Question

add. (\frac{2}{5} + \frac{4}{10} = square) use the model to help you. image contains 2 blue rectangles (each labeled (\frac{1}{5})), a + sign, and 4 yellow rectangles (each labeled (\frac{1}{10})), with a horizontal line below for the sum.

Explanation:

Step1: Convert to common denominator

To add \(\frac{2}{5}\) and \(\frac{4}{10}\), we can convert \(\frac{2}{5}\) to tenths. Since \(5\times2 = 10\), multiply numerator and denominator by 2: \(\frac{2\times2}{5\times2}=\frac{4}{10}\).

Step2: Add the fractions

Now add \(\frac{4}{10}+\frac{4}{10}\). When adding fractions with the same denominator, add the numerators: \(\frac{4 + 4}{10}=\frac{8}{10}\). Simplify by dividing numerator and denominator by 2: \(\frac{8\div2}{10\div2}=\frac{4}{5}\) (or keep as \(\frac{8}{10}\) which simplifies to \(\frac{4}{5}\), or also \(\frac{8}{10}=0.8\), but fraction form is better here). Alternatively, using the model: each \(\frac{1}{5}\) is \(\frac{2}{10}\), so two \(\frac{1}{5}\)s are \(\frac{4}{10}\), plus four \(\frac{1}{10}\)s is \(\frac{8}{10}=\frac{4}{5}\).

Answer:

\(\frac{4}{5}\) (or \(\frac{8}{10}\) but simplified is \(\frac{4}{5}\))