the dividend. Now, the two expressions: \( 573\times5 + 4 \) and \( 573\times5 \). Let's compute \( 573\times5 \): \( 500\times5=2500 \), \( 70\times5 = 350 \), \( 3\times5 = 15 \), so \( 2500+350+15 = 2865 \). Then \( 573\times5+4=2865 + 4=2869 \). And \( 573\times5 = 2865 \). So we can see the difference between them is 4. But the key is from the division formula, \( \text{Dividend}=\text{Divisor}\times\text{Quotient}+\text{Remainder} \), so \( 3442=6\times573 + 4 \), which is why \( 573\times6+4 = 3442 \), and \( 573\times5 \) is part of that expansion.

Answer:

To analyze the expressions \( 573\times5 + 4 \) and \( 573\times5 \) in the context of \( 3442\div6 = 573 \) remainder \( 4 \):

• From the division algorithm (\( \text{Dividend}=\text{Divisor}\times\text{Quotient}+\text{Remainder} \)), \( 3442=6\times573 + 4 \).
• Expanding \( 6\times573 \) as \( 5\times573+1\times573 \), we get \( 3442=(5\times573)+573 + 4 \), but more directly, \( 573\times5 + 4=2865 + 4 = 2869 \), and \( 573\times5 = 2865 \). The former (\( 573\times5 + 4 \)) relates to the division result (as \( 6\times573+4 = 3442 \), and \( 6\times573=5\times573+573 \), but here \( 573\times5 + 4 \) is a separate calculation).

If the question is to compare or explain, the key is the division formula: \( \boldsymbol{3442 = 6\times573 + 4} \), so \( 573\times5 + 4 \) is \( (6\times573 - 573)+4=3442 - 573+4=2873 \)? Wait, no, earlier calculation shows \( 573\times5 + 4 = 2869 \), and \( 573\times5 = 2865 \). The main takeaway is that \( 573\times5 + 4 \) is \( 4 \) more than \( 573\times5 \), and both are related to the division result via the formula \( \text{Dividend}=\text{Divisor}\times\text{Quotient}+\text{Remainder} \).