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Zorluk: OrtaFractions and Decimals

A digital communications system transmits data packets of three specific sizes: 3518\frac{35}{18} MB, 74\frac{7}{4} MB, and 4924\frac{49}{24} MB. To optimize the network buffer, the engineers must define a standardized base unit size. Every transmitted packet must be an exact multiple of this base unit. To maximize efficiency, what is the largest possible size for this base unit?

  1. 772\frac{7}{72} MBCevap
  2. B
    2452\frac{245}{2} MB
  3. C
    72\frac{7}{2} MB
  4. D
    24572\frac{245}{72} MB

Cevap

The largest possible size for the base unit is 772\frac{7}{72} MB.
To find the largest possible base unit that perfectly divides all three packet sizes, the Highest Common Factor (HCF) of the fractions must be calculated. The formula for the HCF of fractions is HCF(Numerators) / LCM(Denominators). The numerators are 35, 7, and 49, which have an HCF of 7. The denominators are 18, 4, and 24, which have an LCM of 72. Thus, the correct largest base unit is 7/72 MB.

Adım Adım Çözüm

1
Identify the required mathematical operation.
Find the Highest Common Factor (HCF) of the three fractions: 3518\frac{35}{18}, 74\frac{7}{4}, and 4924\frac{49}{24}.
The problem asks for the 'largest possible size' that perfectly divides the sizes of all given packets, which is the definition of HCF.
2
Calculate the HCF of the numerators.
The numerators are 35, 7, and 49. Their HCF is 7.
This value forms the numerator of the final fraction according to the formula.
3
Calculate the Least Common Multiple (LCM) of the denominators.
The denominators are 18, 4, and 24. Their LCM is 72.
This value forms the denominator of the final fraction according to the formula.
4
Combine the results to find the final HCF of the fractions.
772\frac{7}{72} MB.
Applying the formula: HCF of fractions = HCF of NumeratorsLCM of Denominators\frac{\text{HCF of Numerators}}{\text{LCM of Denominators}}.

Anahtar Kavram

Highest Common Factor (HCF) of Fractions
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Konular

Fractions and Decimals

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