a. $$ \frac{3}{4}=\frac{1}{8}+\frac{4}{12}= $$ $$ \square $$ b. $$ \frac{4}{6}=\frac{1}{3}+\square= $$ $$ \square $$ Complete the sums. a. $$ \frac{1}{2}=\frac{1}{8}+\square=\square $$ b. $$ \frac{1}{2}=\frac{1}{14}+ $$ $$ \qquad $$

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UpStudy AI · Accepted Answer

Let's solve each part step by step.

### Part a
We need to complete the equation:
$$
\frac{3}{4} = \frac{1}{8} + \frac{4}{12}
$$

First, let's simplify $$\frac{4}{12}$$:
$$
\frac{4}{12} = \frac{1}{3}
$$

Now, we can rewrite the equation:
$$
\frac{3}{4} = \frac{1}{8} + \frac{1}{3}
$$

Next, we need to find a common denominator to add $$\frac{1}{8}$$ and $$\frac{1}{3}$$. The least common multiple of 8 and 3 is 24.

Now, we convert each fraction:
$$
\frac{1}{8} = \frac{3}{24}
$$
$$
\frac{1}{3} = \frac{8}{24}
$$

Now we can add them:
$$
\frac{3}{24} + \frac{8}{24} = \frac{11}{24}
$$

So, we have:
$$
\frac{3}{4} = \frac{11}{24}
$$

Now, we need to find the value of $$\square$$:
$$
\frac{3}{4} = \frac{1}{8} + \square
$$
$$
\square = \frac{3}{4} - \frac{1}{8}
$$

Finding a common denominator (which is 8):
$$
\frac{3}{4} = \frac{6}{8}
$$
$$
\square = \frac{6}{8} - \frac{1}{8} = \frac{5}{8}
$$

Thus, the completed equation is:
$$
\frac{3}{4} = \frac{1}{8} + \frac{5}{8} = \frac{3}{4}
$$

### Part b
Now, we need to complete the equation:
$$
\frac{4}{6} = \frac{1}{3} + \square
$$

First, simplify $$\frac{4}{6}$$:
$$
\frac{4}{6} = \frac{2}{3}
$$

Now we can rewrite the equation:
$$
\frac{2}{3} = \frac{1}{3} + \square
$$

To find $$\square$$:
$$
\square = \frac{2}{3} - \frac{1}{3} = \frac{1}{3}
$$

Thus, the completed equation is:
$$
\frac{4}{6} = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}
$$

### Summary of Results
- For part a: 
  - $$ \square = \frac{5}{8} $$
- For part b: 
  - $$ \square = \frac{1}{3} $$

So the final answers are:
- a. $$ \frac{1}{2} = \frac{1}{8} + \frac{5}{8} = \frac{1}{2} $$
- b. $$ \frac{1}{2} = \frac{1}{14} + \frac{1}{3} $$
a. $$ \frac{1}{2} = \frac{1}{8} + \frac{5}{8} = \frac{1}{2} $$ b. $$ \frac{1}{2} = \frac{1}{14} + \frac{1}{3} $$

a. \( \frac{3}{4}=\frac{1}{8}+\frac{4}{12}= \) \( \square \) b. \( \frac{4}{6}=\frac{1}{3}+\square= \) \( \square \) Complete the sums. a. \( \frac{1}{2}=\frac{1}{8}+\square=\square \) b. \( \frac{1}{2}=\frac{1}{14}+ \) \( \qquad \)

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