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Zorluk: KolayFraction Addition and Subtraction in Context

A storage warehouse is currently filled to 14\frac{1}{4} of its total capacity. A new shipment arrives and is stored, bringing the warehouse to 56\frac{5}{6} of its total capacity. What fraction of the warehouse's capacity was filled by the new shipment?

  1. 712\frac{7}{12}Cevap
  2. B
    35\frac{3}{5}
  3. C
    23\frac{2}{3}
  4. D
    16\frac{1}{6}

Cevap

The new shipment filled 712\frac{7}{12} of the warehouse's capacity.
To find the amount of capacity added, subtract the initial capacity from the final capacity (56−14\frac{5}{6} - \frac{1}{4}). Convert both fractions to a common denominator of 12, resulting in 1012\frac{10}{12} and 312\frac{3}{12}. Subtracting these fractions gives 712\frac{7}{12}.

Adım Adım Çözüm

1
Set up the subtraction expression to find the difference in capacity.
56−14\frac{5}{6} - \frac{1}{4}
The fraction added is equal to the final capacity minus the initial capacity.
2
Find the lowest common denominator (LCD) for the fractions with denominators 6 and 4.
The LCD is 12.
Fractions must have a common denominator before they can be added or subtracted.
3
Convert both fractions to equivalent fractions with a denominator of 12.
56=1012\frac{5}{6} = \frac{10}{12} and 14=312\frac{1}{4} = \frac{3}{12}
This standardizes the parts so they can be accurately subtracted.
4
Subtract the numerators and keep the common denominator.
1012−312=712\frac{10}{12} - \frac{3}{12} = \frac{7}{12}
The numerators represent the specific number of parts being subtracted from the whole.

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Fraction Addition and Subtraction in Context
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Fraction Addition and Subtraction in Context

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