Math Practice Addition

Introduction for math practice addition:

Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+). For example, there is 3 + 2 apple, meaning three apples and two other apples, which is the same as five apples. Therefore, 3 + 2 = 5. Besides counts of fruit, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, decimals and more. I like to share this Positive and Negative z Score Table with you all through my article.

Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1. In primary education, children learn to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. (Source: Wikipedia)


Math addition example problems:


Problem 1:

John has 900 dollars in his checking account. He received from his job a check for 1,300 dollars and deposits the amount in his checking account. How much money does he have in his checking after the deposit?

Solution:

The fact of receiving money from his job is a gain. Therefore, we need to perform addition.

1300
900 (+)
-------
2200
--------
Total amount in checking account = 900 + 1300 = 2200 dollars.

Problem 2:

Peter sells ice cream for a living. On Monday his revenue was 250 dollars. On Tuesday, his revenue was 120 dollars. Finally, on Wednesday, his revenue was 60 dollars. How much is Peter's revenue so far?

Solution

Peter is experiencing a gain in revenue. Therefore, we use addition.

250
120
60 (+)
------
430
-------
Peter's revenue = 250 + 120 + 120 = 430 dollars

Problem 3:

Eiffel Tower is about 1123 feet high. The Statue of Liberty along with its foundation and pedestal is about 350 feet. If you could put the Statue of Liberty on top of the Eiffel Tower, how high up in heaven will the two monuments reach?

Solution:

The situation above is a combination of parts to form a whole. Therefore, we use addition.

1123
350 (+)
-------
1423
--------
Two monuments reach = 1123 + 350 = 1423.

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Math practice problem for addition:


Math practice problem 1:

Your teacher has graded thirty-seven math tests. There are twenty-six still left to grade. How many math tests are there altogether?

Answer: 63 tests

Math practice problem 2:

There are sixteen books on a bookshelf. Twenty one books were borrowed by students. How many books were there altogether?

Answer: 37 books

Math practice problem 3:

There are thirty two pencils in a drawer. The children have already taken twenty-five of them to do their homework with. How many pencils were there in total?

Answer: 57 pencils

Answer Math Teasers

Introduction to Answer math teasers:

Math teasers are brain teasers form math and answers for the given brain teasers. Answers math teasers are challenging problems from math that gives a mind work. The difficulty of the problem make the students think more about the problems. Like the muscles which need exercises to keep in shape, brain teasers work as a exercise for keeping our mind sharp. Let us see answers math teasers, that is brain teasers from math. I like to share this pre algebra answers with you all through my article.


Answer math teasers:


Example 1:

Madison is twice as good a workman as Major and together they finish a piece of work in 18   days. In how many days will Madison alone finish the work?

Solution:

(madison 1 day’s work): (major’s 1 day’s work) = 2:1.

(Madison + major’s) 1 day’s work = `1/18` .

Divide the `1/18` in ratio of  2:1.

Therefore madison’s 1 day’s work = `(1/18 * 2/3)` = `1/27` .

Hence, Madison alone can finish the work in 27 days.

Example 2:

Dace and Ajay work together can dig a ditch in 8 hrs. dace alone can dig it in 12 hrs. In how many hours, Ajay alone can dig such a ditch?

Solution:

(dace +Ajay)’s one hour’s work =`1/8` ,   dace’s one hour’s work =`1/12`

Therefore, ajay’s one hour’s work = `(1/8-1/12)` =`1/24` .

Hence, Ajay alone can dig the ditch in 24 hours.

Answer math teasers:


Example 3:

Jack started a business by investing 36000 dollars. After 3 months walker joined him by investing  36000 dollars Annual profit of both is  37100 dollars, find the share of each?

Solution:

Ratio of jack’s  vs walker capitals= 36000*12 : 36000*9  =  4:3

Jack’s share=(37100*4/7 ) = 21200 dollars.

Walker share=(37100*3/7)  = 15900 dollars.

Example 4:

Rad, jack and walker start a business each investing  20000 dollars After 5 months Rad withdrew  5000 dollars, jack withdrew 4000 dollars and walker invests  6000 dollars more. Total profit is  69,900 dollars was got at the end of year. Find  each ones share.

Solution:

Ratio of the capitals of Rad, jack and walker

= (20000*5+ 15000*7) : (20000*5+16000*7): (20000*5+26000*7)

=205000: 212000 : 282000 = 205:212:282

Therefore,  Rad’s share =  ( 69900*205/699) = 20,500 dollars

Jack’s share  =  (69900*212/699)  = 21200  dollars

Walkers’s share   =  (69900*282/699)  =  28200 dollars

Math Skills Test Practice

Introduction to math skills test practice:
In this article we discuss math skills test practice problems and answer in simpler ways that really make sense for the students. In this article we are going to discuss math skills test practice problem for algebra, geometry, number works, and measurements. In everyday life we are using mathematical concepts often. Math skills test practice problems are easy to solve, this makes students understand. When a math skills practice problem is solved in the easiest way, then that will really makes sense to all peoples. Having problem with Rules of Partial Fractions keep reading my upcoming posts, i will try to help you.


Solving problems on math skills test practice:


Problem 1:

A square has an area of 36 square centimeters. What is the length of each of its sides?

Solution:

The area of the square= (side)^2

Area =side^2

36 =side^2

Side = 6cm

Problem 2:

To solve for 10x+6 = 0

Solution:

Step 1: Given equation is 10x +6 = 0

Step 2: Subtract the 6 on both sides

10x +6-6 = 0-6

Step 3: 10x = -6

Step 4: Divided by 10 on both sides

10x/10 = -6/10

Step 5: x = -0.6

Problem 3:

To find the area of a trapezoid having bases 13 cm and 7cm and a height of 9cm?

Solution:

The area of the trapezoid = h/2*(b1+b2)

=9/2(13+7)

=4.5(20)

=90cm

The area is 90cm.

Example 4 :

Convert 378.6 cm into metre

Solution:

Here the conversion is from centimetre to metre. i.e. from lower unit to higher unit.

100cm = 1m.

Hence 378.6cm =378.6/100 m

= 3.786 m (shifting the decimal two digits to the left)

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Practices problems on math skills test practice:

Practice problem 1:

A square has an area of 64 square centimeters. What is the length of each of its sides?

Answer: side 8 cm

Practice problem 2:

Solve for 5x +5 = 5

Answer :0

Practice problem 3:

To find the area of a four-sided figure having a base of 30cm and a corresponding height of14cm?

Answer : 420cm

Practice problem 4:

Convert 40.1735 km into metre.

Answer: 40173.5 m

Math Subtraction Word problems

Introduction to math subtraction word problems:

Subtraction is one of the four basic arithmetic operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with. Subtraction is denoted by a minus sign in infix notation. I like to share this Y Intercept Calculator with you all through my article.

c − b = a

Here minuend (c) − subtrahend (b) = difference (a).  Here we are going to see some solved math subtraction word problems and give some practice math word problems for subtraction.

(Source: Wikipedia)


Examples of math subtraction word problems:


Subtraction word problems:

Jessica has 1160 beads. 624 beads are red and the rest are blue. How many blue beads does she have?
Solution:

Jessica has 1160 beads,

624 beads are red and the rest are blue,

1160 – 624 = 536

She has 536 blue beads.

2. James and Ken donated $2400 to a charitable organization. Ken donated $650. How much did James donate?

Solution:

James and Ken donated $2400 to a charitable organization

Ken donated $650.

2400 – 650 = 1750

James donated $1750

3. There are twenty-five magazines stacked up on a bookshelf and a desk. Fifteen of them are on the desk. How many magazines are there on the bookshelf?

Solution:

There are twenty-five magazines stacked up on a bookshelf and a desk.

Fifteen of them are on the desk

25 – 15 = 10

Answer: 10 magazines

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Practice math subtraction word problems:


1. There were forty-six birds in a tree, but fourteen of them flew away. How many birds are left in the tree?

Answer: 32 birds

2. There were fifty-seven employees working in an office building. Twenty of them left to go out to lunch. How many employees were left in the building?

Answer: 37 employees

3. Jordan made twenty-six cookies. If he already gave twelve to friends, how many does he have left?

Answer: 14 cookies.

4. The pet store had thirty-six bags of bird feed. Twenty have been eaten. How many bags of bird feed are left?

Answer: 16 bags

How to Solve Metric Conversions

Introduction to how to solve metric conversions:

The Metric Conversions are an international decimal system of measurement, which is the common system of measuring units used by most of the world. It exists with different choices of fundamental units, though the choice of base units does not affect its day-to-day use. Different variants have been considered the metric conversions. Metric units are widely used around the world for personnel, commercial and scientific purposes. The metric conversions are an easiest method to convert one unit from another unit. I like to share this Arithmetic and Geometric Series with you all through my article.


Problems for how to solve metric conversions

We can convert one form of Metric unit into another unit with the simplest calculation. Following example problems show, how to solve the Metric Conversions.

Problem 1: Convert 100 meter into feet

Sol :              1 meter is equal to 3.28 feet. Then,

100 meter = 100 x 3.28

100 meter = 328 feet

Problem 2: Convert 10 feet into centimeter.

Sol:              1 feet is equal to 30.48 centimeter. Then,

10 feet = 10 x 30.48

10 feet = 304.8 centimeter

Problem 3: Convert 25 hours into Minute

Sol :              1 hour is equal to 60 minute. Then,

25 hours = 25 x 60

25 hours = 1500 minute

Problem 4: Convert 15 cubic millimeter into cubic centimeter

Sol :              1 cubic millimeter is equal to 0.001 cubic centimeter. Then,

15 cubic millimeter = 0.001 x 15

15 cubic millimeter = 0.015 cubic centimeter

Problem 5: Convert 4 gallon of liquid into ounce.

Solution:

1 gallon of liquid is equal to 128 ounce of liquid. Then,

4 gallon = 128 x 4

4 gallon = 512 ounce

Problem 6: Convert 25 gallon into liter.

Sol :              1 gallon is equal to 3.785 liter. Then,

25 gallon = 3.785 x 25

25 gallon = 97.635 liter

Problem 7: Convert 60 kilometer in hectometers

Sol :              1 kilometer is equal to 10 hectometers. Then,

60 Kilometer = 10 x 60

60 Kilometer = 600 hectometers

Problem 8: Convert 150 centigram into kilogram.

Sol :              1centigram is equal to 0.00001 kilogram. Then,

150 centigram = 150 x 0.00001

150 centigram = 0.0015 Kilogram

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Practice Problems on How to Solve Metric Conversions

Problem 1: Convert 5 liter into gallon

Answer: 5 liter = 1.32 gallon

Problem 2: Convert 10 kilometer into mile

Answer: 10 kilometer = 6.213 mile

Answer Math Problems

Introduction about Math Home Work Help:

Math Home Work Help is very simple and easier. Math Home Work Help is nothing but learning about how to work out the homework problems in online with the help of the tutors. Tutors help with homework problems with step by step explanations to the students. The students can freely interact with the tutors and ask their doubts to complete their homework. By the process of online tutoring the students learn a lot from the tutors about their homework problems. Here are some of the sample and model problems about Math Home Work Help. Please express your views of this topic tutoring for math by commenting on blog.


Math Home Work Help


1. Add 324 + 261

Tutor Solution

3 2 4                Add the ones digit 4 + 1 = 5
2 7 1 +            Add tens digit 2 + 7 = 9
----------             Add hundred’s digit 3+ 2 = 5
5 9 5
----------
2.  Multiply 6 2 8 * 7

6 2 8            multiply the multiplicand628 with multiplier 7

7 x         multiply 7 with 8 = 56.

----------          multiply 7 with 2 = 14 + 5 = 19

4 3 9 6           multiply 6x 7 = 42 + 1 = 43

----------

3. Divide 80 by 8

10
8)80             Take the first digit 8 1 times of 8 is 8
8               remainder is zero
---------
00
----------
4. Find the value of k in this given equation 3k + 5 = 23

Solution

3k + 5 = 23

Subtract 5 on both sides

3k + 5-5 = 23-5

3k = 18

Divide by 3 on both sides

p =6

5. Find the value of p in the given equation 4+5p = 2p + 37

Solution

4+5p = 2p + 37

Subtract 4 on both sides

4 - 4 + 5p = 2p + 37 – 4

5p = 2p + 33

Subtract 2p on both sides

5p-2p = 2p – 2p +33

3p = 33

Divide by 3 on both sides

p = 11

6. Find the value of s in the given equation 4s + s -7 = -3s +73

Solution

4s + s -7 = -3s +73

Add 4s + s

5s – 7 = - 3s + 73

Add 3s +7 on both sides

5s+3s-7+7 = 3s-3s+73+7

8s = 80

Divide by 8 on both sides

s = 10

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Math Home Work Help


Find the value of s in this given equation 7s - 5 = 23
Find the value of m in the given equation 5m = m + 36
Subtract 913 – 2464
Multiply 451 x 18
Divide 256 / 16

Answers


1. s =4

2.m=9

3.667

4.8118

5.16

Definition of Expected Value

Definition of expected value:
Expected value learning is one of the most essential concepts in probability. The expected value of a real-respected random variable gives the center of the distribution of the variable, in a special sense.

The expected value may be naturally understood by the law of large numbers: The expected value, when it exists, is almost for sure the limit of the sample mean as sample size grows to infinity.

The term "expected value" can be misleading. It must not be a confused with the "most probable value." The expected value is in a general not typical value that the random variable can take on. It is an often helpful to the interpret the expected value of a random variable as the long-run average value of the variable over many independent repetitions of an experiment. Is this topic Expected Value of Uniform Distribution hard for you? Watch out for my coming posts.


Definition of expected value:

The Definition Expected value (EV):

The expected value is the best prediction of an variable's value, and is the computed by multiplying each outcome by the probability of its occurrence and then averaging them.

The calculated value of a variable quantity which is most likely to occur. If a variable x can take any of the values (x1,x2,…..,xn) with corresponding probabilities (p1,p2,.......,pn) then expected value x or expectation of x is written as E(x)=p1x1+p2x2+…….+pnxn.

The general format of the Expected value is

definition,the Expected Value = Number of problem x Particular probability.

Formula for  expection for function f(x):

E[ f(X) ] = S f(x)P(X = x)

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Definition of Expected value : properties and example problems:


Properties of expected value:

The following properties are used to find the expected value. These properties are shows to the real respected random variable that gives the expected value.from definition

1. Show that E(X + Y) = E(X) + E(Y)

2. Show that E (cX) = cE(X)

3. Show that if X 0 then E(X) 0.

4. Show that if X Y then E(X) E(Y

5. Show that |E(X)| E (|X|)

The above five properties are mainly used in solving a problem of expected value.

Expected values Example:

The Experiment is to rotate a standard roulette wheel, and put money on the table minimum, ten dollars, on red.  Let X is my profit in dollars. X has two possible outcomes:  +20 and –20.  Since there are 18 red numbers out of 68 numbers on the wheel, we have P(X = +20) = 18/68, and P(X = –20) = 40/68.

Sol:

So we have, expection formula for function f(x)

E[ f(X) ] = S f(x)P(X = x)

E(X) = (20) (18/68) + (-20) (40/68) = 5.294-11.764 = - 6.47

On average, I lose a bit over fifty cents every time I place the minimum bet on red.

Math Definitions and Examples

Introduction of math definitions and examples:

Mathematics Definition is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics Understanding What is a Common Factor is always challenging for me but thanks to all math help websites to help me out.


Algebra definition for math definitions and examples:


Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. The Algebra executes the four basic operations such as addition, subtraction, multiplication and division. The most important terms in algebra are variables, constant, coefficients, exponents, terms and expressions. In Algebra, besides numerals we use symbols and literals in place of unknown numbers to make a statement. Hence, Algebra may be regarded as an extension of Arithmetic.

Ex :    x+5=-x+15

Sol :   x+5=-x+15

x+5-5  =  -x+15-5

x  = -x+10

x + x =-x+x+10

2x=10

2x/2=10/2

X=5


Geometry in Mathematics for math definitions and examples


The definition of Geometry is associated with the shapes which includes angles, length, properties. Algebra is also used for finding unknown values of length or angle.

Ex :   Find the angle of triangle A when angles B=60 degree and C=80 degree.

Sol :  The sum of angle of the triangle ABC is equal to 180 degree.

That is, angle of A + Angle of B + angle of C = 180 degree

Angle of A + 60 degree + 80 degree = 180 degree

Angle of A + 140 degree = 180 degree

Angle of A + 140 degree - 140 degree = 180 degree - 140 degree

Angle of A = 40 degree


Statistics in Mathematics for math definitions and examples


The definition of Statistics is using for relating numerical data. In statistics, we will do the following operations such as mean, median and range.

Ex : 10, 30, 20, 50, 40. Find mean, median and range.

Sol :  Given is, 10, 30, 20, 50, and 40.

Arrange the numbers is ascending order.

10, 20,30,40,50

Mean= (10+20+30+40+50)/5

Mean=150/5

Mean=30

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Calculus for math definitions and examples:


The definition of Calculus involves two basic parts such as derivatives and integrals. In derivatives, a function is performed on another function is called composite function. Derivative is rate of changes of a point in the curve. Integration is finding area below the curve.

Ex 1:  d/dx(x^2+4x+5)

Sol  :  Given is d/dx(x^2+4x+5)

= d/dx(x^2) + d/dx(4x)+ d/dx(5)

=2x+4

Ex 2:  d/dx(x^2+2x+2)

Sol :  Given is d/dx(x^2+2x+2)

= d/dx(x^2) + d/dx(2x)+ d/dx(2)

=2x+2

applied math problems

Introduction:

Applied math is set of methods aimed for solution of problems in sciences, engineering, economics, or medicine. Applied math methods are proposed by Newton, Lagrange, Euler, and other giants. Modern applied math problems include control theory, aero-space engineering, mathematical physics, and math finance.Majority of applied problems need to make numerical model of occurrence, solve this model and develop recommendations for development of performance.

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Approaches to applied math problems


Math modeling

Basically we deal with large systems (thousands of variables, equations and inequalities). An intelligent model separates the main phenomenon from the noise and allows for analytic treatment of the problem, followed by extensive numerical development. Several models suggested for the same phenomena with various levels of details: No one needs a one-to-one geographical map.

Method of solutions

Selection of applied math problem requires selection of methods.Usually used methods in the practical math are workshop.These methods include linear algebra, differential, linear algebra and integral equations, approximation theory and asymptotic, variational principles, and numerics.

Improvement and recommendation

When people develop model of process, usually want to improve it.  Various theory methods are control theory, optimization, and game theory. Sometimes implement is achieved by varying parameters, but generally it is serious math problem discussed in class. Understanding Online Equation Solver is always challenging for me but thanks to all math help websites to help me out.


Applied Math Sample Problems:


Problem 1: Solve the equation

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Solution to Problem 1:

Given the equation

5(-3x - 2) - (x - 3) = -4(7x + 5) + 25

Multiply factors.

-15x - 10 - x + 3 = -28x - 20 +25

Group like terms

-16x - 7 = -28x +5

12x=12

x=1

Problem 2: Simplify the expression

2(a -3) + 4b - 2(a -b -3) + 5



Solution to Problem 2:

Given the algebraic expression

2(a -3) + 4b - 2(a -b -3) + 5

Multiply factors.

= 2a - 6 + 4b -2a + 2b + 6 + 5

Group like terms.

= 6b + 5

Three Thousand Dollars

Introduction to three thousand dollars:

In this article we discuss about the three thousand dollars. Dollars can used in the nation is United States of America. It is official currency of the United States of America. The USA dollars are usually abbreviated as $ or USD or US$. The value of the one dollar is equals to the 100 penny or 100 cents. We are solving the various three thousand dollars math problems given below.

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Three Thousand Dollars:

The three thousand dollars can be divided into various currency details given below,

Three thousand dollars are equal to 300000 cents.

Three thousand dollars are equal to 300000 pennies.

Three thousand dollars are equal to 60000 nickels.

Three thousand dollars are equal to 30000 dime.

Three thousand dollars are equal to 12000 quarters.

Three thousand dollars are equal to 6000 half dollars.

The following currencies are used in other nations that the currency value is equal to one dollar.

Value of Three thousand dollars is equal to 2361.72 EUR.

Value of Three thousand dollars is equal to 254460 JPY.

Value of Three thousand dollars is equal to 1933.71 GBP.

Value of Three thousand dollars is equal to 3158.01 CAD.

Value of Three thousand dollars is equal to 3346.74 AUD.

Value of Three thousand dollars is equal to 140601.3 INR.

Value of Three thousand dollars is equal to 29400000 IRR.

Example Problems for three Thousand Dollars:

Three thousand dollars problem 1:

Ram has 3000 dollars and john has 560 dollars. What does the total amount of dollar and equal amount of cents both persons?

Solution:

Given that, Ram has 3000 dollars and John has 560 dollars

The above given problem indicates the addition operation.

Therefore, we have to add above both person currency is equal to total amount of dollar.

That is 3000 dollars+ 560 dollars =3560 dollars.

The equal amount of 3560 dollar value is 356000 cents.

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Three thousand dollars problem 2:

The actual price of the Car is 30000 dollars. If the car company provides 50 % discount what will be the selling price of the car?

Solution:

Given that, the actual price of car is 30000 dollars.

Discount = 50 %.

Actual discount = 30000 `xx` `50/100`

=3000 `xx` 5 dollars

= 15000 dollars

Selling price  = actual price – discount dollars

=30000-15000 dollars

=15000 dollars.

Therefore, the selling price of a car is 15000 dollars.

Sum of Reciprocals

Introduction:-

The  reciprocal for a number x, denoted by  `1/x`  or x ^−1, is a number which when multiplied by x yields the multiplicative identity 1. The reciprocal of a fraction `a/b` is `b/a` . For the reciprocal of a real number, divide 1 by the number. For example, the reciprocal of 8 is  one fifth (`1/8` or 0.2), and the reciprocal of 0.25 is (`"1/0.25` or 4).                                                                      Source: - Wikipedia

Sum of Reciprocals

The following are the steps used to find sum of reciprocals:-

Step 1 The first step in finding the sum of reciprocal of a two numbers is to find the reciprocal of the given numbers.

Step 2 Then we need to add the reciprocal of these two numbers.

Find the Sum of reciprocal of real numbers a and b.

As per step 1we need to find the reciprocal of a and b.

The reciprocal of a is `1/ a.`

The reciprocal of b is `1/ b.`

Now according to step 2 we add two reciprocals 1/ a and 1/ b.

Sum of reciprocals of a and b is `1/ a + 1/ b` .

Find the Sum of reciprocal of fractions` a/ b` and `c/ d.`

As per step 1we need to find the reciprocal of `a/b` and `c/ d.`

The reciprocal of `a/b` is `b/ a.`

The reciprocal of `c/d` is `d/ c` .

Now according to step 2 we add two reciprocals `b/ a` and `d/ c.`

Sum of reciprocals of `a/b` and `c/ d` is `b/ a + d/ c.`

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Solved Problems:-

Problem 1:-

Find the sum of reciprocal of 2 and 3.

Solution:-

The given two numbers are 2 and 3.

We need to find the sum of their reciprocals.

To find the sum of reciprocals we first need find the reciprocal of given two numbers.

The reciprocal of 2 is `1/2.`

The reciprocal of 3 is `1/ 3.`

Now we can we need to add these two reciprocal values

`= ` `1/ 2+ 1/ 3.`

By taking LCM of 2 and 3 we get 6

`= (3 + 2 )/6`

`= 5/ 6.`

The sum of reciprocal of 2 and 3 is `5/ 6`

Problem 2:-

Find the sum of reciprocal of two fractions  `1/ 3 ` and `3/ 4.`

Solution:-

The given two numbers are `1/ 3` and `3/ 4.`

We need to find the sum of their reciprocals.

To find the sum of reciprocals we first need find the reciprocal of given two numbers.

The reciprocal of `1/ 3` is `3/ 1.`

The reciprocal of `3/ 4` is ` 4 / 3.`

Now we can we need to add these two reciprocal fraction values

= `3/ 1+ 4/ 3.`

By taking LCM of 1 and 3 we get 3.

`= (9 + 4 )/3`

`= 13/ 3.`

The sum of reciprocal of `1/ 3` and `3/ 4.` is `13 / 3`