Question - Solving Fractions Equations
Solution:
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.
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