Prairie Street is 3 7/8
miles long. Plains Avenue is 3 5/10
miles long. Ellis rides his bike the length of both Prairie Street and Plains Avenue. How many total miles does he ride?(1 point)
Responses
6 7/12
7 3/8
3/8
6 3/8
To find the total distance Ellis rides, we add the length of Prairie Street and Plains Avenue:
3 7/8 + 3 5/10
First, we need to convert the fractions to have the same denominator:
3 7/8 = (8 * 3 + 7)/8 = 31/8
3 5/10 = (10 * 3 + 5)/10 = 35/10
Now, we can add the fractions:
31/8 + 35/10
To add fractions, we need to find a common denominator:
The least common multiple of 8 and 10 is 40.
31/8 = (31 * 5)/(8 * 5) = 155/40
35/10 = (35 * 4)/(10 * 4) = 140/40
Now, we can add the fractions:
155/40 + 140/40 = (155 + 140)/40 = 295/40
The sum of the fractions is 295/40.
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which in this case is 5:
295/40 = (295 ÷ 5)/(40 ÷ 5) = 59/8
So, the total distance Ellis rides is 59/8 miles.
In mixed number form, this can be written as:
59/8 = 7 3/8
Therefore, the correct answer is 7 3/8.
To find the total distance that Ellis rides, we need to add the lengths of Prairie Street and Plains Avenue.
The length of Prairie Street is 3 7/8 miles.
The length of Plains Avenue is 3 5/10 miles, which can be simplified to 3 1/2 miles.
To add these two distances, we need to convert them to a common denominator. Let's convert the length of Plains Avenue to eighths.
3 1/2 miles can be written as 3 4/8 miles.
Now we can add the distances:
3 7/8 miles + 3 4/8 miles = (3 + 3) + (7/8 + 4/8) = 6 + 11/8
To simplify the sum, 11/8 can be rewritten as 1 3/8.
Therefore, the total distance Ellis rides is 6 3/8 miles.
So the answer is 6 3/8 miles.
To find the total length that Ellis rides, we need to add the lengths of Prairie Street and Plains Avenue.
First, let's convert both lengths to the same denominator. Both fractions have different denominators, so we need to find a common denominator. In this case, the least common multiple (LCM) of 8 and 10 is 40.
To convert 3 7/8 to a fraction with a denominator of 40, we multiply the whole number (3) by the denominator (8), which gives us 24. Then we add the numerator (7) to get 31. So, 3 7/8 can be rewritten as 31/8.
To convert 3 5/10 to a fraction with a denominator of 40, we multiply the whole number (3) by the denominator (10), which gives us 30. Then we add the numerator (5) to get 35. So, 3 5/10 can be rewritten as 35/10.
Now, we can add the two fractions together:
31/8 + 35/10.
To add fractions with different denominators, we need to find a common denominator. In this case, the LCM of 8 and 10 is 40.
To convert 31/8 to an equivalent fraction with a denominator of 40, we multiply both the numerator and denominator by 5:
(31 × 5) / (8 × 5) = 155/40.
To convert 35/10 to an equivalent fraction with a denominator of 40, we multiply both the numerator and denominator by 4:
(35 × 4) / (10 × 4) = 140/40.
Now we have:
155/40 + 140/40.
To add the fractions, we add the numerators and keep the denominator the same:
(155 + 140) / 40 = 295/40.
Now, let's simplify the fraction. The greatest common divisor (GCD) of 295 and 40 is 5. So, we divide both the numerator and denominator by 5:
(295 ÷ 5) / (40 ÷ 5) = 59/8.
Therefore, the total length that Ellis rides is 59/8 miles.