**Introduction for ratio and proportion worksheet:**

Algebrais one part of mathematics in which calculation are made by using any arbitrary characters to stand for the quantities or things considered. Which are used to correspond to numbers is often given the name literal numbers or simply literals. Since the literal numbers are used to represent numbers,

In ourdaily life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’. If two ratios are equal, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.

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**Definition of ratio:**

The learning ratio is a comparison by division method. We compare the two quantities in terms of ‘how many times’. This comparison is known asthe Ratio. We denote ratio-using symbol ‘:’

**Examples of sample ratio problems:**

**Sample problem:**

Length and breadth of a rectangular field are 75 m and 25 m** **respectively. Find the ratio of the length to the breadth of the field.

**Solution:**

Length of the rectangular field = 75 m

Breadth of the rectangular field = 25 m

The ratio of the length to the breadth is 75: 25

The ratio can be written as

= 75 / 25 = 3:1

Thus, the required ratio is 3:1

**Ratio worksheet:**

**Practice problem 1:**

Find the ratio of 18 yards to 24 yards.

**Answer: 3: 4**

**Practice problem 2:**

Find the ratio of 26 days to 20 days.

**Answer: 13: 10**

**Practice problem 3:**

Mrs. Alice earns 80 per month, She spends 4 and saves the rest. Find the ratio of her salary to savings?

**Answer: 20: 1**

**Definition of proportion:**

If two ratios are not equal, then we state that they are not in proportion. In a statement of learning proportion, the four quantities involved when taken in order are known as respective terms. First and fourth terms are known as extreme terms. Second and third terms are known as middle terms**.**

** a: b = c : d**

**Examples of simple proportion:**

**Simple problem:**

Are the ratios 20g: 40g and 36 kg: 72 kg in proportion?

**Solution:**

20 g: 40 g =20 / 40 = 2 / 4

= 2:

36 kg: 72 kg = 36 / 72 = 1 / 2

= 1: 2 So, 20: 40 = 36: 72.

Therefore, the ratios 20 g: 40 g and 36 kg: 72 kg are in proportion,

i.e. 20 : 40 :: 36 : 72.

The middle terms in this are 40, 36 and the extreme terms are 20, 72.

**Proportion worksheet:**

**Practice problem 1:**

** **If the numbers x, 14, 12 and 56 are proportional, find x.

** Answer: x = 3**

**Practice problem 2:**

** **Find the third proportional to 9 and 15.

** Answer: x = 25**

**Practice problem 3:**

** ** Find the fourth proportional to 5, 15, and 16

** Answer: x = 48**

**Practice problem 4:**

** ** Find the mean proportional between 7 and 63.

** Answer: 21**