Question

1. communicate and justify juana is adding $3\frac{1}{4} + 2\frac{7}{8}$ using fraction strips. how can she rename the sum of the fraction parts of the problem? explain your thinking.

Explanation:

Step1: Identify fraction parts

The fraction parts of the mixed numbers are $\frac{1}{4}$ (from $3\frac{1}{4}$) and $\frac{7}{8}$ (from $2\frac{7}{8}$).

Step2: Find a common denominator

The denominators are 4 and 8. The least common denominator (LCD) of 4 and 8 is 8.

Step3: Rename $\frac{1}{4}$ with denominator 8

To convert $\frac{1}{4}$ to a fraction with denominator 8, we multiply the numerator and denominator by 2: $\frac{1\times2}{4\times2}=\frac{2}{8}$.

Step4: Add the renamed fraction parts

Now we add the fraction parts: $\frac{2}{8}+\frac{7}{8}=\frac{2 + 7}{8}=\frac{9}{8}$.

Step5: Simplify the improper fraction (optional, but for renaming)

$\frac{9}{8}$ can be written as a mixed number: $1\frac{1}{8}$, or we can keep it as an improper fraction. But the key renaming here was changing $\frac{1}{4}$ to $\frac{2}{8}$ to have a common denominator with $\frac{7}{8}$ so they can be added.

Answer:

Juana can rename $\boldsymbol{\frac{1}{4}}$ (the fraction part of $3\frac{1}{4}$) to $\boldsymbol{\frac{2}{8}}$ (by multiplying numerator and denominator by 2, since the least common denominator of 4 and 8 is 8) so that she can add the fraction parts $\frac{2}{8}$ and $\frac{7}{8}$ (from $2\frac{7}{8}$) together. The sum of the fraction parts is then $\frac{2}{8}+\frac{7}{8}=\frac{9}{8}$ (or $1\frac{1}{8}$).