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Homework 1-3 Greater Numbers

Math Homework Help for Fractions

This introduction will be great math homework help for fractions. You’ll get a quick refresher on fraction fundamentals and the other concepts needed to do your lessons.

The information on this page may seem like a lot of details to remember, but I promise we’ll get you through the actual math lessons like a breeze! This page is simply a tool that takes the place of a “boring” Glossary of Terms.

Math is a building process. To work with fractions, the student needs, at a minimum, strong skills in mathematical fundamentals including adding, subtracting, multiplying and dividing. Without these basic skills, attempting to do higher level work such as fractions will be very frustrating to the student. If the student is weak in these areas, time is better spent reviewing the basics for additional help.

General Homework Help

The Basic Concept of a Fraction

Before you can make “heads” or “tails” out of fractions, it would be helpful if we first agree that the basic idea of a fraction can be ABSTRACT, unless we name the WHOLE to which we are referring. So it is important to keep this in mind while doing your assignments.

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Definition of a Fraction

You might recall that in math a number is a point on the number line. Well, there is a special collection of numbers called fractions, which are usually denoted by a/b, where “a” and “b” are whole numbers and “b” is not equal to “0”.

It may be helpful to get your homework off to a great start by defining what fractions are, that is to say, specifying which of the points on the number line are fractions.

So, here goes…

There are three distinct meanings of fractions —part-whole, quotient, and ratio, which are found in most elementary math programs. To reduce confusion while using this homework helper, our lessons will only cover the part-whole relationship.

The Part-Whole – The part-whole explanation of a fraction is where a number like 1/5 indicates that a whole has been separated into five equal parts and one of those parts are being considered.

This table is a great help to get a feel of how a fractional part compares to the whole…

As a homework helper, this table shows you how the “same” whole can be divided into a different number of equal parts.

The Division Symbol (“/” or “__”) used in a fraction tells you that everything above the division symbol is the numerator and must be treated as if it were one number, and everything below the division symbol is the denominator and also must be treated as if it were one number.

Basically, the numerator tells you how many part we are talking about, and the denominator tells you how many parts the whole is divided into. So a fraction like 6/7 tells you that we are looking at six (6) parts of a whole that is divided into seven (7) equal parts.

Although we do not cover fractions as a quotient or as a ratio, here is a brief explanation of them.

A Quotient – The fraction 2/3 may be considered as a quotient, 2 ÷ 3. This explanation also arises from a dividing up situation.

For example…

Suppose you want to give some cookies to three people. Well, you could give each person one cookie, then another, and so on until you had given the same amount to each. So,…

If you have six cookies, then you could represent this process with simple math by dividing 6 by 3, and each person would get two cookies.

But what if you only have two cookies?

One way to solve the problem is to break-up each cookie into three equal parts and give each person 1/3 of each cookie so that in the end, each person gets 1/3 + 1/3 or 2/3 cookies. So 2 divided by 3 = 2/3.

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Here’s a brief explanation of…

A Ratio – A comparison of things as a ratio can be expressed in one of two ways: first, the “old fashioned” method, a:b, pronounced “a is to b“; and second, as found in newer books, a/b. If the ratio of “a to b” is 1 to 4“, or 1/4, then “a” is one-quarter of “b”. Alternately, “b” is four times as great as “a”.

For example:

The width of a rectangle is 7ft and its length is 19ft. The ratio of its width to its length is 7ft to 19 ft, or…

7ft/19ft = 7/19
Since we are comparing feet to feet, we don’t need to write the units.

The ratio of its length to its width is…19 to 7

That was already a lot of homework help and you haven’t worked a problem yet. So let’s put some this stuff to WORK! But remember this is NOT the actual lesson, just a quick overview of some to the RULES and PRINCIPLES we’ll need to use when working with fractions. Don’t worry about memorizing everything, you’ll see all of this “stuff” again as they apply to a particular operation during the homework lessons. So…

We’ll finish up with the…

Rules for Fraction Operations

Adding Fractions

To add fractions, the denominators must be equal. Complete the following steps to add two fractions.

  1. Build each fraction (if needed) so that both denominators are equal.
  2. Add the numerators of the fractions.
  3. The new denominator will be the denominator of the built-up fractions.
  4. Reduce or simplify your answer, if needed.
    • Factor the numerator.
    • Factor the denominator.
    • Cancel-out fraction mixes that have a value of 1.
    • Re-write your answer as a simplified or reduced fraction.

Learn More

 

Subtracting Fractions

To subtract fractions, the denominators must be equal. You basically following the same steps as in addition.

  1. Build each fraction (if required) so that both denominators are equal.
  2. Combine the numerators according to the operation of subtraction.
  3. The new denominator will be the denominator of the built-up fractions.
  4. Reduce or simplify your answer, if needed.
    • Factor the numerator.
    • Factor the denominator.
    • Cancel-out fraction mixes that have a value of 1.
    • Re-write your answer as a simplified or reduced fraction.

Learn More!

Multiplying Fractions

To multiply two simple fractions, complete the following steps.

  1. Multiply the numerators.
  2. Multiply the denominators.
  3. Reduce or simplify your answer, if needed.
    • Factor the numerator.
    • Factor the denominator.
    • Cancel-out fraction mixes that have a value of 1.
    • Re-write your answer as a simplified or reduced fraction.

To multiply a whole number and a fraction, complete the following steps.

  1. Convert the whole number to a fraction.
  2. Multiply the numerators.
  3. Multiply the denominators.
  4. Reduce or simplify your answer, if needed.
    • Factor the numerator.
    • Factor the denominator.
    • Cancel-out fraction mixes that have a value of 1.
    • Re-write your answer as a simplified or reduced fraction.

Learn More!

Dividing Fractions

To divide one fraction by a second fraction, convert the problem to multiplication and multiply the two fractions.

  1. Change the “÷” sign to “x” and invert the fraction to the right of the sign.
  2. Multiply the numerators.
  3. Multiply the denominators.
  4. Reduce or simplify your answer, if needed.
    • Factor the numerator.
    • Factor the denominator.
    • Cancel-out fraction mixes that have a value of 1.
    • Re-write your answer as a simplified or reduced fraction.

To divide a fraction by a whole number, convert the division process to a multiplication process, by using the following steps.

  1. Convert the whole number to a fraction.
  2. Change the “÷” sign to ” x” and invert the fraction to the right of the sign.
  3. Multiply the numerators.
  4. Multiply the denominators.
  5. Reduce or simplify your answer, if needed.
    • Factor the numerator.
    • Factor the denominator.
    • Cancel-out fraction mixes that have a value of 1.
    • Re-write your answer as a simplified or reduced fraction.

Learn More!

 


Greater Than Less Than Worksheets

Greater Than Less Than Worksheets for Study

Here is a graphic preview for all of the greater than less than worksheets. You can select different variables to customize these greater than less than worksheets for your needs. The greater than less than worksheets are randomly created and will never repeat so you have an endless supply of quality greater than less than worksheets to use in the classroom or at home. Our greater than less than worksheets are free to download, easy to use, and very flexible.

These greater than less than worksheets are a great resource for children in Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, and 5th Grade.

Click here for a Detailed Description of all the Greater Than Less Than Worksheets.



Quick Link for All Greater Than Less Than Worksheets

Click the image to be taken to that Greater Than Less Than Worksheet.


Detailed Description for All Greater Than Less Than Worksheets

Comparing Integer Worksheets
These greater than less than worksheets are great for testing children in their comparison of pairs of integers. You may select 1 though 5 digit problems, or just use numbers in the range of 1 through 20, as well as have the problems be positive, negative, or mixed. These greater than less than worksheets are appropriate for Kindergarten, 1st Grade, and 2nd Grade.

Comparing Fraction Worksheets
These greater than less than worksheets are great for testing children in their comparison of Fractions. You may select different denominators and have the problems be positive, negative or mixed. These greater than less than worksheets are appropriate for Kindergarten, 1st Grade, and 2nd Grade.

Comparing Decimal Worksheets
These greater than less than worksheets are great for testing children in their comparison of pairs of decimal numbers. You may select the problems to be positive, negative, or mixed. These greater than less than worksheets are appropriate for Kindergarten, 1st Grade, and 2nd Grade.

Comparing Fraction and Decimal Worksheets
These greater than less than worksheets are great for testing children in their comparison of a fraction to a decimal number. You may select different denominators and have the problems be positive, negative or mixed. These greater than less than worksheets are appropriate for Kindergarten, 1st Grade, and 2nd Grade.

Comparing Mixed Problems Worksheets
These greater than less than worksheets are great for testing children in their comparison of mixed problems. You may select different groups of mixed operations and change the range of numbers used in teh problems. These greater than less than worksheets are appropriate for 2nd Grade, 3rd Grade, 4th Grade, and 5th Grade.

Comparing US Coins Worksheets
These greater than less than worksheets are great for testing children in their comparison of US Coins. You may select pennies, nickels, dimes and quarters for the problems. These greater than less than worksheets are appropriate for Kindergarten, 1st Grade, and 2nd Grade.

Comparing Shapes Worksheets
These greater than less than worksheets are great for testing children in their comparison of groups of objects. These greater than less than worksheets are appropriate for Kindergarten, 1st Grade, and 2nd Grade.

Kindergarten Comparison Integer Worksheets
These greater than less than worksheets are great for teaching children the concept of greater than and less than. The children will cut out the alligator images for greater than and less than and paste them on the correct locations. These greater than less than worksheets are appropriate for Pre-Kindergarten, and Kindergarten.

Ordering Whole Numbers Worksheets
These greater than less than worksheet will produce problems for ordering 4 whole numbers. You may select the four numbers to have the same number of digits, or produce four whole numbers with different numbers of digits. You may select between 3 and 6 digits for the problems. You may select the ordering of the problems from greatest to least, least to greatest, or both.


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