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Grade 9 Science · Problem type
Mitotic index
Use this for “20 of 100 root-tip cells are in mitosis. How long does mitosis last in a 24-hour cycle?”
Chart
80 + 10 + 5 + 3 + 2 = 100.
This is an example. Type your own values to start a new problem.
t (h)
=
m
×
h (h)
÷
N
I
Cells in interphase
example
P
Cells in prophase
example
M
Cells in metaphase
example
A
Cells in anaphase
example
T
Cells in telophase
example
x
Mitotic index
worked out (not typed) · %
Formulas
N
=
I
+
P
+
M
+
A
+
T
100 = 80 + 10 + 5 + 3 + 2
m
=
P
+
M
+
A
+
T
20 = 10 + 5 + 3 + 2
x
=
100
×
m
N
20
=
100
×
20
100
t
=
m
×
h
N
4.8
=
20
×
24
100
Assumptions
•
The cells are counted in one field of a root tip under a microscope, each in the phase it was in when fixed.
•
Cells divide at random times, so the share of cells in a phase is the share of the cycle spent in it.
•
The mitotic index is the percent of cells in mitosis; a fast-growing tissue, or a tumor, has a high one.
Step-by-step
WE KNOW
I = 80, P = 10, M = 5, A = 3, T = 2, h = 24 h
FIND
cells counted (N), cells in mitosis (m), mitotic index (x), time in mitosis (t)
Step 1 · Find cells counted (N)
Use N = I + P + M + A + T
Every cell counted is in interphase or in one phase of mitosis.
N
=
80
+
10
+
5
+
3
+
2
N
=
100
Step 2 · Find cells in mitosis (m)
Use m = P + M + A + T
The cells in any of the four phases of mitosis.
m
=
10
+
5
+
3
+
2
m
=
20
Step 3 · Find mitotic index (x)
Use x = 100 × m ÷ N
The cells in mitosis as a percent of all the cells counted.
x
=
100
×
20
100
x
=
2,000
100
x
=
20%
Step 4 · Find time in mitosis (t)
Use t = m × h ÷ N
The
share
of
cells
in
mitosis,
m
N
,
is
the
share
of
the
cycle
spent
in
mitosis.
t
=
20
×
24
100
t
=
480
100
t
=
4.8
h
Check
Put the numbers back in. Both sides should match.
100 = 80 + 10 + 5 + 3 + 2 ✓
20 = 10 + 5 + 3 + 2 ✓
20
=
100
×
20
100
✓
4.8
=
20
×
24
100
✓
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