Sure! Let's go through the process of expressing [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex] as equivalent fractions with the same denominator step by step.
1. Identify the Denominators:
The denominators of the given fractions are [tex]\(4\)[/tex] and [tex]\(12\)[/tex].
2. Find the Least Common Multiple (LCM) of the Denominators:
To have a common denominator, find the least common multiple of [tex]\(4\)[/tex] and [tex]\(12\)[/tex].
The LCM of [tex]\(4\)[/tex] and [tex]\(12\)[/tex] is [tex]\(12\)[/tex].
3. Convert Each Fraction to the Common Denominator:
Now, we'll express each fraction with the common denominator of [tex]\(12\)[/tex].
- For [tex]\(\frac{3}{4}\)[/tex]:
- Multiply the numerator and denominator by the same number such that the denominator becomes [tex]\(12\)[/tex].
- Since [tex]\(4 \times 3 = 12\)[/tex], multiply both the numerator and the denominator of [tex]\(\frac{3}{4}\)[/tex] by [tex]\(3\)[/tex]:
[tex]\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\][/tex]
- For [tex]\(\frac{5}{12}\)[/tex]:
- The denominator is already [tex]\(12\)[/tex], so [tex]\(\frac{5}{12}\)[/tex] remains as it is.
4. Result:
Therefore, the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex] expressed as equivalent fractions with the same denominator are:
[tex]\[
\frac{3}{4} = \frac{9}{12} \quad \text{and} \quad \frac{5}{12} = \frac{5}{12}
\][/tex]
So, we have successfully converted [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex] to equivalent fractions with a common denominator of [tex]\(12\)[/tex], which are [tex]\(\frac{9}{12}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex], respectively.
