**Identify equivalent ratios worksheet with answers :**

Here we are going to see some practice problems on identifying equivalent ratios.

**Question 1 :**

Fill in the blanks

**Question 2 :**

Fill in the blanks

**Question 3 :**

Consider the statement: Ratio of breadth and length of a hall is 2 : 5. Complete the following table that shows some possible breadths and lengths of the hall.

Breadth of the hall (in meters) |
10 |
? |
40 |

Length of the hall (in meters) |
25 |
50 |
? |

**Question 1 :**

Fill in the blanks

**Solution :**

The three given ratios are equal,

In order to get the first missing number, we consider the fact that 21 = 3 × 7. i.e. when we divide 21 by 7 we get 3. This indicates that to get the missing number of second ratio, 14 must also be divided by 7.

When we divide, we have, 14 ÷ 7 = 2

Hence, the second ratio is 2/3

Similarly, to get third ratio we multiply both terms of second ratio by 3.

Hence, the third ratio is 6/9

So, 14/21 = 2/3 = 6/9 = [These are all equivalent ratios.]

**Example 2 :**

Fill in the blanks

**Solution :**

(i) In order to get the first missing number, we consider the denominators of first and second fraction.

When we divide 18 by 3, we will get 6, like wise if we divide numerator of first fraction by 3, we will get 5.

Hence the second fraction is 5/6

(ii) Comparing 5/6 = 10/?, if we multiply the numerator 5 by 2 we will get 10

Like wise, if we multiply the denominator 6 by 2, we will get 12.

Hence the third fraction is 10/12

(iii) Comparing 10/12 = ?/30 ,

We cannot say that the number 12 is to be multiplied by which number in order to get 30.

So, let us consider the missing number be "x".

10/12 = x/30

10 x 30 = 12x

x = (10 x 30)/12 = 2.5

(10/12) x (2.5/2.5) = 25/30

Hence the fourth fraction is 25/30.

**Question 3 :**

Consider the statement: Ratio of breadth and length of a hall is 2 : 5. Complete the following table that shows some possible breadths and lengths of the hall.

Breadth of the hall (in meters) |
10 |
? |
40 |

Length of the hall (in meters) |
25 |
50 |
? |

**Solution :**

Let "x" be and "y" be the two unknowns

Breadth and lengths are in the ratio 2 : 5.

If two ratios are equivalent then

Product of means = product of extremes

10 : 25 = x : 50

25 x = 10 (50)

x = 500/25

x = 20

By comparing the first and third column

Product of means = product of extremes

10 : 25 = 40 : x

10 x = 40 (25)

x = 1000/10

x = 100

After having gone through the stuff given above, we hope that the students would have understood "Identify equivalent ratios".

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