Math / Numbers & Operations

Question1.5.PS-14 Flying Home A bird flies from the bottom of a canyon that is $58 \frac{7}{10}$ feet below sea level to a nest that is $517 \frac{4}{5}$ feet sea level. What is the difference in elevation between the bottom of the canyon and the bird's nest?
The difference between the elevation of the canyon and the bird's nest is $\square$ feet. (Simplify your answer. Type an integer, proper fraction, or mixed number.)

Studdy Solution

STEP 1

1. The bird starts at an elevation of $58 \frac{7}{10}$ feet below sea level and flies to a nest located at $517 \frac{4}{5}$ feet above sea level.
2. The difference in elevation can be calculated by finding the absolute difference between the two elevations.
3. Mixed numbers will need to be converted to improper fractions or decimals to perform the subtraction more easily.

STEP 2

1. Convert the mixed numbers to improper fractions or decimals.
2. Calculate the difference in elevation between the two points.
3. Simplify the result if necessary.

STEP 3

Convert $58 \frac{7}{10}$ to an improper fraction.
$58 \frac{7}{10} = \frac{587}{10}$

STEP 4

Convert $517 \frac{4}{5}$ to an improper fraction.
$517 \frac{4}{5} = \frac{2589}{5}$

STEP 5

Since the denominators are different, convert both fractions to have a common denominator.
$\frac{587}{10} = \frac{587 \times 2}{10 \times 2} = \frac{1174}{20}$ $\frac{2589}{5} = \frac{2589 \times 4}{5 \times 4} = \frac{10356}{20}$

STEP 6

Calculate the difference in elevation between the nest and the bottom of the canyon.
$\text{Difference} = \frac{10356}{20} - \left(-\frac{1174}{20}\right)$ $\text{Difference} = \frac{10356}{20} + \frac{1174}{20}$ $\text{Difference} = \frac{10356 + 1174}{20}$ $\text{Difference} = \frac{11530}{20}$

STEP 7

Simplify the fraction $\frac{11530}{20}$ .
$\frac{11530}{20} = \frac{11530 \div 10}{20 \div 10} = \frac{1153}{2}$ $\frac{1153}{2} = 576 \frac{1}{2}$
The difference between the elevation of the canyon and the bird's nest is $576 \frac{1}{2}$ feet.

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Studdy Solution

STEP 1

STEP 2

1. Convert the mixed numbers to improper fractions or decimals.
2. Calculate the difference in elevation between the two points.
3. Simplify the result if necessary.

STEP 3

Convert $58 \frac{7}{10}$ to an improper fraction.
$58 \frac{7}{10} = \frac{587}{10}$

STEP 4

Convert $517 \frac{4}{5}$ to an improper fraction.
$517 \frac{4}{5} = \frac{2589}{5}$

STEP 5

Since the denominators are different, convert both fractions to have a common denominator.
$\frac{587}{10} = \frac{587 \times 2}{10 \times 2} = \frac{1174}{20}$ $\frac{2589}{5} = \frac{2589 \times 4}{5 \times 4} = \frac{10356}{20}$

STEP 6

Calculate the difference in elevation between the nest and the bottom of the canyon.
$\text{Difference} = \frac{10356}{20} - \left(-\frac{1174}{20}\right)$ $\text{Difference} = \frac{10356}{20} + \frac{1174}{20}$ $\text{Difference} = \frac{10356 + 1174}{20}$ $\text{Difference} = \frac{11530}{20}$

STEP 7

Simplify the fraction $\frac{11530}{20}$ .
$\frac{11530}{20} = \frac{11530 \div 10}{20 \div 10} = \frac{1153}{2}$ $\frac{1153}{2} = 576 \frac{1}{2}$
The difference between the elevation of the canyon and the bird's nest is $576 \frac{1}{2}$ feet.

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Studdy Solution

STEP 1

STEP 2

1. Convert the mixed numbers to improper fractions or decimals.2. Calculate the difference in elevation between the two points.3. Simplify the result if necessary.

STEP 3

Convert 5871058 \frac{7}{10}58107​ to an improper fraction.58710=58710 58 \frac{7}{10} = \frac{587}{10} 58107​=10587​

STEP 4

Convert 51745517 \frac{4}{5}51754​ to an improper fraction.51745=25895 517 \frac{4}{5} = \frac{2589}{5} 51754​=52589​

STEP 5

STEP 6

STEP 7

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1. Convert the mixed numbers to improper fractions or decimals.
2. Calculate the difference in elevation between the two points.
3. Simplify the result if necessary.

Convert $58 \frac{7}{10}$ to an improper fraction.
$58 \frac{7}{10} = \frac{587}{10}$

Convert $517 \frac{4}{5}$ to an improper fraction.
$517 \frac{4}{5} = \frac{2589}{5}$