un atleta debe recorrer 30 km en sus ultimos 5 dias de preparacion para una competencia. el primer dia recorre frac{23}{2} km, el segundo frac{15}{4} km, el tercer dia frac{16}{3} km y el cuarto dia frac{35}{6} km. ¿cuanto km recorrió el atleta en estos cuatro dias?

ddaeeric 2021-02-13 Answered

An athlete must travel 30 km in his last 5 days of preparation for a competition. the first day runs 232 km, the second 154 km, the third day 163 km and the fourth day​​​​​​​ 356 km. How much km did the athlete travel in these four days?

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Expert Answer

Macsen Nixon
Answered 2021-02-14 Author has 117 answers

The total distance the athlete traveled over the four days is the sum of the four given fractions.

To add fractions, you must first rewrite them to have a common denominator.

For the fractions, 232, 154, 163, and 356, the denominators are 2, 4, 3, and 6.

To find a common denominator, you then need to find the least common multiple of 2, 3, 4, and 6.

Since 2 and 3 are factors of 6, the lowest common multiply of 2, 3, 4, and 6 is the lowest common multiple of 4 and 6.

The first few multiples of 4 are 4, 8, 12, and 16, The first few multiples of 6 are 6, 12, 18, and 24.

The least common multiple of 4 and 6 is then 12.

You then need to rewrite the fractions to have a denominator of 12:

232=23×62×6=13812

154=15×34×3=4512

163=16×43×4=6412

356=35×26×12=7012

Now that the fractions have a common denominator, you can add them to find the total distance that the athlete traveled.

To add the fractions, add the numerators and leave the denominator the same:

13812+4512+6412+7012=138+45+64+7012=31712

To convert an improper fraction to a mixed number, determine how many times the denominator goes into the numerator. 12 goes into 317 twenty-six times with a remainder of 5 since 317=12×26+5.

Therefore 31712=26×512.

The athlete then traveled a total distance of 26×512 km ​ over the four days.

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