For an art​ project,

Marco
cuts
a

12 and two thirds
ft piece of string into
8
equal pieces. How long is each​ piece?
Maria
cuts
her
string into
8
equal pieces of length
2 and seven twelfths
ft. Which student started with the longer piece of​ string? How much longer was​ it?

I figured it out

Marcos pieces are each 1' 7"inches (which is irrelevant to the final result). Maria started with 8 pieces @ 2' 7" which equals 20' 8". Ergo Maria's string started 8' longer than Marcos was.

To find the length of each piece, we need to divide the total length of the string by the number of equal pieces.

Marco started with a 12 and two-thirds ft piece of string and cuts it into 8 equal pieces:

12 and two-thirds ft ÷ 8 = ?

To divide mixed numbers, we can convert them into improper fractions:

12 and two-thirds = (3 * 12) + 2 = 38/3

Now we can divide:

(38/3) ÷ 8 = (38/3) * (1/8) = 38/24 = 19/12

Therefore, each piece of Marco's string is 19/12 ft long.

Similarly, Maria cuts her string into 8 equal pieces of length 2 and seven twelfths ft:

2 and seven twelfths ft ÷ 8 = ?

Again, let's convert the mixed number into an improper fraction:

2 and seven twelfths = (12 * 2) + 7 = 31/12

Now we can divide:

(31/12) ÷ 8 = (31/12) * (1/8) = 31/96

So, each piece of Maria's string is 31/96 ft long.

To determine which student started with the longer piece of string, we compare the lengths of their original strings: 12 and two-thirds ft and 2 and seven twelfths ft.

To compare fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12. So, let's convert the fractions:

12 and two-thirds = (3 * 12) + 2 = 38/3

2 and seven twelfths = (12 * 2) + 7 = 31/12

Now, let's compare them:

38/3 vs. 31/12

To compare fractions, we can either convert them to decimal form or find a common numerator. Let's find a common numerator by multiplying both fractions by the appropriate factors:

For 38/3, we multiply the numerator and denominator by 4:

(38/3) * (4/4) = 152/12

Now we can compare:

152/12 vs. 31/12

Since the denominators are the same, the longer string is the one with the greater numerator. In this case, 152/12 is greater than 31/12.

Therefore, Marco started with the longer piece of string. To find out how much longer it was, we can subtract the lengths:

Length of Marco's string - Length of Maria's string = (38/3) ft - (31/12) ft = 152/12 ft - 31/12 ft.

Subtracting the fractions:

(152/12) - (31/12) = 121/12

Therefore, Marco's string was 121/12 ft longer than Maria's string.

At​ most, how many two fifths

2
5​-inch-long pieces of string can you cut from a four fifths
4
5​-inch-long piece of​ string?