Question

Q. 3. On a recent math test, Aubrey was asked to find the LCD of and and then to write equivalent fractions using this LCD. Aubrey felt
confident that she answered the question correctly, but when she received her graded test, her answer was marked as incorrect. View
Aubrey's work below to find her mistake and then describe to Aubrey the mistake you found.
Aubrey's work:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24
Multiples of 4: 4, 8, 12, 16, 20, 24
LCD of 3 and 4 is 24. Equivalent fractions with the LCD: and

Answer 1

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;

$\displaystyle \frac{1}{3} \ and \ \mathbf{\frac{2}{4}}$

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;

$\displaystyle \frac{1}{3 } = \frac{4 \times 1}{4 \times 3} = \mathbf{\frac{4}{12}}$

$\displaystyle \frac{2}{4} =\frac{3 \times 2}{3 \times 4} = \mathbf{ \frac{6}{12}}$

$\displaystyle The \ equivalent \ fractions \ are \ \frac{4}{12} \ and \ \frac{6}{12}$

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; $\displaystyle \frac{4}{12} \ and \ \frac{6}{12}$

Learn more about Lowest  Common Denominator, LCD here:

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