01 - What is a Fraction? - Definition & Meaning - Part 1 - Numerator, Denominator & More.
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- Опубліковано 18 вер 2024
- View more at www.MathAndScie.... In this lesson, you will learn what a fraction is, why they are important, and how to write fractions down to represent the amount of an object. We use fractions to describe the amount of an object we have when we have less than 1 whole object. The numerator of the fraction describes how many pieces we have and the denominator of the fraction determines how many pieces we cut the object into. For example, in the fractions 1/2 (one half), the numerator is 1 and the denominator is 2. This means that we have 1 out of 2 pieces of the object. We cut the item into two pieces, but we actually only have one piece. We use fractions in all of math, science, engineering, physics, chemistry, and more. Fractions are one of the most important concepts to learn in all of math.
![Understand Fractions & Their Meaning - Multiplying Fractions & Adding Fractions - [31]](/img/n.gif)

a fraction is a way of indicating parts of a whole. The top number, called the numerator, represents the number of parts you're working with. The bottom number, called the denominator, represents how many parts there are in total.
for example, if you have 1 piece of a pizza that was cut into 4 pieces, you have ¼ of a pizza. If you have 7/3 pizzas, you have two whole pizzas plus 1 piece of a pizza that was cut into three pieces.
Compound Fractions versus Simple Fractions
a compound fraction has a whole number and a fraction, such as 2 1/3 or 45 1/2. Usually, you must convert a compound fraction to a simple fraction before you can add, subtract, multiply or divide it.
Convert compound fractions by multiplying the whole number by the denominator of the fraction and then adding the numerator. Write a new fraction with the total as the numerator and the same number as the denominator.
For example, 2 1/3 becomes 7/3: 2 times 3, plus 1.( 2x3+1=7 )

Change a simple fraction to a compound fraction by dividing the numerator by the denominator. Write down the whole number you get by dividing and make the remainder the numerator of the fraction. The denominator is the same.
For example, for the fraction 7/3, divide 7 by 3 to get 2 with the remainder of one; the compound fraction is 2 1/3. You can only do this if the numerator is larger than the denominator.

Adding & Subtracting Fractions
Find the common denominator of the fractions you are adding or subtracting. To do this, you can multiply the denominators together, then multiply each numerator by the number you used to find its denominator. Sometimes you can find a common denominator that is a smaller number than you would get if you simply multiplied denominators together.
For example, to add the fractions 1/2 and 1/3, you first make the denominators the same by multiplying them together to get 6. Multiply 1 by 3 to get 3 as the new numerator for the first fraction. Multiply 1 by 2 to get 2 as the new numerator for the second fraction. Your new fractions are 3/6 and 2/6.
Add the numerators together and keep the same denominator.

Use the same technique to subtract fractions as you did to add fractions by finding the common denominator first, but instead of adding, subtract the numerator of the second fraction from the numerator of the first.

Multiplying & Dividing Fractions
Multiply the numerators and denominators separately to get the result, For example, when you multiply 1/2 and 1/3, you will get 1/6 (1 times 1 over 2 times 3). It's not necessary to find a common denominator when multiplying. Reduce or convert the result if you can.

To divide fractions, turn the second fraction upside down, the multiply them together., For example, if you want to divide 1/2 by 1/3, first rewrite the equation so the second fraction is 3/1.

Reduce the fraction if you can by dividing the numerator and denominator by the same number.
For example, a fraction such as 5/6 can't be reduced, but 3/6 can be reduced to 1/2 by dividing both halves by 3.

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@@MathAndScience Did Part 2 of “What is a Fraction” ever get released?
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Excellent, thank you! A suggestion if I may: it might be useful to clarify that, in all cases, you are cutting the shapes in a number of EQUAL or IDENTICAL pieces.
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In music each tune is equal to 9 stacks or you can call them 9 slashes. So if the tune is divided into 4 quarters and then we take 3/4 out of the 4/4 then we add to the 3/4 half of 1/4 what is the number we get and how many slashes out of the 9 slashes that will be?
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I think, we can write the fraction 2/3 as 1/3 ×2 meaning that we have sliced one whole piece into 3 parts and kept 2 pieces with us.
If I have 10 pens, given away 4 pens making a fraction 4/10 and the remaining pens making a fraction 6/10. Here, adding these fractions gives 1. But I have 10 pens, does it make a fraction ?
If we place these ten pens in the fractional circle, treating it as an unit, we can set up a fractional equation to solve for the number of pens i.e given or left. Like, X/10 + y/10 =1.
If we have 150 pens and 12% given away, the remaining pens can be calculated using this fractional equation instead of other methods. Right ?.
12%×150/150 + y/150 =1.
No doubts,no questions means either we have understood fully or nothing at all(not to mention partially). Anyway, doubts are initial part of our learning and question is later part of it.
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Can u say me 1/√3 is a fraction or not..and 1/√3 is a rational no.or irrational no.
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Gidday mate, nice presentation. I'm assuming you are American. In Australia 🇦🇺 we call the line between the numerator and denominator the 'vinculum'. Is that the same in America or do you use 'fraction bar/line'?
Wow I have never hear of "vinculum". We always called it a fraction bar. Thank you! DIdn't know there was a real name for that.
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2/1 is a fraction or not ??
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