Use the table to answer the question

Question

6th grade average. Total of students
100-90. 32
89-80. 65
79-70. 27

What is the part-to-part ratio for the 6th grade averages of 100-90 to 89-80 written using a colon

Answer 1

To find the part-to-part ratio of the 6th grade averages for the ranges 100-90 and 89-80, we look at the total number of students in each range.

• For the range 100-90, there are 32 students.
• For the range 89-80, there are 65 students.

The part-to-part ratio of the 100-90 range to the 89-80 range is:

\[ 32 : 65 \]

To express this ratio in simplest form, we can divide both numbers by their greatest common divisor (GCD). The GCD of 32 and 65 is 1 (since they have no common divisors other than 1).

Therefore, the simplest form of the ratio remains:

\[ 32 : 65 \]

So, the part-to-part ratio for the 6th grade averages of 100-90 to 89-80 is 32:65.

Answer 2

What is the part-whole ratio of the 6th grade averages of 79-70 using the same table using a colon

Answer 3

To find the part-whole ratio of the 6th grade averages for the range 79-70, we need to determine how many students fall in that range compared to the total number of students in all ranges.

From the table:

• Number of students in the range 79-70: 27
• Number of students in the ranges 100-90 (32) + 89-80 (65) + 79-70 (27):

\[ 32 + 65 + 27 = 124 \]

The total number of students is 124.

Now, the part-whole ratio of the 79-70 range (27 students) to the total (124 students) is:

\[ 27 : 124 \]

This ratio is already in its simplest form, as 27 and 124 have no common divisors other than 1.

Thus, the part-whole ratio for the 6th grade averages of 79-70 is 27:124.