Many difficulties in mathematics resolve whole numbers, i beg your pardon are provided to count whole units the things. For example, you can count college student in a classroom and also the number of dollar bills. You require other type of number to define units that are not whole. Because that example, an aquarium might be partially full. A group may have actually a meeting, however only some of the members are present.

You are watching: This number represents the equal number of parts that equal a whole in a fraction.

Fractions are numbers offered to refer to a component of a whole. This has measurements the cannot be written as whole numbers. For example, the broad of a piece of notebook paper is an ext than 8 inches but less than 9 inches. The component longer 보다 8 inches is written as a fraction. Here, you will investigate how fractions have the right to be written and also used come represent amounts that are components of the whole.


Identifying Numerators and Denominators


A entirety can be divided into components of same size. In the example below, a rectangle has been divided into eight same squares. 4 of this eight squares room shaded.

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The shaded area can be represented by a fraction. A fraction is created vertically as 2 numbers v a line in between them.

The denominator (the bottom number) represents the variety of equal components that comprise the whole. The numerator (the optimal number) defines the variety of parts the you space describing. So return to the instance above, the rectangle has actually been split into 8 same parts, and also 4 of them have actually been shaded. You can use the fraction

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 to explain the shaded component of the whole.

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← The numerator tells how countless parts are shaded.

← The denominator tells how plenty of parts are required to make up the whole.


Parts that a Set


The rectangle model above provides a good, straightforward introduction come fractions. However, what perform you execute with instances that can not be as quickly modeled by shading component of a figure? for example, think about the following situation:

Marc works as a top quality Assurance Manager in ~ an automotive plant. Every hour that inspects 10 cars;

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 of those happen inspection.

In this case, 10 cars make up the whole group. Each car can be represented as a circle, as displayed below.

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To show  of the entirety group, you very first need to divide the totality group into 5 same parts. (You recognize this due to the fact that the fraction has a denominator that 5.)

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To show , circle 4 the the equal parts.

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Here is another example. Imagine that Aneesh is placing together a puzzle make of 12 pieces. In ~ the beginning, nobody of the pieces have been put right into the puzzle. This method that

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 of the puzzle is complete. Aneesh climate puts four pieces together. The puzzle is
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 complete. Soon, the adds four much more pieces. Eight out of twelve piece are now connected. This portion can be created as
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. Finally, Aneesh to add four an ext pieces. The puzzle is whole, utilizing all 12 pieces. The fraction can be written as
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.

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Note the the number in the denominator cannot be zero. The denominator tells how countless parts comprise the whole. Therefore if this number is 0, then there space no parts and therefore there can be no whole.

The numerator have the right to be zero, together it speak how many parts you are describing. Notice that in the puzzle instance above, you have the right to use the portion

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 to represent the state of the puzzle when 0 pieces have been placed.

Fractions can additionally be supplied to analysis data. In the data table below, 3 out of 5 tosses that a coin came up heads, and also 2 out of five tosses come up tails. The end of the total variety of coin tosses, the section that was heads have the right to be written as

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. The portion that to be tails can be created as .


Coin Toss

Result

1

Heads

2

Tails

3

Heads

4

Heads

5

Tails

Sophia, Daphne, and Charlie are all participating in a relay race to advanced money because that charity. First, Sophia will run 2 miles. Then, Daphne will run 5 miles. Finally, Charlie will finish the race by running 3 miles. What portion of the race will certainly Daphne run?

A) 5 mi

B)

C)

D)


Show/Hide Answer

A) 5 mi

Incorrect. Daphne will certainly run 5 miles, however that go not indicate the fractional component of the race that she will certainly run. To uncover the fraction, very first find the whole length that the gyeongju by combining the distances the three world will run (2 + 5 + 3 = 10). Then consider the street that Daphne will certainly run. The exactly answer is .

B)

Correct. The whole race is 10 miles long, and Daphne will run 5 miles. This means she will run

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 of the race.

C)

Incorrect. To discover the fraction, first find the entirety length the the race by combine the distances the three civilization will operation (2 + 5 + 3 = 10). Then consider the street that Daphne will run. The correct answer is .

D)

Incorrect. To uncover the fraction, an initial find the entirety length of the race by combine the ranges the three civilization will operation (2 + 5 + 3 = 10). Then take into consideration the distance that Daphne will certainly run. The correct answer is .

Parts that a Whole


The “parts of a whole” ide can it is in modeled with pizzas and also pizza slices. For example, imagine a pizza is cut into 4 pieces, and someone takes 1 piece. Now,

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of the pizza is gone and also  remains. Keep in mind that both of these fractions have a denominator the 4, which refers to the number of slices the entirety pizza has actually been cut into.

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Example

Problem

Joaquim bakes a blueberry pie because that a potluck dinner. The full pie is reduced into 6 equal slices. After ~ everybody eats dessert, just one part of the pie remains. What fraction of the pie remains?

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The pie was reduced into six equal slices, for this reason the denominator the the portion will it is in 6.

 

Only 1 part remains, so the numerator of the portion will be 1.

Answer

 of the pie remains.

Example

Problem

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Write a fraction to represent the section of the octagon that is not shaded.

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The octagon has eight same sections, for this reason the denominator of the portion will it is in 8.

Five sections are not shaded, for this reason the molecule of the portion will be 5.

Answer

 of the octagon is no shaded.

Measurement Contexts


You deserve to use a fraction to represent the quantity in a container. This measure cup is  filled with a liquid. Keep in mind that if the cup to be

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 full, it would be a entirety cup.

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You can also use fractions in measure up the length, width, or height of something that is not a complete unit. Using a 12-inch ruler, you measure a covering that is 6 customs long. You know that 12 inches amounts to one foot. So, the length of this shell is

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 of a foot; the 12-inch leader is the “whole”, and also the size of the shell is the “part.”

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Which portion represents the portion of the form that is shaded?

A)

B)


Show/Hide Answer

A)

Incorrect. The total variety of parts that comprise the whole, 8, is the denominator. The is the number listed below the portion bar. The variety of parts that space shaded, 7, is the numerator. That is the number above the portion bar. The exactly answer is .

B)

Correct. The total variety of parts that make up the whole, 8, is the denominator (below the fraction bar). The variety of parts that room shaded, 7, is the molecule (above the fraction bar).

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Summary


Fractions are supplied to represent parts of a whole. You deserve to use fractions once describing substances, quantities, or diagrams that room not complete. You also use fractions to describe numbers of human being or objects that do not make up a finish group. Fractions space written with a numerator and also denominator. The numerator (above the portion bar) tells the number of parts being described, and the denominator (below the fraction bar) tells the variety of parts that make up the whole.