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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

Show All Workout

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

Math Challenge

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