Ratios and Proportions

A ratio that is used to show the relation between two or more values. For example: if there are 12 pencils and 17 pens then we can write the ratio as: 12:17; In other word for every 12 pencils there are 17 pens. If any equation written in the form of P / Q = R / S, here both the ratios are equal are said to be proportion. For example (5 / 9) = (20 / 32). Let's see how find the Ratios and Proportions? Steps for ratio and proportions are shown below:
Step1: First we have two values for which we have to find the relation.
Step2: Then we find the relation in both the values.
Step3: Let we have two proportion sets, these two ratios are equal to each other. In one ratio, the quantities of two proportions do not fulfill, so we use cross multiplication and solve the equation and fulfill the quantities. There are different ways to find the ratios and proportions.
If 60 books for 32 students that can be represented in the ratio as 60:32. Now set the second ratio for another larger group of students, assume that the numbers of books move in the numerator and the numbers of students move in the denominator. Here we don’t know the total number of students. (know more about Ratios and Proportions, here)
Here assume the number of students be ‘U’. The total number of students is 42, and then the ratios of students are U / 42. Now we set these ratios according to the definition of ratio and proportion. So the ratio is:
=> (60 / 32)= U / 42,
Now find these ratios with the help of cross multiplication:
When we cross multiply these ratios we get:
⇒(60) (42) = (32) (U), Now solve these values for ‘U’.
⇒2520 = 32 U, here we find the value of ‘U’.
⇒32 U = 2520
⇒U = 2520 / 32
⇒U = 78.75;
After solving we get the value of U = 78.75;
There are 78.75 books for 42 students.

Surface Area of a Cylinder Formula is given as:
Surface area of cylinder = 2 * pi * r² + 2 * pi * r * h. We get new information about all grades syllabus in cbse syllabus 2013 and In the next session we will discuss about Fibonacci Numbers. 

  

LCM, GCF, ratios and proportions

Previously we have discussed about rational expressions applications and now we are going to study about LCM and GCF  which stand for least common multiple and greatest common factor respectively. In icse text books of Grade V, we are going to study about LCM and GCF.

If we have two numbers and need to find LCM of the given numbers, then we first write the factors of the two numbers and then find the product of all the factors. We should remember that the factor occurring in both the list should be written only once. Let us use an example to make it clearer:

Find the LCM of 10 and 15.

First write the numbers as the product of prime factors separately.

 10 = 1 * 2 * 5

15 = 1 * 3 * 5

5 and 1 appear in both set of prime factors, so they will be written only once while finding LCM.

 So LCM of 10 and 15 = 1 * 5 * 2 * 3

                                  = 30

 Now to find GCF, first find the prime factorization of the numbers whose GCF is to be calculated.

Then take the factors which exist in both the lists and find their product.

Thus we will get GCF. (Know more about proportions in broad manner here,)

E.g. Find the GCF of 10 and 15.

First write the numbers as the product of prime factors separately.

 10 = 1 * 2 * 5

15 = 1 * 3 * 5

 5 and 1 appear in both set of prime factors.

 So GCF of 10 and 15 = 1 * 5

The ratio of two quantities with same unit or same kind is the fraction of one quantity over another, we can also express in lowest term. The two terms are in proportion if we see that the lowest form of the two ratios gives the same result.

e.g. 5 :50 and 1: 10 are the two ratios, to check these ratios are in proportion, we convert 5 : 50 to lowest term by dividing both numerator and denominator by 5 and get 1: 10 . So we observe the two given ratios are in proportion.

In the next blog we will discuss the topic of Order of Operations in Grade V and if anyone want to know about predictions then they can refer to Internet and text books for understanding it more precisely.

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