The Lowest Common Denominator of 3 and 4 is the denominator that will
simplify mathematical operations such as addition of the fractions.
- The mistake is the LCD of 3 and 4 is 12 rather than 24
Reasons:
The given fractions are;
[tex]\displaystyle \frac{1}{3} \ and \ \mathbf{\frac{2}{4}}[/tex]
The Lowest Common Denominator, is given by the Least Common Multiple of the denominators, which is 3 × 4 = 12
Therefore;
The LCD = 12
The equivalent fractions are therefore;
[tex]\displaystyle \frac{1}{3 } = \frac{4 \times 1}{4 \times 3} = \mathbf{\frac{4}{12}}[/tex]
[tex]\displaystyle \frac{2}{4} =\frac{3 \times 2}{3 \times 4} = \mathbf{ \frac{6}{12}}[/tex]
[tex]\displaystyle The \ equivalent \ fractions \ are \ \frac{4}{12} \ and \ \frac{6}{12}[/tex]
Therefore, the mistake is using a LCD of 24 rather than 12, given that 12 is lower than 24 and therefore is the LCD of 3 and 4.
By having an LCD of 12, we have;
The equivalent fractions with the LCD will be; [tex]\displaystyle \frac{4}{12} \ and \ \frac{6}{12}[/tex]
Learn more about Lowest Common Denominator, LCD here:
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