Sure, I can help guide you through creating and understanding equivalent fractions with step-by-step instructions.
### Understanding Equivalent Fractions
Equivalent fractions are different fractions that represent the same value or proportion of the whole. For example, [tex]\(\frac{1}{2}\)[/tex] is equivalent to [tex]\(\frac{2}{4}\)[/tex], because both represent the same part of the whole.
### Problem 1: Write an equivalent fraction
a. [tex]\(\frac{1}{4}\)[/tex]
To create an equivalent fraction, you can multiply the numerator and the denominator by the same non-zero number.
#### Step-by-Step Solution:
1. Choose a number to multiply both the numerator and denominator by. Let's choose 2 for this example.
[tex]\[
\text{Numerator: } 1 \times 2 = 2
\][/tex]
[tex]\[
\text{Denominator: } 4 \times 2 = 8
\][/tex]
So, [tex]\(\frac{1}{4} = \frac{2}{8}\)[/tex].
Let's check another equivalent fraction by multiplying the numerator and the denominator by 3.
2. Choose a number to multiply both the numerator and denominator by. This time, let's choose 3.
[tex]\[
\text{Numerator: } 1 \times 3 = 3
\][/tex]
[tex]\[
\text{Denominator: } 4 \times 3 = 12
\][/tex]
So, [tex]\(\frac{1}{4} = \frac{3}{12}\)[/tex].
Thus, [tex]\(\frac{1}{4}\)[/tex] is equivalent to both [tex]\(\frac{2}{8}\)[/tex] and [tex]\(\frac{3}{12}\)[/tex]. These fractions all represent the same part of the whole.
### Summary:
a. [tex]\(\frac{1}{4} = \frac{2}{8}\)[/tex] or [tex]\(\frac{1}{4} = \frac{3}{12}\)[/tex]
By multiplying the numerator and the denominator of [tex]\(\frac{1}{4}\)[/tex] by the same number, we find that [tex]\(\frac{2}{8}\)[/tex] and [tex]\(\frac{3}{12}\)[/tex] are equivalent fractions to [tex]\(\frac{1}{4}\)[/tex].
