Question

add.
\\(\frac{7}{12} + \frac{3}{4} = \square\\)
use the model to help you.
+ \\(\

$$\begin{array}{|c|c|c|c|c|c|c|}\\hline \\frac{1}{12} & \\frac{1}{12} & \\frac{1}{12} & \\frac{1}{12} & \\frac{1}{12} & \\frac{1}{12} & \\frac{1}{12} \\\\ \\hline \\end{array}$$

\\)
\\(\

$$\begin{array}{|c|c|c|}\\hline \\frac{1}{4} & \\frac{1}{4} & \\frac{1}{4} \\\\ \\hline \\end{array}$$

\\)

Explanation:

Step1: Convert to common denominator

To add \(\frac{7}{12}\) and \(\frac{3}{4}\), we need a common denominator. The least common denominator of 12 and 4 is 12. So we convert \(\frac{3}{4}\) to twelfths: \(\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}\).

Step2: Add the fractions

Now we add \(\frac{7}{12}+\frac{9}{12}\). When adding fractions with the same denominator, we add the numerators: \(7 + 9 = 16\), so the sum is \(\frac{16}{12}\).

Step3: Simplify the fraction

Simplify \(\frac{16}{12}\) by dividing numerator and denominator by their greatest common divisor, which is 4. \(\frac{16\div4}{12\div4}=\frac{4}{3}\) or as a mixed number \(1\frac{1}{3}\). But looking at the model, we can also count the total parts. The red has 7 twelfths, and each blue \(\frac{1}{4}\) is 3 twelfths (since \(\frac{1}{4}=\frac{3}{12}\)), so 3 blue parts are \(3\times3 = 9\) twelfths. Total twelfths: \(7 + 9 = 16\) twelfths, which is \(\frac{16}{12}=\frac{4}{3}\).

Answer:

\(\frac{4}{3}\) (or \(1\frac{1}{3}\))