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Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now (25)/(4) meters directly to her right, and her labrador is (51)/(20) meters directly to her left. Which 2 of the following expressions represents how far apart the two dogs are? Choose 2 answers: A. |(25)/(4)+(51)/(20)| B |-(51)/(20)+(25)/(4)| c. |-(51)/(20)-(25)/(4)|

Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now 254 \frac{25}{4} meters directly to her right, and her labrador is 5120 \frac{51}{20} meters directly to her left.\newlineWhich 22 of the following expressions represents how far apart the two dogs are?\newlineChoose 22 answers:\newline(A) ∣254+5120∣ \left|\frac{25}{4}+\frac{51}{20}\right| \newline(B) ∣−5120+254∣ \left|-\frac{51}{20}+\frac{25}{4}\right| \newline(C) ∣−5120−254∣ \left|-\frac{51}{20}-\frac{25}{4}\right|

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Q. Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now 254 \frac{25}{4} meters directly to her right, and her labrador is 5120 \frac{51}{20} meters directly to her left.\newlineWhich 22 of the following expressions represents how far apart the two dogs are?\newlineChoose 22 answers:\newline(A) ∣254+5120∣ \left|\frac{25}{4}+\frac{51}{20}\right| \newline(B) ∣−5120+254∣ \left|-\frac{51}{20}+\frac{25}{4}\right| \newline(C) ∣−5120−254∣ \left|-\frac{51}{20}-\frac{25}{4}\right|
  1. Understand the situation: Understand the situation.\newlineNatasha's beagle is 254\frac{25}{4} meters to her right, and her labrador is 5120\frac{51}{20} meters to her left. Since they ran in opposite directions, the distance between them is the sum of these two distances.
  2. Convert fractions to common denominator: Convert the fractions to have a common denominator to add them easily.\newlineThe common denominator for 44 and 2020 is 2020. Convert (254)(\frac{25}{4}) to a fraction with a denominator of 2020.\newline(254)×(55)=(12520)(\frac{25}{4}) \times (\frac{5}{5}) = (\frac{125}{20})
  3. Add distances together: Add the distances together.\newlineNow that both fractions have the same denominator, add them together.\newline(12520)+(5120)=(17620)(\frac{125}{20}) + (\frac{51}{20}) = (\frac{176}{20})
  4. Simplify the fraction: Simplify the fraction.\newline(176/20)(176/20) can be simplified by dividing both the numerator and the denominator by 44.\newline(176/20)/(4/4)=(44/5)(176/20) / (4/4) = (44/5)
  5. Convert to mixed number: Convert the simplified fraction to a mixed number.\newline(44/5)(44/5) is equal to 88 with a remainder of 44, so it can be written as 88 4/54/5 or 8.88.8 meters.
  6. Determine correct expressions: Determine the correct expressions.\newlineThe distance between the two dogs is the absolute value of the sum of the distances from Natasha to each dog. The correct expressions must add the two distances together.\newlineA. ∣254+5120∣\left|\frac{25}{4} + \frac{51}{20}\right| is correct because it adds the two distances.\newlineB. ∣−5120+254∣\left|-\frac{51}{20} + \frac{25}{4}\right| is also correct because it represents the same sum, just starting with the labrador's distance.\newlineC. ∣−5120−254∣\left|-\frac{51}{20} - \frac{25}{4}\right| is incorrect because it subtracts the distances, which does not represent the total distance between the two dogs.

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