Reciprocals

Reciprocals:

Introduction:

In this Blog Let us see the meaning of Reciprocal .In general definition of reciprocal number is multiplicative inverse of a number. The reciprocal number is commonly specified in following way. The number is n it is commonly denoted the reciprocal is 1/n. Another method for the denoted the reciprocal number is m/n the multiplicative inverse of a fraction is n/m. The example reciprocal of 91 is 1/91.Reciprocal math is nothing but the reciprocal of a number in math. Reciprocal is any number that divides 1.If any number is considered and that number is represented as 1 divided by the considered number then such form of the number is called as reciprocal math.

Example:

If the number is 5 then the reciprocal of the number 5 is [1/5]

Reciprocal Math is mostly used in the division of a fraction number. In the case of dividing a fraction number by another fraction number then we just change the division symbol as multiplication symbol and take reciprocal math of the second number and perform multiplication. So in many cases to solve the math problem of different chapter reciprocal math is being used.

Examples on Reciprocal Math:

1. Find the reciprocal math of the following numbers.

a) 5

b) 21

c) 99

d) 10

e) [5/3]

f) [2/7]

g) [ 1/6]

Solution

The Reciprocal math of the number 5 is [1/5]

The Reciprocal math of the number 21 is [1/21]

The Reciprocal math of the number 99 is [1/99]

The Reciprocal math of the number 10 is [1/10]

The Reciprocal math of the number [5/3] is [3/5]

The Reciprocal math of the number [2/7 ] is [7/2]

The Reciprocal math of the number [1/6 ] is [6/1.] [6/1 ] can be written as 6

2. Divide [2/3] and [8/6]

Solution

[ 2/3] / [8/6]

Keep the first fraction as it is and change the divisible sign as multiplication and find the reciprocal math of second fraction [8/6]

The reciprocal of [8/6 ] is [6/8]

[2/3] * [6/8]

Now by simplifying these we get [1/2]

3. Perform the operation

[7/9] divide by 3

Solution

Here 3 can be written as [3/1]

[7/9] / [3/1]

Reciprocal math of [ 3/1] is [1/3]

[ 7/9] / [1/3]

[ 7/27]

Scatterplots

Scatterplots:
The general meaning of a scatter is to unevenly distribute,something that is not in an order.But here in mathematics the meaning of a scatterplot is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data.

It is very important to learn about the uses of a scatterplot,in Statistics a scatterplot is a graphic tool used to show the relationship between two quantitative variables. The variable that might be measured an expounding variable is plotted on the x-axis, and the response variable is plotted on the y-axis.It provides a graphical expose of the link between the two variables. It is also useful in the early stages of study when exploring records ahead of really devious a parallel coefficient or corrects a regression curve. For example, a scatter plot can aid one to decide whether a linear waning model is proper.

Statistical Scatterplots can explain a variety of patterns and associations in Statistics, such as:

• Data association
• Optimistic or direct relations between variables
• Pessimistic or opposite associations between variables
• Scattered record points
• Non-linear pattern
• Increase of data
• Outliers.

Histogram

Histogram:

A two dimensional frequency density diagram is called a histogram. A histogram is a diagram which represents the class interval and frequency in the form of a rectangle. There will be as many adjoining rectangles as there are class intervals.

In statistics,simple explanation of a histogram is- a histogram is a graphical display of tabular frequencies, shown as adjacent rectangles. Each rectangle is erected over an interval, with an area equal to the frequency of the interval. The height of a rectangle is also equal to the frequency density of the interval, i.e. the frequency divided by the width of the interval. The total area of the histogram is equal to the number of data. A histogram may also be based on the relative frequencies instead. It then shows what proportion of cases fall into each of several categories (a form of data binning), and the total area then equals 1. The categories are usually specified as consecutive, non-overlapping intervals of some variable. The categories (intervals) must be adjacent, and often are chosen to be of the same size, but not necessarily so.

Now we will learn about the uses of a Histogram.Histograms are used to plot density of data, and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot.