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Mixed Numbers & Improper Fractions

What are mixed numbers?

Mixed numbers are the type of fractions. When we have some wholes and also some parts of whole, then we use mixed numbers to represent this. For example; consider there are 3 whole apples in a basket and a girl ate half of an apple. Now if we want to count number of apples in the basket, which is more than two and less than three, which is a mixed number and we can say it "two and a half".

Hence mixed numbers have two parts, whole number and a proper fractions.

What are improper fractions?

Improper fractions are also a type of fractions. When there is fraction with the numerator greater than its denominator, then this fraction is called an improper fraction.

For example; the fraction 5/2 have 5 as its numerator and which is greater than its denominator which is 2. Hence, 5/2 is an improper fraction.

Note that we can convert an improper fractions into mixed numbers or mixed numbers back into improper fractions.

Below are the links to mixed numbers and improper fractions lessons and worksheets:

1. How to convert a mixed number into an improper fraction

2. Improper fraction to mixed number

To learn more about fractions and other math topics from KG to Grade 12, keep visiting this blog. We keep updating it whenever we have anything new at one of our sites.

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Fraction Worksheets - How To Use?

When it comes to using fraction worksheets, the best idea is to start using basic fraction worksheets. As the basic ideas get more clear in the mind of the learner, fractions get easier and easier for him/her.

In basic fraction worksheets, first of all kids can learn writing fractions in different forms, such as in words, draw a shape or write using numerals. The next step after learning basic fractions is to understand equivalent fractions. Two equivalent fractions are the fractions which have exactly the same value. Following is a basic fraction worksheet on equivalent fractions:

Above is the basic fraction worksheet on equivalent fractions. Similar fraction worksheets can be found online in many of the math websites.

Once kids are comfortable with equivalent fractions the next step is to learn how to compare fractions and three types of fractions, named, proper fractions, improper fractions and mixed numbers.

The next stop in the fractions journey is to learn reducing fractions into lowest terms and then operations on fractions.

Click here to find more topics like this and other math related content.

Best Regards.

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How To Simplify Fractions

Simplifying Fractions

Reducing Fractions into lowest terms

To learn this skill the knowledge of equivalent fractions and greatest common factor (gcf) of two numbers is necessary. If kids don’t know the equivalent fractions, then they should learn them before learning reducing fractions into lowest terms or simplifying fractions.

Once kids understand the equivalent fractions, then they should learn reducing the fractions into lowest terms. Reducing the fractions into lowest terms is the converting the given fraction into its equivalent proper fraction (proper fraction is the fraction having numerator smaller than the denominator and they both have “1” as their gcf only).

For example, let’s reduce the fraction 4/12 into lowest terms. To simplify the given fraction, we have to find the gcf of 4 and 12, which is 4. In other words, 4 is the greatest number which can divide both 4 and 12.

Hence divide the numerator and denominator of the given fraction by 4 as shown below:

(4/4)/(12/4)= 1/3

Hence, the reduced form of the fraction is 1/3

Notice that, the numerator and denominator both got divided by “4” and that’s why both of the fractions are equivalent fractions.

Finally, it can be said that for reducing fractions into lowest terms the knowledge of gcf and equivalent fractions is the key. Use of reducing fractions worksheets can make you perfect on this key skill of reducing fractions.

For learning all about fractions, visit  “http://www.fractionsworksheets.ca” which explains all the fraction topics step by step.

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Basic Algebra Explained

What is algebra and what it does?

Algebra is a branch of mathematics. Algebra deals with the variable activities in our daily lives. It comes after learning the arithmetic in math.

What are the variable activities?

Variable means something that keeps on changing. Variable activities are the activities which don't stay the same over time. They keep on changing, for example; some trends can go up or down, left or right and east or west etc.

For example; the weight of a person never remains the same, it keeps on changing by getting lower or higher every day. Sun doesn't stay at the same spot whole day; it looks changing its position all the day along (it is because of motion of Earth around the Sun though). Share markets keep getting higher and lower on every single moment. A worker's pay changers according to number of hours he/she worked.

Finally, it can be said that algebra is study of activities which keep on changing with time. As we have hundreds of changing activities around us, therefore, algebra is everywhere in our daily lives.

What are the basic concepts need to be learned before starting algebra?

There is some basic PreAlgebra concepts need to learned before starting algebra. These topics are given below;

* Basic addition, subtraction, multiplication and division.

* Times tables at least up to times by 10.

* Know how to write all the factors of a number, finding greatest common factor (gcf) and least common multiple (LCM).

* Fractions and operations on fractions.

* Decimals

* Integers and Order of operations

What are the main topics learned in algebra?

The main topics in algebra are;

* Knowledge about the variables

* Know the coefficients and constants

* Writing algebraic expressions

* Simple linear equations in one variable

* Polynomials, degree and type

* Operations with the polynomials, such as, adding polynomials, subtracting polynomials, multiplying and dividing polynomials

* Rational expressions, Factorization

* System of linear equations in two and three variables

* Quadratic equations, absolute value equations and inequalities

* Patterns in general like sequences and series.

Why is algebra hard?

Algebra is not that hard. One can take it as a challenging course. It looks hard as it is based on very very general terms. Generic terms mean, for example; let's say you are looking for your younger brother, Vicky, in a crowd. You can call him by saying his name, Vicky aloud. Also your brother is a boy, and you can call him by saying, boy aloud. This time the problem is, there is too many boys in the crowd and may be, all of them start looking at you. So, boy is a general name and Vicky is a proper name.

Now if you recognize your brother from his clothes, height or other appearance you can even find him in the crowd by saying boy aloud. It looks hard, though but once your brother recognizes your voice, he will come to you. Same way you need to call algebra aloud (I mean learning it) and it will come to you like your brother.

Algebra has some rules to follow (as your brother has some unique appearance other than his name) and if you follow these rules, algebra is not hard at all.

So, that's all about basic algebra terminology, I could open in front of you according to my little knowledge of the topic. In my coming articles you will find, how to use algebra for our good, rules to follow to do math4kids and exploring the algebra and algebraic expressions.

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Rational and Irrational Numbers

Rational and Irrational Numbers

Rational and irrational numbers are taught in grade nine math. Students start learning rational numbers from grade six, but irrational numbers are introduced in grade nine (in most schools).

When I start teaching grade nine students, they look very confused about these two kinds of numbers. Let's take on these both types of numbers one by one.

Rational numbers: 

In the real number system, rational numbers are the fractions (mainly). Any number that can be written in the form "p/q", where "p" and "q" are both integers and "q" is not equal to zero, is called the rational number. There is a letter symbol of "Q" to denote them.

For example; 2/3 and -2/3 are both the examples of rational number. But they are not limited to fractions only. All the terminating (ending) decimals and repeating decimals are the in the this category.

For example; 2.5, - 2.5, 5.009 and repeating decimals like 0.3333... and 2.666.... fall under the symbol Q. Also, all the integers can be changed to fractions by making one as their denominator; hence all the integers such as - 5, - 4, - 3, 0, 1, 2, 3 and so on fall in this category.

Therefore rational numbers contain a variety of numbers in them. Below there are more example of rational numbers.

0, 1, -1, 2, -2, 0.56, 3.125, 3/6,-5/2, 3.22222...., 0.99999....

Irrational Numbers:

These are defined as the non-repeating and non-terminating decimals. In other words, if a decimal is not ending and numbers after decimals are not in a pattern that number is a rational number.

These kinds of numbers are obtained when square root of a number (which is not a perfect square) is calculated.

For example; 3.013004751224... is an irrational number.

Look at the pattern after the decimal are not in a pattern and no body can predict what is coming after last digit "4" and also this is a non-terminating decimal.

If we find the square root of number "2" using the calculator, we find a decimal which is an irrational number. Similarly the square root of number "3" falls in the same category.

But be careful in case of perfect squares such as "4", as the square root of four is "2" which is a natural number and hence a rational number but not an irrational number because four is a perfect square. Similarly all other perfect squares like, 16, 25, 36, 49, 64, 81, 100, 121, 144 and so on should be cared about their category. Similarly the square root of next perfect square "9" is "3" which is not an irrational.

I always ask my students to remember the irrational number as they are non-ending and non-repeating decimals and everything else is rational numbers.

If you want free fractions worksheets on all levels of fractions, you can visit a good site about fractions by clicking any of the links below:

Adding fractions: All levels of adding fractions, lessons and worksheets.

Multiply fractions: Learn how to multiply fractions with fractions at this page.

Including all the other topics on fractions.

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Why Do We Need Fractions?

Fractions - Learn Them To Make Math Easier For You!

Mathematics is a necessity for today’s life. All of us use math in our daily life in one or the other way.

But why is this only subject hated by kids in our schools?

There may be many answers to the above question but what I noticed; the reason is lack of basic math skills in kids. When kids are in elementary grades, they need to learn lot of basic math skills and educators and parents need to make sure that kids have learned those skills in the appropriate elementary grade levels.

In basic math skills, fractions are at the highest priority for kids to learn. Students can start learning fractions as early as grade one but the main goal for teaching fraction should be to cover all concepts about fractions up to grade seven.

If kids can’t understand and apply fractions properly in other math concepts, there should be supplemental fraction courses for these kids. Fractions are so important in math that they can be called at the heart of mathematics.

Fractions are often used in our daily life, for example, moms use them in the kitchen as recipes, and trades persons use them in workplaces for wrench measures or tape measures.

In advance math there are numerous applications of fractions. First of all, fractions are applied in algebra to solve rational expressions or rational equations, radicals (such as square root and cube roots) when they are simplified, students need fractions. Actually radicals are fractional exponents.

Trigonometry involves fractions, without knowing ratios (which are the other form of fractions), nobody can do trigonometry.

In geometry fractions are the life blood, as slopes of lines being a ratio again are the fractions. Now all the above math concepts are used in today’s technology in one or the other way.

For example, trigonometry is used in aviation industry, slopes are used in regression analysis to forecast many industrial data.

Hence, it can be said that if students have to succeed in math they have to learn fractions. Without fractions studying math is a nightmare therefore kids should start learning fractions as early as possible.

If students in grades seven or eight don’t understand fractions, other math concepts for them are impossible to understand and they should learn fractions before doing anything else in math. Kids can use basic fraction worksheets to practice the missed sections of the fraction learning.

The main fractions topics which kids should know are given below and I will explain them one by one in my coming articles, so stay tuned to learn the following topics:

1. Fractions, many ways to represent

2. Types of fractions

3. Equivalent fractions

4. Comparing fractions

5. Reducing fractions into lowest terms

6. Adding fractions

7. Subtracting fractions

8. Multiplying fractions

9. Dividing fractions

10. Order of operations involving fractions

So, stay tuned to learn all the above skills about fractions. If you want to learn more about fractions, you can visit fractions website instantly by clicking at fractions worksheets. This site is all about fractions and makes kids fractions smart.

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Many ways to write fractions

Many ways to represent fractions:

Fractions are also known as rational numbers. Fractions are parts of whole numbers or integers. They are needed when whole numbers or integers are not enough to give full information in many circumstances.

For example, two friends equally share an apple. How much apple each friend got? The answer can’t be given using whole numbers or integers. To represent parts of whole numbers, mathematicians evolved fractions. There are many ways to represent them. The main form to represent them is using numerator, denominator and solidus (or fraction line between numerator and denominator)

In the above example of two friends, one whole apple is cut equally into two parts. To total number of parts of the whole makes the denominator of the fraction, hence the denominator for the apple example is “2” because apple is cut into two equal parts. Number of parts of interest makes the numerator of the fraction. As each friend got one out of two parts of the apple, hence the numerator of the fraction is “1”.

To write the fraction, numerator is written on the top and denominator is written on the bottom and they have solidus (line) between them. Therefore the fraction of apple, each friend got can be written as “1/2” which is read as “one over two” also known as half. The above is the mathematical method to represent fractions. Kids can draw half apple to show the sharing of apple between two friends.

So, fractions can be represented by drawings or models. Actually, using the drawings and models is the best method to introduce kids with halves, quarters and three quarters.

Another method to represent fractions is writing them in words. For example, 3/8 can be written as “three eighths”, 3/16 is read as “three sixteenths” and 2/5 can be written as “two fifth”.

Fractions are not limited to above ways only but they can be represented by decimals, ratios, rates and percentages. There are whole units of conversions between fractions and decimals for grade six or grade seven math kids. Decimal system has base ten and can easily be represented into fractions. For example; 3.5 can be written as “35/10” using fractions and can be reduced to “7/2”.

Percentages have 100 as the base and all percentages can be converted into fractions and vice versa. For example; 85% can be written as “85/100” and which can be reduced to “17/20” further.

Similarly ratios and rates are other forms of fractions. The goal of this presentation is to make students aware of many forms of fractions. As students understand the different forms of fractions they can sort out and prioritize them according to their grade levels and their understanding levels.

To learn any level of fractions, to print free fractions lessons for all grades and to get free fractions worksheets click any link in this post. You will find a special site on fractions and only fractions.

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2nd grade math

Math for kids in grade two Kids in grade two are around 6 - 7 years of age in most schools around the world. They have already two to three years of school experience. These kids have learned many things about their surroundings, such as they have friends, they know road signs they can tell some what directions to their school from home. In grade two math, kids have many new things to learn and also they have to explore many concepts they have learned in grade one. There are the following main topics, grade two math kids need to introduce with and they need to learn.

1. Taking numbers to higher level:

Basically in grade one, kids have learned counting from 1 to 100 and writing the numbers from one to twenty in words. In grade two, it is a good time to teach higher numbers, such as numbers greater than one hundred and students should know at least up to thousands. It is good for kids if they know both, numerals and spelling of the numbers up to thousands.

2. Place value:

As students can count numbers beyond hundred, they should be introduced with the concept of place value. Kids in grade two at least know the place value to thousands.

3. Rounding numbers:

Rounding numbers to nearest tens, to nearest hundreds and nearest thousands is another key math skill kids in grade two should be comfortable doing it.

4. Types of numbers:

In hundreds chart kids should be introduced with even and odd numbers in grade two.

5. Skip counting:

Skip counting is another skill that can be introduced to grade two kids using the hundred chart. The even and odd numbers are actually the skip counting by two's. Also kids in grade two should know the skip counting by 5's and 10's.

6. Geometric Shapes:

Kids in second grade should have a good special knowledge, which means, kids should be given the opportunity to learn the basic two dimensional and three dimensional shapes.

7. Fractions:

Fractions can be said to be the basic foundation of mathematics, as without learning fractions, kids can't be successful in math and many skills in daily life. Second grade kids should be introduced with basic fraction models to familiarize them with wholes, halves, quarters and three quarters.

8. Patterns:

Simple number patterns, shape patterns or patterns using letters from alphabet are a good way to introduce grade two kids with patterns.

9. Addition: As addition is one of the math operations, in grade two, kids should know how to add one digit numbers vertically and horizontally.

10. Subtraction:

Subtracting numbers up to 50 is another very important math skill needs to be learned by grade two kids. Above is the list and range of basic math topics average grade two students learn. There can be less or more of these topics covered in different schools, but if a grade two student learn all the above topics from the list, he/she must score best grades in higher math.

There can be more topics depending on the geography or country, but above list is the main basic topics kids in 2nd grade math can learn and get ready for higher grade maths.

Article Source: http://EzineArticles.com/?expert=Manjit_Singh_Atwal

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Fun math games - Cool Tool To Learn Math.

Most of the students take math as hard, dry and boring subject in our schools. Kids in elementary grades specifically, don't like to sit very long to study maths, rather they like to play some game. But maths is thus important in ones life, these kids are too young to understand this. All over the world, mathematics is taught as mandatory topic for kids. Most schools around the world, keep maths compulsory up to grade ten Not only math is compulsory in schools but in daily life too, math has an integral place. Chefs use fractions and measurement in the kitchen for recipes, mechanics use it at the workplace, scientists use math in research and technology. Question arises, if math is then important then why it is taken that hard by studets and is there any way to make it easier? Yes, there are many ways to make maths easier, fun and interesting for kids. There are many ways mathematics can be fun. Fun mathematics games is one of the most important methods to make maths interesting and fun for kids. There are many advantages of the fun math games, such as: * Fun math games create playground environment and kids forget that they are doing math. * Kids learn mathematics while playing with board games and even don't realize they have learned a lot from these games at the time they play. Kids don't realize the maths progress right away but it can be seen in their report cards. * Fun mathematics games make many basic maths concepts so easy for kids, so that kids can do and understand higher maths concepts very easily. * Easy, inexpensive and entertaining method to train kids with maths. * Kids can use them to play with their parents at home or they can use these games at school. Finally, it can be said that funmathgames make mathematics easy and entertaining for kids. Students don't get bored with these games and they discover these games and hence mathematics easier and easier for them.