Question

complete the equations.
538 = 5 hundreds + 3 tens + 8 ones
538 = 0 hundreds + □ tens + 8 ones
538 = 0 hundreds + 0 tens + □ ones

Explanation:

Step1: Analyze the second equation

We know that \( 538 = 0\times100 + \square\times10 + 8\times1\). First, calculate \( 0\times100 = 0\) and \( 8\times1 = 8\). Then, let the number of tens be \( x \), so the equation becomes \( 538 = 0 + 10x + 8\). Subtract 8 from both sides: \( 538 - 8 = 10x \), which is \( 530 = 10x \). Divide both sides by 10: \( x=\frac{530}{10}=53 \).

Step2: Analyze the third equation

We know that \( 538 = 0\times100 + 0\times10 + \square\times1\). Calculate \( 0\times100 = 0\) and \( 0\times10 = 0\). Then, let the number of ones be \( y \), so the equation becomes \( 538 = 0 + 0 + y\), so \( y = 538 \).

Answer:

For the second equation, the number of tens is \( 53 \). For the third equation, the number of ones is \( 538 \). So the filled blanks are \( 53 \) (in the tens place of the second equation) and \( 538 \) (in the ones place of the third equation).