Question

another look!
draw a model to add $1\frac{7}{8}+2\frac{1}{4}$.
remember that you can use what you know about adding fractions to help you add mixed numbers.
step 1
model each addend using fraction strips.
$1\frac{7}{8}$
$2\frac{1}{4}=2\frac{2}{8}$
step 2
add the fractions. regroup if possible.
$\

$$\begin{array}{r}\\frac{7}{8}\\\\ +\\frac{2}{8}\\\\ \\hline \\frac{9}{8}=1\\frac{1}{8}\\end{array}$$

$
step 3
add the whole numbers to the regrouped fractions. write the sum.
so, $1\frac{7}{8}+2\frac{1}{4}=3\frac{9}{8}=4\frac{1}{8}$.
in 1–12, use fraction strips to find each sum.

1. $3\frac{1}{2}+1\frac{4}{8}$
2. $2\frac{5}{12}+4\frac{1}{4}$
3. $3\frac{3}{4}+3\frac{1}{2}$
4. $2\frac{5}{8}+4\frac{3}{4}$
5. $5\frac{1}{3}+3\frac{5}{6}$
6. $2\frac{1}{2}+6\frac{3}{4}$
7. $3\frac{1}{4}+4\frac{7}{8}$
8. $4\frac{5}{6}+5\frac{7}{12}$
9. $2\frac{1}{4}+4\frac{5}{8}$
10. $6\frac{1}{2}+7\frac{3}{4}$
11. $4\frac{5}{8}+6\frac{1}{2}$
12. $2\frac{1}{3}+4\frac{5}{12}$

Explanation:

Let's solve problem 1: \( 3\frac{1}{2} + 1\frac{4}{8} \)

Step 1: Convert to like fractions

First, simplify \( 1\frac{4}{8} \) to \( 1\frac{1}{2} \), or convert \( 3\frac{1}{2} \) to eighths. Let's convert \( 3\frac{1}{2} \) to eighths. \( 3\frac{1}{2} = 3\frac{4}{8} \) (since \( \frac{1}{2} = \frac{4}{8} \)) and \( 1\frac{4}{8} \) remains as is.

Step 2: Add the fractions

Now add the mixed numbers: \( 3\frac{4}{8} + 1\frac{4}{8} \). Add the whole numbers: \( 3 + 1 = 4 \). Add the fractions: \( \frac{4}{8} + \frac{4}{8} = \frac{8}{8} = 1 \).

Step 3: Combine whole and fraction

Now combine the results: \( 4 + 1 = 5 \). Wait, let's check again. Wait, \( 3\frac{1}{2} = 3\frac{4}{8} \), \( 1\frac{4}{8} \) is \( 1\frac{4}{8} \). Adding the fractions: \( \frac{4}{8} + \frac{4}{8} = \frac{8}{8} = 1 \). Adding the whole numbers: \( 3 + 1 = 4 \). Then \( 4 + 1 = 5 \). Wait, but let's do it step by step with fraction strips (conceptually). The fraction part of \( 3\frac{1}{2} \) is \( \frac{1}{2} = \frac{4}{8} \), and \( 1\frac{4}{8} \) has \( \frac{4}{8} \). So \( \frac{4}{8} + \frac{4}{8} = \frac{8}{8} = 1 \). Then whole numbers: \( 3 + 1 = 4 \). Then \( 4 + 1 = 5 \). Wait, but maybe I made a mistake. Wait, \( 3\frac{1}{2} + 1\frac{4}{8} \). Simplify \( 1\frac{4}{8} \) to \( 1\frac{1}{2} \). Then \( 3\frac{1}{2} + 1\frac{1}{2} = (3 + 1) + (\frac{1}{2} + \frac{1}{2}) = 4 + 1 = 5 \). Yes, that's correct.

Wait, let's solve problem 2: \( 2\frac{5}{12} + 4\frac{1}{4} \)

Step 1: Convert to like fractions

Convert \( 4\frac{1}{4} \) to twelfths. \( \frac{1}{4} = \frac{3}{12} \), so \( 4\frac{1}{4} = 4\frac{3}{12} \).

Step 2: Add the mixed numbers

Now add \( 2\frac{5}{12} + 4\frac{3}{12} \). Add whole numbers: \( 2 + 4 = 6 \). Add fractions: \( \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3} \). So the sum is \( 6\frac{8}{12} = 6\frac{2}{3} \). Wait, but let's check with the method. \( 2\frac{5}{12} + 4\frac{3}{12} = (2 + 4) + (\frac{5}{12} + \frac{3}{12}) = 6 + \frac{8}{12} = 6\frac{2}{3} \).

Let's do problem 3: \( 3\frac{3}{4} + 3\frac{1}{2} \)

Step 1: Convert to like fractions

Convert \( 3\frac{1}{2} \) to fourths. \( \frac{1}{2} = \frac{2}{4} \), so \( 3\frac{1}{2} = 3\frac{2}{4} \).

Step 2: Add the mixed numbers

Add \( 3\frac{3}{4} + 3\frac{2}{4} \). Whole numbers: \( 3 + 3 = 6 \). Fractions: \( \frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1\frac{1}{4} \).

Step 3: Combine

Now combine: \( 6 + 1\frac{1}{4} = 7\frac{1}{4} \).

Let's do problem 4: \( 2\frac{5}{8} + 4\frac{3}{4} \)

Step 1: Convert to like fractions

Convert \( 4\frac{3}{4} \) to eighths. \( \frac{3}{4} = \frac{6}{8} \), so \( 4\frac{3}{4} = 4\frac{6}{8} \).

Step 2: Add the mixed numbers

Add \( 2\frac{5}{8} + 4\frac{6}{8} \). Whole numbers: \( 2 + 4 = 6 \). Fractions: \( \frac{5}{8} + \frac{6}{8} = \frac{11}{8} = 1\frac{3}{8} \).

Step 3: Combine

Combine: \( 6 + 1\frac{3}{8} = 7\frac{3}{8} \).

Let's do problem 5: \( 5\frac{1}{3} + 3\frac{5}{6} \)

Step 1: Convert to like fractions

Convert \( 5\frac{1}{3} \) to sixths. \( \frac{1}{3} = \frac{2}{6} \), so \( 5\frac{1}{3} = 5\frac{2}{6} \).

Step 2: Add the mixed numbers

Add \( 5\frac{2}{6} + 3\frac{5}{6} \). Whole numbers: \( 5 + 3 = 8 \). Fractions: \( \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1\frac{1}{6} \).

Step 3: Combine

Combine: \( 8 + 1\frac{1}{6} = 9\frac{1}{6} \).

Let's do problem 6: \( 2\frac{1}{2} + 6\frac{3}{4} \)

Step 1: Convert to like fractions

Convert \( 2\frac{1}{2} \) to fourths. \( \frac{1}{2} = \frac{2}{4} \), so \( 2\frac{1}{2} = 2\frac{2}{4} \).

Step 2: Add the mixed numbers

Add \( 2\frac{2}{4} + 6\frac{3}{4} \). W…

Step 1: Convert to like fractions

\( 3\frac{1}{2} = 3\frac{4}{8} \) (since \( \frac{1}{2} = \frac{4}{8} \)) and \( 1\frac{4}{8} \) remains.

Step 2: Add whole and fraction parts

Whole numbers: \( 3 + 1 = 4 \). Fractions: \( \frac{4}{8} + \frac{4}{8} = \frac{8}{8} = 1 \).

Step 3: Combine results

\( 4 + 1 = 5 \).

Step 1: Convert to twelfths

\( 4\frac{1}{4} = 4\frac{3}{12} \) (since \( \frac{1}{4} = \frac{3}{12} \)).

Step 2: Add parts

Whole numbers: \( 2 + 4 = 6 \). Fractions: \( \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3} \).

Step 3: Combine

\( 6 + \frac{2}{3} = 6\frac{2}{3} \).

Answer:

\( 5 \)

Problem 2: \( 2\frac{5}{12} + 4\frac{1}{4} \)