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Questions10
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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

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

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

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

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

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,similarly,

So,

2 x 52 = 8 x 13 can be written as

28

=

1352

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

2:8 = 13:52

or

4:8 = 13:26

step 8

Therefore, the two proportions are

2:8 :: 13:52 & 4:8 :: 13:26

2:8 :: 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

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

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

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

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

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,similarly,

So,

4 x 42 = 8 x 21 can be written as

48

=

2142

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

4:8 = 21:42

or

2:8 = 21:84

step 8

Therefore, the two proportions are

4:8 :: 21:42 & 2:8 :: 21:84

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

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

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

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

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

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,similarly,

So,

2 x 85 = 10 x 17 can be written as

210

=

1785

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

2:10 = 17:85

or

5:10 = 17:34

step 8

Therefore, the two proportions are

2:10 :: 17:85 & 5:10 :: 17:34

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

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

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

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

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

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,similarly,

So,

4 x 49 = 7 x 28 can be written as

47

=

2849

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

4:7 = 28:49

or

2:7 = 28:98

step 8

Therefore, the two proportions are

4:7 :: 28:49 & 2:7 :: 28:98

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

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

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

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

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

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,similarly,

So,

3 x 18 = 6 x 9 can be written as

36

=

918

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

3:6 = 9:18

or

2:6 = 9:27

step 8

Therefore, the two proportions are

3:6 :: 9:18 & 2:6 :: 9:27

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

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

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

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

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

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,similarly,

So,

2 x 55 = 5 x 22 can be written as

25

=

2255

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

2:5 = 22:55

or

10:5 = 22:11

step 8

Therefore, the two proportions are

2:5 :: 22:55 & 10:5 :: 22:11

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

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

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

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

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

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,similarly,

So,

10 x 19 = 5 x 38 can be written as

105

=

3819

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

10:5 = 38:19

or

2:5 = 38:95

step 8

Therefore, the two proportions are

10:5 :: 38:19 & 2:5 :: 38:95

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

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

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

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

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

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,similarly,

So,

9 x 22 = 3 x 66 can be written as

93

=

6622

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

9:3 = 66:22

or

11:3 = 66:18

step 8

Therefore, the two proportions are

9:3 :: 66:22 & 11:3 :: 66:18

9:3 :: 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

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

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

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

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

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,similarly,

So,

3 x 12 = 6 x 6 can be written as

36

=

612

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

3:6 = 6:12

or

4:6 = 6:9

step 8

Therefore, the two proportions are

3:6 :: 6:12 & 4:6 :: 6:9

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

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

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

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

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

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,similarly,

So,

3 x 58 = 2 x 87 can be written as

32

=

8758

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

3:2 = 87:58

or

6:2 = 87:29

step 8

Therefore, the two proportions are

3:2 :: 87:58 & 6:2 :: 87:29

3:2 :: 87:58 & 6:2 :: 87:29

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.

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.

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.

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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