Question

1. \\(\frac{1}{2}+\frac{1}{4}=\frac{\square}{\square}+\frac{\square}{\square}=\frac{\square}{\square}\\)

(there is a diagram with colored blocks labeled 1, \\(\frac{1}{2}\\), \\(\frac{1}{4}\\) etc.)
remember that you can use multiples to find a common denominator.

1. \\(\

$$\begin{array}{r}\\frac{1}{4}=\\frac{\\square}{8}\\\\ -\\frac{1}{8}=\\frac{\\square}{8}\\\\ \\hline \\frac{\\square}{\\square}\\end{array}$$

\\)
(there is a diagram with colored blocks labeled 1, \\(\frac{1}{4}\\), \\(\frac{1}{8}\\) etc.)
topic 8 | lesson 8-3

Explanation:

Step1: Solve \(\frac{1}{2}+\frac{1}{4}\)

To add these fractions, find a common denominator. The common denominator of 2 and 4 is 4. Convert \(\frac{1}{2}\) to a fraction with denominator 4: \(\frac{1}{2}=\frac{1\times2}{2\times2}=\frac{2}{4}\). Now add \(\frac{2}{4}+\frac{1}{4}=\frac{2 + 1}{4}=\frac{3}{4}\).

Step2: Solve \(\frac{1}{4}=\frac{\square}{8}\)

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

Step3: Solve \(-\frac{1}{8}=\frac{\square}{8}\)

The fraction \(-\frac{1}{8}\) already has denominator 8, so the numerator is - 1.

Step4: Subtract the fractions

Now subtract \(\frac{2}{8}-\frac{1}{8}=\frac{2-1}{8}=\frac{1}{8}\).

Answer:

For \(\frac{1}{2}+\frac{1}{4}\): \(\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\) (blanks: 2, 4, 1, 4, 3, 4)
For \(\frac{1}{4}-\frac{1}{8}\): \(\frac{2}{8}-\frac{1}{8}=\frac{1}{8}\) (blanks: 2, - 1, 1, 8)