Solving Fractions Equations
To solve the equations given in the image, we will work with fractions.
The first equation provided is:
\(\frac{13}{100} + \frac{5}{10} = \frac{13}{100} + \square\)
Before we can add the fractions, we need to make sure they have a common denominator. The fractions \(\frac{13}{100}\) and \(\frac{5}{10}\) don't have the same denominator. To add them together, we should convert \(\frac{5}{10}\) to a fraction with a denominator of 100. We can do this by multiplying both the numerator and the denominator by 10.
\(\frac{5}{10} \times \frac{10}{10} = \frac{50}{100}\)
Now we can add the fractions:
\(\frac{13}{100} + \frac{50}{100} = \frac{63}{100}\)
The equation becomes:
\(\frac{13}{100} + \frac{50}{100} = \frac{13}{100} + \square\)
Now, to find the value that the square must represent to make the equation true, we can set up another equation:
\(\frac{13}{100} + \square = \frac{63}{100}\)
Subtract \(\frac{13}{100}\) from both sides of the equation to isolate the square:
\(\square = \frac{63}{100} - \frac{13}{100} = \frac{63 - 13}{100} = \frac{50}{100}\)
However, since the instructions ask for whole numbers, fractions, or decimals, and \(\frac{50}{100}\) can be simplified to \(\frac{1}{2}\) or converted to the decimal 0.5, we should provide the answer in one of those formats:
The square would therefore be filled with the simplified fraction \(\frac{1}{2}\) or the decimal 0.5.
