Question

practice
add and regroup, if needed.
5.
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$$\begin{array}{r} 5\\frac{1}{4}\\\\ +\\ 6\\frac{3}{4}\\\\ \\hline \\end{array}$$

\\
6.
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$$\begin{array}{r} 3\\\\ +\\ 4\\frac{9}{12}\\\\ \\hline \\end{array}$$

\\

1. \\( 2\frac{5}{6} + 2\frac{5}{6} \\)
2. \\( 2\frac{3}{8} + 4\frac{7}{8} \\)
3. \\( 3\frac{6}{12} + 5\frac{4}{12} \\)
4. \\( 10\frac{5}{8} + 2\frac{4}{8} \\)

Explanation:

Problem 5:

Step1: Add the fractions

The fractions are $\frac{1}{4}$ and $\frac{3}{4}$. Adding them: $\frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1$.

Step2: Add the whole numbers

The whole numbers are 5 and 6. Adding them: $5 + 6 = 11$.

Step3: Combine the results

Add the result from the fractions (1) to the result from the whole numbers (11): $11 + 1 = 12$.

Step1: Convert the whole number to a fraction with denominator 12

3 can be written as $\frac{36}{12}$ (since $3 = \frac{3\times12}{12} = \frac{36}{12}$).

Step2: Add the fractions

Now add $\frac{36}{12}$ and $\frac{9}{12}$: $\frac{36}{12} + \frac{9}{12} = \frac{45}{12}$. Simplify $\frac{45}{12}$: divide numerator and denominator by 3, we get $\frac{15}{4} = 3\frac{3}{4}$.

Step3: Add the whole number part from the mixed number

The mixed number $4\frac{9}{12}$ has a whole number part 4. Wait, actually, we should add the whole number (3) and the mixed number's whole number (4) first? Wait, no, better to handle as mixed numbers. Wait, 3 is a whole number, $4\frac{9}{12}$ is a mixed number. So add the whole numbers: $3 + 4 = 7$. Then add the fraction: $\frac{9}{12}$. Wait, my first step was wrong. Let's correct.

Correct Step1: Treat 3 as $3\frac{0}{12}$.
Step2: Add the mixed numbers: $3\frac{0}{12} + 4\frac{9}{12} = (3 + 4) + (\frac{0}{12} + \frac{9}{12}) = 7 + \frac{9}{12} = 7\frac{9}{12} = 7\frac{3}{4}$.

Step1: Add the fractions

The fractions are $\frac{5}{6}$ and $\frac{5}{6}$. Adding them: $\frac{5}{6} + \frac{5}{6} = \frac{10}{6} = \frac{5}{3} = 1\frac{2}{3}$.

Step2: Add the whole numbers

The whole numbers are 2 and 2. Adding them: $2 + 2 = 4$.

Step3: Combine the results

Add the result from the fractions (1$\frac{2}{3}$) to the result from the whole numbers (4): $4 + 1\frac{2}{3} = 5\frac{2}{3}$.

Answer:

12

Problem 6: