How To Draw A Model To Represent 6/2

Learning Outcomes

• Write fractions that correspond portions of objects
• Apply fraction circles to make wholes given
• Utilise models to visualize improper fractions and mixed numbers.

Representing Parts of a Whole as Fractions

Andy and Bobby love pizza. On Monday dark, they share a pizza equally. How much of the pizza does each ane get? Are you thinking that each boy gets half of the pizza? That's right. There is ane whole pizza, evenly divided into two parts, so each boy gets one of the ii equal parts.
In math, nosotros write [latex]\frac{1}{ii}[/latex] to mean one out of two parts.

On Tuesday, Andy and Bobby share a pizza with their parents, Fred and Christy, with each person getting an equal amount of the whole pizza. How much of the pizza does each person go? In that location is one whole pizza, divided evenly into four equal parts. Each person has one of the 4 equal parts, so each has [latex]\frac{1}{four}[/latex] of the pizza.

On Wednesday, the family invites some friends over for a pizza dinner. At that place are a total of [latex]12[/latex] people. If they share the pizza equally, each person would get [latex]\frac{ane}{12}[/latex] of the pizza.

Fractions

A fraction is written [latex]\frac{a}{b}[/latex], where [latex]a[/latex] and [latex]b[/latex] are integers and [latex]b\ne 0[/latex]. In a fraction, [latex]a[/latex] is called the numerator and [latex]b[/latex] is called the denominator.

A fraction is a way to represent parts of a whole. The denominator [latex]b[/latex] represents the number of equal parts the whole has been divided into, and the numerator [latex]a[/latex] represents how many parts are included. The denominator, [latex]b[/latex], cannot equal zero because segmentation by aught is undefined.
In the paradigm beneath, the circle has been divided into three parts of equal size. Each part represents [latex]\frac{one}{3}[/latex] of the circumvolve. This type of model is called a fraction circle. Other shapes, such as rectangles, can also be used to model fractions.

Doing the Manipulative Mathematics activity Model Fractions will help you lot develop a amend understanding of fractions, their numerators and denominators.
What does the fraction [latex]\frac{ii}{3}[/latex] represent? The fraction [latex]\frac{2}{3}[/latex] means two of 3 equal parts.

Example

Name the fraction of the shape that is shaded in each of the figures.

Solution:
We need to ask two questions. First, how many equal parts are at that place? This will be the denominator. 2nd, of these equal parts, how many are shaded? This will be the numerator.

[latex]\brainstorm{assortment}{cccc}\text{How many equal parts are there?}\hfill & & & \text{There are eight equal parts}\text{.}\hfill \\ \text{How many are shaded?}\hfill & & & \text{Five parts are shaded}\text{.}\hfill \end{array}[/latex]
5 out of eight parts are shaded. Therefore, the fraction of the circumvolve that is shaded is [latex]\frac{5}{8}[/latex].

[latex]\begin{array}{cccc}\text{How many equal parts are there?}\hfill & & & \text{In that location are nine equal parts}\text{.}\hfill \\ \text{How many are shaded?}\hfill & & & \text{Two parts are shaded}\text{.}\hfill \end{assortment}[/latex]
Two out of nine parts are shaded. Therefore, the fraction of the foursquare that is shaded is [latex]\frac{2}{ix}[/latex].

Try it

Case

Shade [latex]\frac{iii}{4}[/latex] of the circle.

Try it

Shade [latex]\frac{half dozen}{8}[/latex] of the circle.

Show Solution

Shade [latex]\frac{2}{5}[/latex] of the rectangle.

Evidence Solution

Watch the following video to encounter more examples of how to write fractions given a model.

In earlier examples, we used circles and rectangles to model fractions. Fractions can also exist modeled as manipulatives called fraction tiles, as shown in the image below. Here, the whole is modeled as ane long, undivided rectangular tile. Beneath information technology are tiles of equal length divided into different numbers of as sized parts.

We'll be using fraction tiles to discover some basic facts about fractions. Refer to the fraction tiles above to answer the following questions:

How many [latex]\frac{1}{two}[/latex] tiles does it take to make one whole tile?	It takes ii halves to make a whole, and then two out of two is [latex]\frac{2}{ii}=i[/latex].
How many [latex]\frac{1}{iii}[/latex] tiles does it take to make i whole tile?	It takes three thirds, so three out of three is [latex]\frac{3}{3}=1[/latex].
How many [latex]\frac{1}{four}[/latex] tiles does it take to make one whole tile?	It takes 4 fourths, and so four out of 4 is [latex]\frac{iv}{iv}=one[/latex].
How many [latex]\frac{ane}{6}[/latex] tiles does it accept to make one whole tile?	Information technology takes six sixths, then six out of 6 is [latex]\frac{6}{vi}=1[/latex].
What if the whole were divided into [latex]24[/latex] equal parts? (We have not shown fraction tiles to stand for this, but try to visualize it in your mind.) How many [latex]\frac{1}{24}[/latex] tiles does it take to make one whole tile?	It takes [latex]24[/latex] xx-fourths, and so [latex]\frac{24}{24}=1[/latex].

It takes [latex]24[/latex] xx-fourths, and so [latex]\frac{24}{24}=1[/latex].
This leads the states to the Belongings of I.

Property of 1

Any number, except nothing, divided by itself is one.

[latex]\frac{a}{a}=1\left(a\ne 0\right)[/latex]

Doing the Manipulative Mathematics activity "Fractions Equivalent to 1" volition aid you develop a better understanding of fractions that are equivalent to one

Example

Apply fraction circles to make wholes using the following pieces:

1. [latex]four[/latex] fourths
2. [latex]v[/latex] fifths
3. [latex]6[/latex] sixths

Effort it

Apply fraction circles to make wholes with the following pieces: [latex]3[/latex] thirds.

Show Solution

Use fraction circles to make wholes with the post-obit pieces: [latex]8[/latex] eighths.

Bear witness Solution

What if we accept more fraction pieces than we demand for [latex]1[/latex] whole? We'll look at this in the next example.

Example

Use fraction circles to make wholes using the post-obit pieces:

1. [latex]3[/latex] halves
2. [latex]viii[/latex] fifths
3. [latex]7[/latex] thirds

try it

Use fraction circles to make wholes with the following pieces: [latex]five[/latex] thirds.

Testify Solution

Use fraction circles to make wholes with the post-obit pieces: [latex]5[/latex] halves.

Show Solution

Model Improper Fractions and Mixed Numbers

In an earlier case, you had eight equal fifth pieces. You used 5 of them to brand one whole, and yous had iii fifths left over. Let us utilize fraction notation to show what happened. You had 8 pieces, each of them 1 fifth, [latex]\frac{i}{5}[/latex], so birthday you had viii fifths, which we tin write as [latex]\frac{8}{v}[/latex]. The fraction [latex]\frac{8}{5}[/latex] is i whole, [latex]i[/latex], plus three fifths, [latex]\frac{3}{5}[/latex], or [latex]1\frac{3}{five}[/latex], which is read equally ane and three-fifths.
The number [latex]i\frac{3}{v}[/latex] is chosen a mixed number. A mixed number consists of a whole number and a fraction.

Mixed Numbers

A mixed number consists of a whole number [latex]a[/latex] and a fraction [latex]\frac{b}{c}[/latex] where [latex]c\ne 0[/latex]. It is written as follows.

[latex]a\frac{b}{c}\text{, }c\ne 0[/latex]

Fractions such every bit [latex]\frac{v}{4},\frac{3}{two},\frac{five}{5}[/latex], and [latex]\frac{7}{3}[/latex] are called improper fractions. In an improper fraction, the numerator is greater than or equal to the denominator, so its value is greater than or equal to 1. When a fraction has a numerator that is smaller than the denominator, it is called a proper fraction, and its value is less than i. Fractions such equally [latex]\frac{1}{2},\frac{3}{seven}[/latex], and [latex]\frac{11}{18}[/latex] are proper fractions.

Proper and Improper Fractions

The fraction [latex]\frac{a}{b}[/latex] is a proper fraction if [latex]a<b[/latex] and an improper fraction if [latex]a\ge b[/latex].

Doing the Manipulative Mathematics activity "Model Improper Fractions" and "Mixed Numbers" will help yous develop a amend understanding of how to convert betwixt improper fractions and mixed numbers.

Example

Proper noun the improper fraction modeled. Then write the improper fraction as a mixed number.

Solution:
Each circle is divided into three pieces, then each piece is [latex]\frac{1}{3}[/latex] of the circle. There are iv pieces shaded, so there are four thirds or [latex]\frac{4}{three}[/latex]. The effigy shows that we also have one whole circle and 1 third, which is [latex]1\frac{one}{3}[/latex]. So, [latex]\frac{4}{3}=ane\frac{ane}{iii}[/latex].

attempt it

Example

Draw a effigy to model [latex]\frac{11}{eight}[/latex].

Try it

Draw a figure to model [latex]\frac{7}{6}[/latex].

Evidence Solution

Draw a effigy to model [latex]\frac{six}{v}[/latex].

Testify Solution

Case

Utilise a model to rewrite the improper fraction [latex]\frac{11}{6}[/latex] as a mixed number.

Attempt information technology

In the next video nosotros show another way to draw a model that represents a fraction.  You will see example of both proper and improper fractions shown.

Example

Employ a model to rewrite the mixed number [latex]1\frac{4}{5}[/latex] as an improper fraction.

Endeavour it

Source: https://courses.lumenlearning.com/prealgebra/chapter/visualize-fractions/

Posted by: solistheaks.blogspot.com

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