**Introduction for sample ratio problems:**

In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. Example: For every Spoon of sugar, you need 2 spoons of flour (1:2) (Source: Wikipedia)

In our daily 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.

**Sample Ratio Definition and Example Problems:**

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 as the Ratio. We denote ratio-using symbol ‘:’

Examples of sample ratio problems:

Sample problem 1:

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

Sample problem 2:

There are 60 persons working in an office. If the number of females is 25 and the left over are males, find the ratio of,

(a) The number of females to number of males.

(b) The number of males to number of females.

Solution:

Number of females = 25

Total number of workers = 60

Number of males = 60 – 25 = 35

Therefore, the ratio of number of females to the number of males

= 35: 25 = 7: 5

And the ratio of number of males to the number of females

= 25: 35 = 5: 7.

(Notice that there is a difference between the two ratios 7: 5 and 5: 7).I have recently faced lot of problem while learning Electric Field Definition, But thank to online resources of math which helped me to learn myself easily on net.

**Sample Practice Problem for Ratio:**

Problem 1:

In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:5. If the bag contains 150 green sweets, how many red sweets are there?

Answer: There are 90 red sweets.

Problem 2:

A fence post in Tina's garden is 6 feet tall. When she measured the fence post’s shadow, she found that it was 12 feet long. A tree in Tina’s yard had a shadow of 72 feet. How tall is the tree?

Answer: 36 tall is the tree

Problem 3:

The ratio of Kate's stickers to Jenna's stickers is 7:5. Kate has 21 stickers. How many stickers does Jenna have?

Answer: 15 Stickers

Problem 4:

Chef Pillsbury's secret recipe requires 8 eggs for every 4 cups of flour. How many eggs will he need if he uses 6 cups of flour?

Answer: 12 eggs

Problem 5:

The ratio of the length of a rectangle to its width is 5:6. Its length is 25 inches. What is its width?

Answer: 30 inches

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