To identify fractions equivalent to [tex]\(\frac{1}{2}\)[/tex], let's follow the instructions step by step to build rows of length [tex]\(\frac{1}{2}\)[/tex] using different fractional pieces.
### Step 1: Use [tex]\(\frac{1}{8}\)[/tex] pieces to build a row of length [tex]\(\frac{1}{2}\)[/tex]
To find out how many [tex]\(\frac{1}{8}\)[/tex] pieces will make up [tex]\(\frac{1}{2}\)[/tex], we can set up the following equation:
[tex]\[ \frac{n}{8} = \frac{1}{2} \][/tex]
Now, solve for [tex]\(n\)[/tex]:
[tex]\[ n = \frac{1}{2} \times 8 = 4 \][/tex]
Thus, it takes 4 pieces of [tex]\(\frac{1}{8}\)[/tex] to make [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{4 \cdot 1}{8} = \frac{4}{8} = \frac{1}{2} \][/tex]
So, [tex]\(\frac{4}{8}\)[/tex] is equivalent to [tex]\(\frac{1}{2}\)[/tex].
### Step 2: Use [tex]\(\frac{1}{12}\)[/tex] pieces to build a row of length [tex]\(\frac{1}{2}\)[/tex]
To find out how many [tex]\(\frac{1}{12}\)[/tex] pieces will make up [tex]\(\frac{1}{2}\)[/tex], we set up the following equation:
[tex]\[ \frac{n}{12} = \frac{1}{2} \][/tex]
Now, solve for [tex]\(n\)[/tex]:
[tex]\[ n = \frac{1}{2} \times 12 = 6 \][/tex]
Thus, it takes 6 pieces of [tex]\(\frac{1}{12}\)[/tex] to make [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{6 \cdot 1}{12} = \frac{6}{12} = \frac{1}{2} \][/tex]
So, [tex]\(\frac{6}{12}\)[/tex] is equivalent to [tex]\(\frac{1}{2}\)[/tex].
### Step 3: Use [tex]\(\frac{1}{16}\)[/tex] pieces to build a row of length [tex]\(\frac{1}{2}\)[/tex]
To find out how many [tex]\(\frac{1}{16}\)[/tex] pieces will make up [tex]\(\frac{1}{2}\)[/tex], we set up the following equation:
[tex]\[ \frac{n}{16} = \frac{1}{2} \][/tex]
Now, solve for [tex]\(n\)[/tex]:
[tex]\[ n = \frac{1}{2} \times 16 = 8 \][/tex]
Thus, it takes 8 pieces of [tex]\(\frac{1}{16}\)[/tex] to make [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{8 \cdot 1}{16} = \frac{8}{16} = \frac{1}{2} \][/tex]
So, [tex]\(\frac{8}{16}\)[/tex] is equivalent to [tex]\(\frac{1}{2}\)[/tex].
### Summary of Equivalent Fractions
We have identified the following fractions which are equivalent to [tex]\(\frac{1}{2}\)[/tex]:
1. [tex]\(\frac{4}{8}\)[/tex]
2. [tex]\(\frac{6}{12}\)[/tex]
3. [tex]\(\frac{8}{16}\)[/tex]
All these fractions simplify to [tex]\(\frac{1}{2}\)[/tex], showing their equivalence.
