Christopher has a stick that he has marked out in tenths. He has to break the stick into three pieces of which no two pieces can have the same length. Give three equations that show different ways in which he could break the stick.
(4 points)
Let's assume that the stick has a total length of 1 unit.
First equation:
Let's say Christopher breaks the stick at the 0.3 mark and 0.6 mark.
This can be represented by the equation:
x + y + z = 1,
where x represents the length of the first piece (0 ≤ x < 0.3), y represents the length of the second piece (0.3 < y < 0.6), and z represents the length of the third piece (0.6 < z ≤ 1).
Second equation:
Let's say Christopher breaks the stick at the 0.2 mark and 0.8 mark.
This can be represented by the equation:
x + y + z = 1,
where x represents the length of the first piece (0 ≤ x < 0.2), y represents the length of the second piece (0.2 < y < 0.8), and z represents the length of the third piece (0.8 < z ≤ 1).
Third equation:
Let's say Christopher breaks the stick at the 0.1 mark and 0.5 mark.
This can be represented by the equation:
x + y + z = 1,
where x represents the length of the first piece (0 ≤ x < 0.1), y represents the length of the second piece (0.1 < y < 0.5), and z represents the length of the third piece (0.5 < z ≤ 1).
Christopher has a stick that he has marked out in tenths. He has to break the stick into three pieces of which no two pieces can have the same length. Give three equations that show different ways in which he could break the stick.
(4 points)
Let's assume that the stick has a total length of 1 unit, marked out in tenths.
First equation:
Let's say Christopher breaks the stick at the 0.1 mark and 0.4 mark. This can be represented by the equation:
x + y + z = 1,
where x represents the length of the first piece (0 ≤ x < 0.1), y represents the length of the second piece (0.1 < y < 0.4), and z represents the length of the third piece (0.4 < z ≤ 1).
Second equation:
Let's say Christopher breaks the stick at the 0.2 mark and 0.7 mark. This can be represented by the equation:
x + y + z = 1,
where x represents the length of the first piece (0 ≤ x < 0.2), y represents the length of the second piece (0.2 < y < 0.7), and z represents the length of the third piece (0.7 < z ≤ 1).
Third equation:
Let's say Christopher breaks the stick at the 0.3 mark and 0.9 mark. This can be represented by the equation:
x + y + z = 1,
where x represents the length of the first piece (0 ≤ x < 0.3), y represents the length of the second piece (0.3 < y < 0.9), and z represents the length of the third piece (0.9 < z ≤ 1).
Select the equation represented by the fraction strips below.
3 whole unit fraction strips are shown lined up horizontally and side to side. Each whole unit is labeled with a 1. Directly below these unit strips and to the left are 5 smaller strips that are each a quarter of the length of a unit strip. Farther down and to the right of these smaller strips are 2 more quarter-length strips with an arrow pointing from these two strips to a dashed outline next to the original 5 fraction strips.
(1 point)
Responses
54+14=64
5 4 + 1 4 = 6 4
54+24=74
5 4 + 2 4 = 7 4
54+24=2
5 4 + 2 4 = 2
54+24=78
The equation represented by the fraction strips is:
5/4 + 2/4 = 7/4
Select which option is most appropriate for describing the number line below.
A number line is divided into eighths. A dashed arrow is shown starting at seven-eighths and ending at, as well as pointing to, two-eighths.
(1 point)
Responses
subtraction of 78
subtraction of 7 8
addition of 28
addition of 2 8
addition of 58
addition of 5 8
subtraction of 58
subtraction of 5 8
The most appropriate description for the number line below is:
subtraction of 5/8