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A jeweler created a parallelogram-shaped pendant.
(1)/(4) of the pendant is covered in emeralds,
(1)/(6) of it is covered in rubies,
(1)/(12) of it is covered in diamonds, and the rest of it is covered in sapphires. How many square centimeters of the pendant are covered in sapphires? Round to the nearest tenth.

$8$ . A jeweler created a parallelogram-shaped pendant. $\frac{1}{4}$ of the pendant is covered in emeralds, $\frac{1}{6}$ of it is covered in rubies, $\frac{1}{12}$ of it is covered in diamonds, and the rest of it is covered in sapphires. How many square centimeters of the pendant are covered in sapphires? Round to the nearest tenth.

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Add, subtract, multiply, or divide two fractions: word problems

Full solution

Q.

8

. A jeweler created a parallelogram-shaped pendant.

\frac{1}{4}

of the pendant is covered in emeralds,

\frac{1}{6}

of it is covered in rubies,

\frac{1}{12}

of it is covered in diamonds, and the rest of it is covered in sapphires. How many square centimeters of the pendant are covered in sapphires? Round to the nearest tenth.

Calculate Total Fraction: First, let's find the total fraction of the pendant covered by emeralds, rubies, and diamonds. $\newline$ $(\frac{1}{4}) + (\frac{1}{6}) + (\frac{1}{12}) = (\frac{3}{12}) + (\frac{2}{12}) + (\frac{1}{12}) = (\frac{6}{12}) = (\frac{1}{2})$
Determine Sapphire Coverage: Now, since half of the pendant is covered by emeralds, rubies, and diamonds, the other half must be covered in sapphires. $\newline$ So, $(1/2)$ of the pendant is covered in sapphires.
Find Area of Sapphires: Let's assume the total area of the pendant is $A$ square centimeters. $\newline$ Then, the area covered in sapphires is $(1/2) \times A$ .
Unable to Calculate: But, we don't know the total area $A$ . Without this information, we can't calculate the exact area covered in sapphires.

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