QuestionOrder the fractions of students moving up to Level 2: $\frac{2}{3}, \frac{7}{12}, \frac{17}{24}, \frac{3}{4}$ .

Studdy Solution

STEP 1

Assumptions1. The fractions represent the proportion of students who move up to Level for each swim instructor. . The fractions are $\frac{}{3}$ , $\frac{7}{12}$ , $\frac{17}{24}$ , and $\frac{3}{4}$ .
3. We need to order these fractions from least to greatest.

STEP 2

To compare fractions, it is easier if they have the same denominator. The least common multiple (LCM) of the denominators,12,24, and4 is24. So, we will convert all fractions to have the denominator as24.

STEP 3

Convert $\frac{2}{3}$ to a fraction with denominator24. Multiply the numerator and the denominator by8.
$\frac{2}{3} = \frac{2 \times8}{3 \times8} = \frac{16}{24}$

STEP 4

Convert $\frac{7}{12}$ to a fraction with denominator24. Multiply the numerator and the denominator by2.
$\frac{7}{12} = \frac{7 \times2}{12 \times2} = \frac{14}{24}$

STEP 5

$\frac{17}{24}$ already has24 as the denominator, so we don't need to change it.

STEP 6

Convert $\frac{3}{4}$ to a fraction with denominator24. Multiply the numerator and the denominator by6.
$\frac{3}{4} = \frac{3 \times6}{4 \times6} = \frac{18}{24}$

STEP 7

Now, all the fractions have the same denominator (24), we can easily compare the numerators to order the fractions.The fractions are now $\frac{16}{24}$ , $\frac{14}{24}$ , $\frac{17}{24}$ , and $\frac{18}{24}$ .

STEP 8

Order the fractions from least to greatest by comparing the numerators.
$\frac{14}{24}, \frac{16}{24}, \frac{17}{24}, \frac{18}{24}$

STEP 9

Convert these fractions back to their original form to get the final answer.
$\frac{7}{12}, \frac{2}{3}, \frac{17}{24}, \frac{3}{4}$ The list that orders the fractions from least to greatest is $\frac{7}{12}, \frac{2}{3}, \frac{17}{24}, \frac{3}{4}$ .

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QuestionOrder the fractions of students moving up to Level 2: $\frac{2}{3}, \frac{7}{12}, \frac{17}{24}, \frac{3}{4}$ .

Studdy Solution

STEP 1

Assumptions1. The fractions represent the proportion of students who move up to Level for each swim instructor. . The fractions are $\frac{}{3}$ , $\frac{7}{12}$ , $\frac{17}{24}$ , and $\frac{3}{4}$ .
3. We need to order these fractions from least to greatest.

STEP 2

To compare fractions, it is easier if they have the same denominator. The least common multiple (LCM) of the denominators,12,24, and4 is24. So, we will convert all fractions to have the denominator as24.

STEP 3

Convert $\frac{2}{3}$ to a fraction with denominator24. Multiply the numerator and the denominator by8.
$\frac{2}{3} = \frac{2 \times8}{3 \times8} = \frac{16}{24}$

STEP 4

Convert $\frac{7}{12}$ to a fraction with denominator24. Multiply the numerator and the denominator by2.
$\frac{7}{12} = \frac{7 \times2}{12 \times2} = \frac{14}{24}$

STEP 5

$\frac{17}{24}$ already has24 as the denominator, so we don't need to change it.

STEP 6

Convert $\frac{3}{4}$ to a fraction with denominator24. Multiply the numerator and the denominator by6.
$\frac{3}{4} = \frac{3 \times6}{4 \times6} = \frac{18}{24}$

STEP 7

Now, all the fractions have the same denominator (24), we can easily compare the numerators to order the fractions.The fractions are now $\frac{16}{24}$ , $\frac{14}{24}$ , $\frac{17}{24}$ , and $\frac{18}{24}$ .

STEP 8

Order the fractions from least to greatest by comparing the numerators.
$\frac{14}{24}, \frac{16}{24}, \frac{17}{24}, \frac{18}{24}$

STEP 9

Convert these fractions back to their original form to get the final answer.
$\frac{7}{12}, \frac{2}{3}, \frac{17}{24}, \frac{3}{4}$ The list that orders the fractions from least to greatest is $\frac{7}{12}, \frac{2}{3}, \frac{17}{24}, \frac{3}{4}$ .

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QuestionOrder the fractions of students moving up to Level 2: 23,712,1724,34\frac{2}{3}, \frac{7}{12}, \frac{17}{24}, \frac{3}{4}32​,127​,2417​,43​.

Studdy Solution

STEP 1

Assumptions1. The fractions represent the proportion of students who move up to Level for each swim instructor. . The fractions are 3\frac{}{3}3​, 712\frac{7}{12}127​, 1724\frac{17}{24}2417​, and 34\frac{3}{4}43​.3. We need to order these fractions from least to greatest.

STEP 2

To compare fractions, it is easier if they have the same denominator. The least common multiple (LCM) of the denominators,12,24, and4 is24. So, we will convert all fractions to have the denominator as24.

STEP 3

Convert 23\frac{2}{3}32​ to a fraction with denominator24. Multiply the numerator and the denominator by8.23=2×83×8=1624\frac{2}{3} = \frac{2 \times8}{3 \times8} = \frac{16}{24}32​=3×82×8​=2416​

STEP 4

Convert 712\frac{7}{12}127​ to a fraction with denominator24. Multiply the numerator and the denominator by2.712=7×212×2=1424\frac{7}{12} = \frac{7 \times2}{12 \times2} = \frac{14}{24}127​=12×27×2​=2414​

STEP 5

1724\frac{17}{24}2417​ already has24 as the denominator, so we don't need to change it.

STEP 6

Convert 34\frac{3}{4}43​ to a fraction with denominator24. Multiply the numerator and the denominator by6.34=3×64×6=1824\frac{3}{4} = \frac{3 \times6}{4 \times6} = \frac{18}{24}43​=4×63×6​=2418​

STEP 7

Now, all the fractions have the same denominator (24), we can easily compare the numerators to order the fractions.The fractions are now 1624\frac{16}{24}2416​, 1424\frac{14}{24}2414​, 1724\frac{17}{24}2417​, and 1824\frac{18}{24}2418​.

STEP 8

Order the fractions from least to greatest by comparing the numerators.1424,1624,1724,1824\frac{14}{24}, \frac{16}{24}, \frac{17}{24}, \frac{18}{24}2414​,2416​,2417​,2418​

STEP 9

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QuestionOrder the fractions of students moving up to Level 2: $\frac{2}{3}, \frac{7}{12}, \frac{17}{24}, \frac{3}{4}$ .

Assumptions1. The fractions represent the proportion of students who move up to Level for each swim instructor. . The fractions are $\frac{}{3}$ , $\frac{7}{12}$ , $\frac{17}{24}$ , and $\frac{3}{4}$ .
3. We need to order these fractions from least to greatest.

Convert $\frac{2}{3}$ to a fraction with denominator24. Multiply the numerator and the denominator by8.
$\frac{2}{3} = \frac{2 \times8}{3 \times8} = \frac{16}{24}$

Convert $\frac{7}{12}$ to a fraction with denominator24. Multiply the numerator and the denominator by2.
$\frac{7}{12} = \frac{7 \times2}{12 \times2} = \frac{14}{24}$

$\frac{17}{24}$ already has24 as the denominator, so we don't need to change it.

Convert $\frac{3}{4}$ to a fraction with denominator24. Multiply the numerator and the denominator by6.
$\frac{3}{4} = \frac{3 \times6}{4 \times6} = \frac{18}{24}$

Now, all the fractions have the same denominator (24), we can easily compare the numerators to order the fractions.The fractions are now $\frac{16}{24}$ , $\frac{14}{24}$ , $\frac{17}{24}$ , and $\frac{18}{24}$ .

Order the fractions from least to greatest by comparing the numerators.
$\frac{14}{24}, \frac{16}{24}, \frac{17}{24}, \frac{18}{24}$