For an art project Marco cuts a 14 2/7 piece of string into 8 equal pieces. How long is each piece? Maria cuts her string into 8 equal pieces of length 2 11/14 ft. Which student started with the longer piece of string? How much longer was it? How long is each of Marcos 8 pieces of string?
14 2/7 = 100/7
(100 / 7) / 8 = ________ pieces
8 * 2 11/14 = _________ inches
1/5
To find the length of each piece of string that Marco cuts, we need to divide the total length of the string (14 2/7) by the number of equal pieces (8).
Step 1: Convert the mixed number (14 2/7) to an improper fraction.
14 2/7 = (7 * 14 + 2) / 7 = 98/7
Step 2: Divide the total length of the string by the number of equal pieces.
98/7 ÷ 8 = 98/7 * 1/8 = (98 * 1) / (7 * 8) = 98/56
Each of Marco's 8 pieces of string is 98/56, which can be simplified to 49/28 or 1 21/28.
Now let's determine the length of each piece of string that Maria cuts.
Step 1: Convert the mixed number (2 11/14 ft) to an improper fraction.
2 11/14 = (14 * 2 + 11) / 14 = 39/14
Step 2: Divide the total length of the string by the number of equal pieces.
39/14 ÷ 8 = 39/14 * 1/8 = (39 * 1) / (14 * 8) = 39/112
Each of Maria's 8 pieces of string is 39/112.
To determine who started with the longer piece of string, we can compare the lengths by finding the decimal equivalents of the fractions.
The decimal equivalent of 49/28 is approximately 1.75 ft and 39/112 is approximately 0.35 ft.
Therefore, Marco started with the longer piece of string, which is 1.75 - 0.35 = 1.4 ft longer than Maria's piece.
In summary:
- Each of Marco's 8 pieces of string is 1 21/28 ft.
- Each of Maria's 8 pieces of string is 39/112 ft.
- Marco started with the longer piece of string, which was 1.4 ft longer than Maria's piece.