Ratios:
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.Now let us understand the more specific meaning of a Ratio-Ratios means pairs of numbers and they are used to formulate comparisons of numbers.Now let us understand the basic use of a Ratio,a ratio can be used to compares two numbers using a fraction.Ratios can be written in three different ways:
(1) 5 to 3
(2) 5:3
(3) 5/3
They all mean the same thing. I have a class of 35 students, 20 students are boys and 15 are girls. I can compare number of boys to girls using the ratio (or 20:15; or 20 to 15). You can reduce this fraction to by dividing both numerator and denominator by 5.
Notation and Terminology of Ratios
The ratio of quantity A and B can be expressed as
• The ratio of A to B
• A is to B
• A: B
The quantity A and B are sometimes called terms with A being the antecedent and B being the consequent.
Finding Ratios
A ratio is a fraction that is numerator and denominator can have different units. For example: if you travel 100 miles in 2 hours, we can write that as a ratio:
2hours
100miles
And we can simplify that ratio, using the same techniques for simplifying fractions:
2hours100miles = 1hour50miles
If there are 4 oranges and 5 apples, the ratios of oranges to apples is exposed as 2:3; where as the fraction of oranges to total fruit is
Ex 1: In a bag of red and green balls, the ratios of red ball to green ball are 3:4. If the bag contains 120 green balls, how many red balls are there?
Solution:
Step 1: Assign variables:
Let x = red sweets
Write down the items in the ratio as a fraction.
= =
Step 2: Solve the equation
Cross multiply the equation
4 × 120 = 5 × x
480 = 5x
Isolate variable x
X= =96
Ans: There are 96 red balls.
Ex 2: A special mixture contains rice, water and corn in the ratio of 2:3:6. If a bag contains 3 pounds of rice, how much corn it contains?
Solution:
Step 1: Assign variables:
Let x = amount of corn
Write down the items in the ratio as a fraction.
= =
Step 2: Solve the equation
Cross multiply the equitation
2 × x = 3 × 6
2x = 16
Isolate variable x
X= = 9
Ans: The bag contains mixture 9 pounds of corn.
Hope you like the above example of Ratios.Please leave your comments, if you have any doubts.
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.Now let us understand the more specific meaning of a Ratio-Ratios means pairs of numbers and they are used to formulate comparisons of numbers.Now let us understand the basic use of a Ratio,a ratio can be used to compares two numbers using a fraction.Ratios can be written in three different ways:
(1) 5 to 3
(2) 5:3
(3) 5/3
They all mean the same thing. I have a class of 35 students, 20 students are boys and 15 are girls. I can compare number of boys to girls using the ratio (or 20:15; or 20 to 15). You can reduce this fraction to by dividing both numerator and denominator by 5.
Notation and Terminology of Ratios
The ratio of quantity A and B can be expressed as
• The ratio of A to B
• A is to B
• A: B
The quantity A and B are sometimes called terms with A being the antecedent and B being the consequent.
Finding Ratios
A ratio is a fraction that is numerator and denominator can have different units. For example: if you travel 100 miles in 2 hours, we can write that as a ratio:
2hours
100miles
And we can simplify that ratio, using the same techniques for simplifying fractions:
2hours100miles = 1hour50miles
If there are 4 oranges and 5 apples, the ratios of oranges to apples is exposed as 2:3; where as the fraction of oranges to total fruit is
Ex 1: In a bag of red and green balls, the ratios of red ball to green ball are 3:4. If the bag contains 120 green balls, how many red balls are there?
Solution:
Step 1: Assign variables:
Let x = red sweets
Write down the items in the ratio as a fraction.
= =
Step 2: Solve the equation
Cross multiply the equation
4 × 120 = 5 × x
480 = 5x
Isolate variable x
X= =96
Ans: There are 96 red balls.
Ex 2: A special mixture contains rice, water and corn in the ratio of 2:3:6. If a bag contains 3 pounds of rice, how much corn it contains?
Solution:
Step 1: Assign variables:
Let x = amount of corn
Write down the items in the ratio as a fraction.
= =
Step 2: Solve the equation
Cross multiply the equitation
2 × x = 3 × 6
2x = 16
Isolate variable x
X= = 9
Ans: The bag contains mixture 9 pounds of corn.
Hope you like the above example of Ratios.Please leave your comments, if you have any doubts.
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