2.6 as a fraction. Here is the answer to the question: 2.6 as a fraction or what is 2.6 as a fraction. Use the decimal to fraction converter/calculator below to write any decimal number as a fraction. The number 2, an integer, can be written as the improper fraction 2/1 and it's multiples which are all improper fractions. 2 = 2/1 = 4/2 = 6/3 = 8/4 = 10/5. Tuneskit screen recorder 1 0 15.
- 0.6% As A Fraction
- Write The Ratio 2/3 To 6 As A Fraction In Simplest Form
- Write 2% As A Fraction
- Write 7% As A Fraction
- Write 6 2/3 As A Fraction
Alignments to Content Standards:5.NF.A.1
Task
Ancient Egyptians used unit fractions, such as $frac{1}{2}$ and $frac{1}{3}$,to represent all fractions. For example, they might write the number $frac{2}{3}$ as $frac{1}{2} + frac{1}{6}$.
We often think of $frac{2}{3}$ as $frac{1}{3}+frac{1}{3}$, but the ancient Egyptians would not write it this way because they didn't use the same unit fraction twice.
- Write each of the following Egyptian fractions as a single fraction:
- $frac{1}{2} + frac{1}{3}$,
- $frac{1}{2}+ frac{1}{3} + frac{1}{5}$,
- $frac{1}{4} + frac{1}{5} + frac{1}{12}$.
- How might the ancient Egyptians have writen the fraction we write as $frac{3}{4}$?
IM Commentary
One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions. Because the Egyptians represented fractions differently than we do, it can also help students understand that there can be many ways of representing the same number. This helps prepare them for writing algebraic expressions in 6th grade.This task is an instructional task; the teacher may wish to supplement part (b) of the question in two directions:
![Simplest Simplest](https://www.calculatorsoup.com/images/thumbnails/calculators_math_mixed-number-to-improper-fraction.png)
- As is indicated in the solution, there are many ways to write $frac{3}{4}$ as a sum of unit fractions and student work may naturally lead to a discussion of this issue.
- Students might be prompted to try to express some other fractions, suchas $frac{2}{5}$ or $frac{3}{5}$ as sums of unit fractions.
For historical accuracy, it should be noted that the ancient Egyptians hadspecial hieroglyphic symbols for the two fractions $frac{2}{3}$ and $frac{3}{4}$considered in this problem. In general, however, they used tables in orderto break down fractions into sums of unit fractions.
One issue which comes up in the solution is that there are apparently manyways to write an Egyptian fraction. This leads to an interesting question: how do you find the 'best' Egyptian fraction representing a given fraction? Here a reasonable interpretation of 'best' would be one which has the smallest number of unit fractions. This problem will be addressed in a second task which falls under the high school algebra standards.
Solution
- For the Egyptian fraction $frac{1}{2} + frac{1}{3}$, a common denominatorwould be $6$ since $6$ is divisible by both $2$ and $3$. Converting tothis common denominator we findbegin{align}frac{1}{2} + frac{1}{3} &= frac{3 times 1}{3 times 2} + frac{2 times 1}{2 times 3} &= frac{3}{6} + frac{2}{6} &= frac{5}{6}.end{align}For $frac{1}{2} + frac{1}{3} + frac{1}{5}$ we could use what we have just found,namely that $frac{1}{2} + frac{1}{3} = frac{5}{6}$. To add $frac{5}{6}$ and$frac{1}{5}$ we can use $5 times 6 = 30$as a common denominator:begin{align}frac{1}{2} + frac{1}{3} + frac{1}{5} &= frac{5}{6} + frac{1}{5} &= frac{5 times 5}{5 times 6} + frac{6 times 1}{6 times 5} &= frac{25 + 6}{30} &= frac{31}{30}.end{align}For $frac{1}{4}$, $frac{1}{5}$, and $frac{1}{12}$ note that $12$ is divisibleby $4$ so we can look for a common denominator of $frac{1}{5}$ and $frac{1}{12}$ and thiswill also work with $frac{1}{4}$. For $frac{1}{5}$ and $frac{1}{12}$ we canuse $5 times 12$ as a common denominator:begin{align}frac{1}{4} + frac{1}{5} + frac{1}{12} &= frac{15 times 1}{15 times 4} + frac{12 times 1}{12 times 5} + frac{5 times 1}{5 times 12} &= frac{15}{60} + frac{12}{60} + frac{5}{60} &= frac{15+12+5}{60} &= frac{32}{60}.end{align}As a parenthetical note, this gives an example where even though we found theleast common denominator to perform the addition, the resulting fractionis not in reduced form: the reduced form is $frac{8}{15}$.
- To write $frac{3}{4}$ as an Egyptian fraction, we might notice thatbegin{align}frac{3}{4} &= frac{2+1}{4} &= frac{2}{4} + frac{1}{4} &= frac{1}{2} + frac{1}{4}.end{align}Alternatively, since $frac{1}{2}$ is the largest of the unit fractions that isless than $frac{3}{4}$ it would be reasonable to take $frac{1}{2}$ as oneof the unit fractions in the Egyptian fraction expression for $frac{3}{4}$. Performing subtraction givesbegin{align}frac{3}{4} - frac{1}{2} &= frac{3}{4} - frac{2 times 1}{2 times 2} &= frac{3}{4} - frac{2}{4} &= frac{1}{4}.end{align}This gives us the same expression as above: $frac{3}{4} = frac{1}{2} + frac{1}{4}$.There are many other ways to write $frac{3}{4}$ as an Egyptian fraction.Sincebegin{align}frac{1}{2} &= frac{3}{6} &= frac{2}{6} + frac{1}{6} &= frac{1}{3} + frac{1}{6}end{align}and since $frac{3}{4} = frac{1}{2} + frac{1}{4}$ we have another expression of$frac{3}{4}$ as an Egyptian fraction, namely$$frac{3}{4} = frac{1}{3} + frac{1}{6} + frac{1}{4}.$$All Egyptian fractions share this same property: there are always endless waysto write an Egyptian fraction.
Egyptian Fractions
Ancient Egyptians used unit fractions, such as $frac{1}{2}$ and $frac{1}{3}$,to represent all fractions. For example, they might write the number $frac{2}{3}$ as $frac{1}{2} + frac{1}{6}$.
We often think of $frac{2}{3}$ as $frac{1}{3}+frac{1}{3}$, but the ancient Egyptians would not write it this way because they didn't use the same unit fraction twice.
- Write each of the following Egyptian fractions as a single fraction:
- $frac{1}{2} + frac{1}{3}$,
- $frac{1}{2}+ frac{1}{3} + frac{1}{5}$,
- $frac{1}{4} + frac{1}{5} + frac{1}{12}$.
- How might the ancient Egyptians have writen the fraction we write as $frac{3}{4}$?
- Converting Fractions to Decimals
- Writing a Decimal and a Fraction for a Shaded Region
- Converting a Fraction With a Denominator of 10 or 100 to a Decimal
- Converting a Fraction With a Denominator of 100 or 1000 to a Decimal
- Converting a Proper Fraction With a Denominator of 2, 4, or 5 to a Decimal
- Converting a Mixed Number With a Denominator of 2, 4, or 5 to a Decimal
- Converting a Fraction to a Terminating Decimal - Basic
- Converting a Fraction to a Terminating Decimal - Advanced
- Converting a Fraction to a Repeating Decimal - Basic
- Converting a Fraction to a Repeating Decimal - Advanced
- Using a Calculator to Convert a Fraction to a Rounded Decimal
- Converting a Mixed Number to a Terminating Decimal - Basic
- Converting a Mixed Number to a Terminating Decimal - Advanced
- Ordering Fractions and Decimals
- Selected Reading
Here a figure is given in the form of a circle or a rectangular strip or some other shape. It is then divided into certain number of equal parts. Some of these equal parts are shaded with colors.
Considering the figure as a one unit, it is required to find the fraction that represents the shaded region of the given figure.
It is also required to find the decimal representing the same shaded region.
Following examples will make it easy to write a fraction and a decimal that represent a shaded region in a figure.
Write a decimal or fraction for the shaded region shown below. Imazing 2 1 1.
Solution
Step 1:
Total parts of the circle = 3
Shaded parts of the circle = 2
Step 2:
Fraction representing shaded region of circle = $frac{2}{3}$
0.6% As A Fraction
Step 3:
Writing the fraction as a repeating decimal $frac{2}{3} = 0.666… = 0.bar{6}$
Write a decimal or a fraction for the shaded region shown below.
Solution
Step 1:
Total parts of the rectangular strip = 5
Shaded parts of the strip = 1
Step 2:
Fraction representing shaded region of strip = $frac{1}{5}$
Step 3:
Writing the fraction as a decimal $frac{1}{5} = frac{2}{10} = 0.2$
Write a decimal or fraction for the shaded region shown below.
Solution
Step 1:
Total parts of the circle = 5
Shaded parts of the circle = 4
Write The Ratio 2/3 To 6 As A Fraction In Simplest Form
Step 2:
Write 2% As A Fraction
Fraction representing shaded region of circle = $frac{4}{5}$
Write 7% As A Fraction
Step 3:
Write 6 2/3 As A Fraction
Writing the fraction as a decimal $frac{4}{5} = frac{8}{10} = 0.8$