Adding Tenths and Hundredths

Task

Find the sums.

1. $\displaystyle \frac{9}{10} + \frac{8}{100}$


2. $\displaystyle \frac{7}{100} + \frac{3}{10}$


3. $\displaystyle \frac{2}{10} + \frac{41}{100}$


4. $\displaystyle \frac{23}{100} + \frac{7}{10}$


5. $\displaystyle \frac{7}{10} + \frac{20}{100}$


6. $\displaystyle \frac{1}{10} + \frac{9}{100} + \frac{13}{10} + \frac{21}{100} $

IM Commentary

Each part of this task emphasizes a unique aspect of 4.NF.5.

1. This problem simply asks students to add the tenths and hundredths together.
2. This problem is similar to the previous one, but it emphasizes that order doesn't matter in addition - yet order is everything in positional notation! In this problem, you must really think to encode the quantity in positional notation.
3. Students must realize that $\frac{2}{10}$ is equivalent to $\frac{20}{100}$ and then add $\frac{20}{100} + \frac{41}{100}$.
4. This problem is similar to the previous one. However, the tenths and hundredths have once again been switched, requiring students to link the values of the parts with the order of the digits in the positional system.
5. This part results in a fraction that can be simplified from hundredths to tenths.
6. This problem requires that students pay attention to which fractions have tenths, which have hundreds, and then add. This is also the only part that requires students to grapple with a total that is greater than one.

Solution

1. $\displaystyle \frac{98}{100}$


2. $\displaystyle \frac{37}{100}$


3. $\displaystyle \frac{61}{100}$


4. $\displaystyle \frac{93}{100}$


5. $\displaystyle \frac{90}{100} = \frac{9}{10}$ (Either of these answers is correct.)


6. $\displaystyle \frac{170}{100} = 1 \frac{70}{100} = 1 \frac{7}{10}$ (Any of these answers is correct.)