Solved on Nov 19, 2023

Order the fractions and mixed numbers in ascending order: $\frac{3}{2}, \frac{11}{4}, 1 \frac{1}{4}, 2 \frac{7}{8}$

STEP 1

Assumptions1. We are asked to arrange the given values in ascending order. . The given values are $\frac{3}{}$ , $\frac{11}{4}$ , $1 \frac{1}{4}$ , and $\frac{7}{8}$ .

STEP 2

To compare the numbers easily, we need to convert all the given values into the same format. Let's convert the mixed fractions into improper fractions.
The conversion from a mixed fraction to an improper fraction can be done using the formula $\text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{umerator}$

STEP 3

Convert $1 \frac{1}{}$ into an improper fraction.
$1 \frac{1}{} =1 \times +1 = \frac{5}{}$

STEP 4

Convert $2 \frac{7}{8}$ into an improper fraction.
$2 \frac{7}{8} =2 \times8 +7 = \frac{23}{8}$

STEP 5

Now we have all the fractions in the same format $\frac{3}{2}$ , $\frac{11}{4}$ , $\frac{5}{4}$ , and $\frac{23}{8}$ .

STEP 6

To compare these fractions, it's easier if they all have the same denominator. The least common denominator (LCD) of2,4,4, and8 is8.

STEP 7

Convert each fraction to have the LCD as the denominator.For $\frac{3}{2}$ , multiply both the numerator and the denominator by4 to get $\frac{12}{}$ .

STEP 8

For $\frac{11}{4}$ , multiply both the numerator and the denominator by2 to get $\frac{22}{8}$ .

STEP 9

For $\frac{5}{4}$ , multiply both the numerator and the denominator by2 to get $\frac{}{8}$ .

STEP 10

Now we have all the fractions with the same denominator $\frac{12}{8}$ , $\frac{22}{8}$ , $\frac{10}{8}$ , and $\frac{23}{8}$ .

STEP 11

Arrange these fractions in ascending order by comparing their numerators.
The ascending order is $\frac{10}{8}$ , $\frac{}{8}$ , $\frac{22}{8}$ , and $\frac{23}{8}$ .

STEP 12

Convert these fractions back to their original form.
$\frac{10}{8}$ is $\frac{}{4}$ , $\frac{12}{8}$ is $\frac{}{2}$ , $\frac{22}{8}$ is $\frac{11}{4}$ , and $\frac{23}{8}$ is $2 \frac{7}{8}$ .
So, the ascending order of the given values is $\frac{}{4}$ , $\frac{}{2}$ , $\frac{11}{4}$ , and $2 \frac{7}{8}$ .

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Order the fractions and mixed numbers in ascending order: $\frac{3}{2}, \frac{11}{4}, 1 \frac{1}{4}, 2 \frac{7}{8}$

STEP 1

Assumptions1. We are asked to arrange the given values in ascending order. . The given values are $\frac{3}{}$ , $\frac{11}{4}$ , $1 \frac{1}{4}$ , and $\frac{7}{8}$ .

STEP 2

STEP 3

Convert $1 \frac{1}{}$ into an improper fraction.
$1 \frac{1}{} =1 \times +1 = \frac{5}{}$

STEP 4

Convert $2 \frac{7}{8}$ into an improper fraction.
$2 \frac{7}{8} =2 \times8 +7 = \frac{23}{8}$

STEP 5

Now we have all the fractions in the same format $\frac{3}{2}$ , $\frac{11}{4}$ , $\frac{5}{4}$ , and $\frac{23}{8}$ .

STEP 6

To compare these fractions, it's easier if they all have the same denominator. The least common denominator (LCD) of2,4,4, and8 is8.

STEP 7

Convert each fraction to have the LCD as the denominator.For $\frac{3}{2}$ , multiply both the numerator and the denominator by4 to get $\frac{12}{}$ .

STEP 8

For $\frac{11}{4}$ , multiply both the numerator and the denominator by2 to get $\frac{22}{8}$ .

STEP 9

For $\frac{5}{4}$ , multiply both the numerator and the denominator by2 to get $\frac{}{8}$ .

STEP 10

Now we have all the fractions with the same denominator $\frac{12}{8}$ , $\frac{22}{8}$ , $\frac{10}{8}$ , and $\frac{23}{8}$ .

STEP 11

Arrange these fractions in ascending order by comparing their numerators.
The ascending order is $\frac{10}{8}$ , $\frac{}{8}$ , $\frac{22}{8}$ , and $\frac{23}{8}$ .

STEP 12

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Order the fractions and mixed numbers in ascending order: 32,114,114,278\frac{3}{2}, \frac{11}{4}, 1 \frac{1}{4}, 2 \frac{7}{8}23​,411​,141​,287​

STEP 1

Assumptions1. We are asked to arrange the given values in ascending order. . The given values are 3\frac{3}{}3​, 114\frac{11}{4}411​, 1141 \frac{1}{4}141​, and 78 \frac{7}{8}87​.

STEP 2

STEP 3

Convert 111 \frac{1}{}11​ into an improper fraction.11=1×+1=51 \frac{1}{} =1 \times +1 = \frac{5}{}11​=1×+1=5​

STEP 4

Convert 2782 \frac{7}{8}287​ into an improper fraction.278=2×8+7=2382 \frac{7}{8} =2 \times8 +7 = \frac{23}{8}287​=2×8+7=823​

STEP 5

Now we have all the fractions in the same format 32\frac{3}{2}23​, 114\frac{11}{4}411​, 54\frac{5}{4}45​, and 238\frac{23}{8}823​.

STEP 6

To compare these fractions, it's easier if they all have the same denominator. The least common denominator (LCD) of2,4,4, and8 is8.

STEP 7

Convert each fraction to have the LCD as the denominator.For 32\frac{3}{2}23​, multiply both the numerator and the denominator by4 to get 12\frac{12}{}12​.

STEP 8

For 114\frac{11}{4}411​, multiply both the numerator and the denominator by2 to get 228\frac{22}{8}822​.

STEP 9

For 54\frac{5}{4}45​, multiply both the numerator and the denominator by2 to get 8\frac{}{8}8​.

STEP 10

Now we have all the fractions with the same denominator 128\frac{12}{8}812​, 228\frac{22}{8}822​, 108\frac{10}{8}810​, and 238\frac{23}{8}823​.

STEP 11

Arrange these fractions in ascending order by comparing their numerators.The ascending order is 108\frac{10}{8}810​, 8\frac{}{8}8​, 228\frac{22}{8}822​, and 238\frac{23}{8}823​.

STEP 12

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Order the fractions and mixed numbers in ascending order: $\frac{3}{2}, \frac{11}{4}, 1 \frac{1}{4}, 2 \frac{7}{8}$

Assumptions1. We are asked to arrange the given values in ascending order. . The given values are $\frac{3}{}$ , $\frac{11}{4}$ , $1 \frac{1}{4}$ , and $\frac{7}{8}$ .

Convert $1 \frac{1}{}$ into an improper fraction.
$1 \frac{1}{} =1 \times +1 = \frac{5}{}$

Convert $2 \frac{7}{8}$ into an improper fraction.
$2 \frac{7}{8} =2 \times8 +7 = \frac{23}{8}$

Now we have all the fractions in the same format $\frac{3}{2}$ , $\frac{11}{4}$ , $\frac{5}{4}$ , and $\frac{23}{8}$ .

Convert each fraction to have the LCD as the denominator.For $\frac{3}{2}$ , multiply both the numerator and the denominator by4 to get $\frac{12}{}$ .

For $\frac{11}{4}$ , multiply both the numerator and the denominator by2 to get $\frac{22}{8}$ .

For $\frac{5}{4}$ , multiply both the numerator and the denominator by2 to get $\frac{}{8}$ .

Now we have all the fractions with the same denominator $\frac{12}{8}$ , $\frac{22}{8}$ , $\frac{10}{8}$ , and $\frac{23}{8}$ .

Arrange these fractions in ascending order by comparing their numerators.
The ascending order is $\frac{10}{8}$ , $\frac{}{8}$ , $\frac{22}{8}$ , and $\frac{23}{8}$ .