Use tenths or hundredths to determine the fraction that makes the equation true. Show your thinking.
□ + $\frac{7}{10} = \frac{100}{100}$
The problem asks us to find a missing value, represented by \(\square\), that satisfies the equation:
\[\square + \frac{7}{10} = \frac{100}{100}\]
Our goal is to isolate \(\square\) and express it as a fraction. To do this, we need to handle the fractions on both sides of the equation. We know that \(\frac{100}{100}\) simplifies to \(1\), and we have a fraction \(\frac{7}{10}\) on the left side. Converting these terms to a common denominator will make the subtraction straightforward.
First, let's simplify the right side of the equation:
\[\frac{100}{100} = 1\]
Next, to subtract the fraction \(\frac{7}{10}\) from the right side, it is helpful to express \(1\) as a fraction with a denominator of 10. Since any number divided by itself is \(1\), we can write:
\[1 = \frac{10}{10}\]
Now, our equation becomes:
\[\square + \frac{7}{10} = \frac{10}{10}\]
To find the value of \(\square\), we subtract \(\frac{7}{10}\) from both sides of the equation:
\[\square = \frac{10}{10} - \frac{7}{10}\]
Performing the subtraction by keeping the common denominator:
\[\square = \frac{10 - 7}{10} = \frac{3}{10}\]
Thus, the value that fills the box is \(\frac{3}{10}\). We can also express this in hundredths by multiplying the numerator and denominator by 10:
\[\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}\]
Both \(\frac{3}{10}\) and \(\frac{30}{100}\) are correct, but \(\frac{3}{10}\) is the simplified fraction.
We have successfully determined that the missing value is \(\frac{3}{10}\). Substituting this back into the original equation, we get \(\frac{3}{10} + \frac{7}{10} = \frac{10}{10} = 1\), which confirms our result is correct. Therefore, the missing fraction is \(\boxed{\frac{3}{10}}\).
Imagine you have a cake cut into 10 equal slices, and you've already eaten 7 of them. If you want to know how many slices are left to have eaten the whole cake (the "100/100" or 1 whole), you are solving a fraction problem just like this one! Calculating \(\frac{10}{10} - \frac{7}{10} = \frac{3}{10}\) helps you understand that 3 slices remain. This type of mental math is useful in everyday activities like cooking, measuring ingredients, or managing your time efficiently throughout the day.