## Write Any Two Proportions by Using Means

Name
Date

1
Using 8 and 13 as means, write any two proportions.
2
Using 8 and 21 as means, write any two proportions.
3
Using 10 and 17 as means, write any two proportions.
4
Using 7 and 28 as means, write any two proportions.
5
Using 6 and 9 as means, write any two proportions.
6
Using 5 and 22 as means, write any two proportions.
7
Using 5 and 38 as means, write any two proportions.
8
Using 3 and 66 as means, write any two proportions.
9
Using 6 and 6 as means, write any two proportions.
10
Using 2 and 87 as means, write any two proportions.

Answers Key
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1
Using 8 and 13 as means, write any two proportions.
2:8 :: 13:52 and 4:8 :: 13:26
step 1
Find the product of Means
8 x 13 = 104
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 8 x 13
Product of Extremes = 104
step 3
To find the Extremes, find the factors of 104
Factors of 104 = 2, 4, 52, 26
step 4
Write the possible pair of multiplication factors (Extremes) that makes 104
2 x 52 = 104
4 x 26 = 104
Either 2 & 52 or 4 & 26 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
2 x 52 = 8 x 13
or
4 x 26 = 8 x 13
or
step 6
Write the above expression in the fraction form
So,
2 x 52 = 8 x 13 can be written as
28
=
1352
similarly,
4 x 26 = 8 x 13 can be written as
48
=
1326
step 7
Write the above fractions in the ratio form
2:8 = 13:52
or
4:8 = 13:26
step 8
Therefore, the two proportions are
2:8 :: 13:52 & 4:8 :: 13:26
2
Using 8 and 21 as means, write any two proportions.
4:8 :: 21:42 and 2:8 :: 21:84
step 1
Find the product of Means
8 x 21 = 168
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 8 x 21
Product of Extremes = 168
step 3
To find the Extremes, find the factors of 168
Factors of 168 = 4, 2, 42, 84
step 4
Write the possible pair of multiplication factors (Extremes) that makes 168
4 x 42 = 168
2 x 84 = 168
Either 4 & 42 or 2 & 84 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
4 x 42 = 8 x 21
or
2 x 84 = 8 x 21
or
step 6
Write the above expression in the fraction form
So,
4 x 42 = 8 x 21 can be written as
48
=
2142
similarly,
2 x 84 = 8 x 21 can be written as
28
=
2184
step 7
Write the above fractions in the ratio form
4:8 = 21:42
or
2:8 = 21:84
step 8
Therefore, the two proportions are
4:8 :: 21:42 & 2:8 :: 21:84
3
Using 10 and 17 as means, write any two proportions.
2:10 :: 17:85 and 5:10 :: 17:34
step 1
Find the product of Means
10 x 17 = 170
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 10 x 17
Product of Extremes = 170
step 3
To find the Extremes, find the factors of 170
Factors of 170 = 2, 5, 85, 34
step 4
Write the possible pair of multiplication factors (Extremes) that makes 170
2 x 85 = 170
5 x 34 = 170
Either 2 & 85 or 5 & 34 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
2 x 85 = 10 x 17
or
5 x 34 = 10 x 17
or
step 6
Write the above expression in the fraction form
So,
2 x 85 = 10 x 17 can be written as
210
=
1785
similarly,
5 x 34 = 10 x 17 can be written as
510
=
1734
step 7
Write the above fractions in the ratio form
2:10 = 17:85
or
5:10 = 17:34
step 8
Therefore, the two proportions are
2:10 :: 17:85 & 5:10 :: 17:34
4
Using 7 and 28 as means, write any two proportions.
4:7 :: 28:49 and 2:7 :: 28:98
step 1
Find the product of Means
7 x 28 = 196
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 7 x 28
Product of Extremes = 196
step 3
To find the Extremes, find the factors of 196
Factors of 196 = 4, 2, 49, 98
step 4
Write the possible pair of multiplication factors (Extremes) that makes 196
4 x 49 = 196
2 x 98 = 196
Either 4 & 49 or 2 & 98 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
4 x 49 = 7 x 28
or
2 x 98 = 7 x 28
or
step 6
Write the above expression in the fraction form
So,
4 x 49 = 7 x 28 can be written as
47
=
2849
similarly,
2 x 98 = 7 x 28 can be written as
27
=
2898
step 7
Write the above fractions in the ratio form
4:7 = 28:49
or
2:7 = 28:98
step 8
Therefore, the two proportions are
4:7 :: 28:49 & 2:7 :: 28:98
5
Using 6 and 9 as means, write any two proportions.
3:6 :: 9:18 and 2:6 :: 9:27
step 1
Find the product of Means
6 x 9 = 54
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 6 x 9
Product of Extremes = 54
step 3
To find the Extremes, find the factors of 54
Factors of 54 = 3, 2, 18, 27
step 4
Write the possible pair of multiplication factors (Extremes) that makes 54
3 x 18 = 54
2 x 27 = 54
Either 3 & 18 or 2 & 27 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
3 x 18 = 6 x 9
or
2 x 27 = 6 x 9
or
step 6
Write the above expression in the fraction form
So,
3 x 18 = 6 x 9 can be written as
36
=
918
similarly,
2 x 27 = 6 x 9 can be written as
26
=
927
step 7
Write the above fractions in the ratio form
3:6 = 9:18
or
2:6 = 9:27
step 8
Therefore, the two proportions are
3:6 :: 9:18 & 2:6 :: 9:27
6
Using 5 and 22 as means, write any two proportions.
2:5 :: 22:55 and 10:5 :: 22:11
step 1
Find the product of Means
5 x 22 = 110
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 5 x 22
Product of Extremes = 110
step 3
To find the Extremes, find the factors of 110
Factors of 110 = 2, 10, 55, 11
step 4
Write the possible pair of multiplication factors (Extremes) that makes 110
2 x 55 = 110
10 x 11 = 110
Either 2 & 55 or 10 & 11 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
2 x 55 = 5 x 22
or
10 x 11 = 5 x 22
or
step 6
Write the above expression in the fraction form
So,
2 x 55 = 5 x 22 can be written as
25
=
2255
similarly,
10 x 11 = 5 x 22 can be written as
105
=
2211
step 7
Write the above fractions in the ratio form
2:5 = 22:55
or
10:5 = 22:11
step 8
Therefore, the two proportions are
2:5 :: 22:55 & 10:5 :: 22:11
7
Using 5 and 38 as means, write any two proportions.
10:5 :: 38:19 and 2:5 :: 38:95
step 1
Find the product of Means
5 x 38 = 190
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 5 x 38
Product of Extremes = 190
step 3
To find the Extremes, find the factors of 190
Factors of 190 = 10, 2, 19, 95
step 4
Write the possible pair of multiplication factors (Extremes) that makes 190
10 x 19 = 190
2 x 95 = 190
Either 10 & 19 or 2 & 95 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
10 x 19 = 5 x 38
or
2 x 95 = 5 x 38
or
step 6
Write the above expression in the fraction form
So,
10 x 19 = 5 x 38 can be written as
105
=
3819
similarly,
2 x 95 = 5 x 38 can be written as
25
=
3895
step 7
Write the above fractions in the ratio form
10:5 = 38:19
or
2:5 = 38:95
step 8
Therefore, the two proportions are
10:5 :: 38:19 & 2:5 :: 38:95
8
Using 3 and 66 as means, write any two proportions.
9:3 :: 66:22 and 11:3 :: 66:18
step 1
Find the product of Means
3 x 66 = 198
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 3 x 66
Product of Extremes = 198
step 3
To find the Extremes, find the factors of 198
Factors of 198 = 9, 11, 22, 18
step 4
Write the possible pair of multiplication factors (Extremes) that makes 198
9 x 22 = 198
11 x 18 = 198
Either 9 & 22 or 11 & 18 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
9 x 22 = 3 x 66
or
11 x 18 = 3 x 66
or
step 6
Write the above expression in the fraction form
So,
9 x 22 = 3 x 66 can be written as
93
=
6622
similarly,
11 x 18 = 3 x 66 can be written as
113
=
6618
step 7
Write the above fractions in the ratio form
9:3 = 66:22
or
11:3 = 66:18
step 8
Therefore, the two proportions are
9:3 :: 66:22 & 11:3 :: 66:18
9
Using 6 and 6 as means, write any two proportions.
3:6 :: 6:12 and 4:6 :: 6:9
step 1
Find the product of Means
6 x 6 = 36
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 6 x 6
Product of Extremes = 36
step 3
To find the Extremes, find the factors of 36
Factors of 36 = 3, 4, 12, 9
step 4
Write the possible pair of multiplication factors (Extremes) that makes 36
3 x 12 = 36
4 x 9 = 36
Either 3 & 12 or 4 & 9 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
3 x 12 = 6 x 6
or
4 x 9 = 6 x 6
or
step 6
Write the above expression in the fraction form
So,
3 x 12 = 6 x 6 can be written as
36
=
612
similarly,
4 x 9 = 6 x 6 can be written as
46
=
69
step 7
Write the above fractions in the ratio form
3:6 = 6:12
or
4:6 = 6:9
step 8
Therefore, the two proportions are
3:6 :: 6:12 & 4:6 :: 6:9
10
Using 2 and 87 as means, write any two proportions.
3:2 :: 87:58 and 6:2 :: 87:29
step 1
Find the product of Means
2 x 87 = 174
step 2
If 2 ratios are in proportion, the product of Extremes and product of Means should be equal
Product of Extremes = Product of Means
Product of Extremes = 2 x 87
Product of Extremes = 174
step 3
To find the Extremes, find the factors of 174
Factors of 174 = 3, 6, 58, 29
step 4
Write the possible pair of multiplication factors (Extremes) that makes 174
3 x 58 = 174
6 x 29 = 174
Either 3 & 58 or 6 & 29 are the the Extremes of this proportion
step 5
Apply the Extreme values in the proportion statement
Product of Extremes = Product of Means
3 x 58 = 2 x 87
or
6 x 29 = 2 x 87
or
step 6
Write the above expression in the fraction form
So,
3 x 58 = 2 x 87 can be written as
32
=
8758
similarly,
6 x 29 = 2 x 87 can be written as
62
=
8729
step 7
Write the above fractions in the ratio form
3:2 = 87:58
or
6:2 = 87:29
step 8
Therefore, the two proportions are
3:2 :: 87:58 & 6:2 :: 87:29

# Finding Extremes from Means of Proportion Worksheet

Find the extremes & write any two proportions by using means worksheet with answers for 6th grade math curriculum is available online for free in printable and downloadable (pdf & image) format. Tap on PRINT, PDF or IMAGE button to print or download this grade-6 ratio & proportion worksheet to practice how to find the extremes of the proportion by using means.

How to Use this Worksheet

In this sixth grade ratio & proportion worksheet, students are required to write any two proportions for the given means of ratios. In proportions, the product of means equals to product of extremes.
The product of extremes = The product of means

The antecedent of first ratio and consequent of second ratio is called as EXTREMES. Similarly, the consequent of first ratio and antecedent of second ratio is called as MEANS.

To find the extremes, find the product of means, find any two factors as extremes for the product of means and exchange the extremes and means to form the proportion.

Answers Key

Teachers, tutors, parents or students can check or validate the solved questions by using the corresponding answers key which comprises the step by step work on how to find two extremes of the proportion, for each problem of this worksheet.

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Students, teachers, tutors or parents can generate unlimited set of questions and answers by using this "NEW WORKSHEET" button to prepare exam, assignments, classwork or homework problems, or step by step work on writing two extremes for given means of proportion and ratios.

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