Question Find the expression that does not answer "What fraction of 8 is $2 \frac{1}{2}$ ?". A) $2 \frac{1}{2} \div 8$ B) $\frac{5}{2} \times \frac{1}{8}$ C) $8 \div 2 \frac{1}{2}$ D) $? \times 8=2 \frac{1}{2}$

Studdy Solution

STEP 1

Assumptions
1. We are looking for the expression or equation that does not represent the fraction of 8 that is $2 \frac{1}{2}$ .
2. We are given four options to evaluate: A, B, C, and D.
3. We need to interpret each expression or equation correctly to determine which one is not a valid representation of the question asked.

STEP 2

Understand the question being asked. The question "What fraction of 8 is $2 \frac{1}{2}$ ?" is asking us to find the fraction that represents the part of 8 that equals $2 \frac{1}{2}$ .

STEP 3

Convert the mixed number $2 \frac{1}{2}$ to an improper fraction to make calculations easier.
$2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$

STEP 4

Evaluate option A: $2 \frac{1}{2} \div 8$
Convert the mixed number to an improper fraction and then divide by 8.
$A = \frac{5}{2} \div 8$

STEP 5

When dividing by a whole number, we can multiply by its reciprocal.
$A = \frac{5}{2} \times \frac{1}{8}$

STEP 6

Calculate the result for option A.
$A = \frac{5}{2} \times \frac{1}{8} = \frac{5}{16}$
Option A represents the fraction of 8 that is $2 \frac{1}{2}$ .

STEP 7

Evaluate option B: $\frac{5}{2} \times \frac{1}{8}$
This is the same expression we obtained in STEP_6, so it also represents the fraction of 8 that is $2 \frac{1}{2}$ .

STEP 8

Evaluate option C: $8 \div 2 \frac{1}{2}$
Convert the mixed number to an improper fraction and then divide 8 by this fraction.
$C = 8 \div \frac{5}{2}$

STEP 9

When dividing by a fraction, we multiply by its reciprocal.
$C = 8 \times \frac{2}{5}$

STEP 10

Calculate the result for option C.
$C = 8 \times \frac{2}{5} = \frac{16}{5} = 3 \frac{1}{5}$
Option C represents the number of times $2 \frac{1}{2}$ fits into 8, not the fraction of 8 that is $2 \frac{1}{2}$ .

STEP 11

Evaluate option D: ? $\times 8=2 \frac{1}{2}$
This equation is asking us to find the number that, when multiplied by 8, gives $2 \frac{1}{2}$ .

STEP 12

To solve for the unknown number in option D, we need to divide $2 \frac{1}{2}$ by 8.
$D = \frac{5}{2} \div 8$

STEP 13

This is the same operation we performed in STEP_4 and STEP_5, so option D also represents the fraction of 8 that is $2 \frac{1}{2}$ .

STEP 14

Identify the incorrect option.
Since options A, B, and D all represent the fraction of 8 that is $2 \frac{1}{2}$ , the incorrect option is C, which represents the number of times $2 \frac{1}{2}$ fits into 8, not the fraction of 8 that is $2 \frac{1}{2}$ .
The expression or equation that does not answer the question "What fraction of 8 is $2 \frac{1}{2}$ ?" is:
$C: 8 \div 2 \frac{1}{2}$

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Question Find the expression that does not answer "What fraction of 8 is $2 \frac{1}{2}$ ?". A) $2 \frac{1}{2} \div 8$ B) $\frac{5}{2} \times \frac{1}{8}$ C) $8 \div 2 \frac{1}{2}$ D) $? \times 8=2 \frac{1}{2}$

Studdy Solution

STEP 1

STEP 2

Understand the question being asked. The question "What fraction of 8 is $2 \frac{1}{2}$ ?" is asking us to find the fraction that represents the part of 8 that equals $2 \frac{1}{2}$ .

STEP 3

Convert the mixed number $2 \frac{1}{2}$ to an improper fraction to make calculations easier.
$2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$

STEP 4

Evaluate option A: $2 \frac{1}{2} \div 8$
Convert the mixed number to an improper fraction and then divide by 8.
$A = \frac{5}{2} \div 8$

STEP 5

When dividing by a whole number, we can multiply by its reciprocal.
$A = \frac{5}{2} \times \frac{1}{8}$

STEP 6

Calculate the result for option A.
$A = \frac{5}{2} \times \frac{1}{8} = \frac{5}{16}$
Option A represents the fraction of 8 that is $2 \frac{1}{2}$ .

STEP 7

Evaluate option B: $\frac{5}{2} \times \frac{1}{8}$
This is the same expression we obtained in STEP_6, so it also represents the fraction of 8 that is $2 \frac{1}{2}$ .

STEP 8

Evaluate option C: $8 \div 2 \frac{1}{2}$
Convert the mixed number to an improper fraction and then divide 8 by this fraction.
$C = 8 \div \frac{5}{2}$

STEP 9

When dividing by a fraction, we multiply by its reciprocal.
$C = 8 \times \frac{2}{5}$

STEP 10

Calculate the result for option C.
$C = 8 \times \frac{2}{5} = \frac{16}{5} = 3 \frac{1}{5}$
Option C represents the number of times $2 \frac{1}{2}$ fits into 8, not the fraction of 8 that is $2 \frac{1}{2}$ .

STEP 11

Evaluate option D: ? $\times 8=2 \frac{1}{2}$
This equation is asking us to find the number that, when multiplied by 8, gives $2 \frac{1}{2}$ .

STEP 12

To solve for the unknown number in option D, we need to divide $2 \frac{1}{2}$ by 8.
$D = \frac{5}{2} \div 8$

STEP 13

This is the same operation we performed in STEP_4 and STEP_5, so option D also represents the fraction of 8 that is $2 \frac{1}{2}$ .

STEP 14

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Question Find the expression that does not answer "What fraction of 8 is 2122 \frac{1}{2}221​ ?". A) 212÷82 \frac{1}{2} \div 8221​÷8 B) 52×18\frac{5}{2} \times \frac{1}{8}25​×81​ C) 8÷2128 \div 2 \frac{1}{2}8÷221​ D) ?×8=212? \times 8=2 \frac{1}{2}?×8=221​

Studdy Solution

STEP 1

STEP 2

Understand the question being asked. The question "What fraction of 8 is 2122 \frac{1}{2}221​?" is asking us to find the fraction that represents the part of 8 that equals 2122 \frac{1}{2}221​.

STEP 3

Convert the mixed number 2122 \frac{1}{2}221​ to an improper fraction to make calculations easier.212=2+12=42+12=522 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}221​=2+21​=24​+21​=25​

STEP 4

Evaluate option A: 212÷82 \frac{1}{2} \div 8221​÷8Convert the mixed number to an improper fraction and then divide by 8.A=52÷8A = \frac{5}{2} \div 8A=25​÷8

STEP 5

When dividing by a whole number, we can multiply by its reciprocal.A=52×18A = \frac{5}{2} \times \frac{1}{8}A=25​×81​

STEP 6

Calculate the result for option A.A=52×18=516A = \frac{5}{2} \times \frac{1}{8} = \frac{5}{16}A=25​×81​=165​Option A represents the fraction of 8 that is 2122 \frac{1}{2}221​.

STEP 7

Evaluate option B: 52×18\frac{5}{2} \times \frac{1}{8}25​×81​This is the same expression we obtained in STEP_6, so it also represents the fraction of 8 that is 2122 \frac{1}{2}221​.

STEP 8

Evaluate option C: 8÷2128 \div 2 \frac{1}{2}8÷221​Convert the mixed number to an improper fraction and then divide 8 by this fraction.C=8÷52C = 8 \div \frac{5}{2}C=8÷25​

STEP 9

When dividing by a fraction, we multiply by its reciprocal.C=8×25C = 8 \times \frac{2}{5}C=8×52​

STEP 10

Calculate the result for option C.C=8×25=165=315C = 8 \times \frac{2}{5} = \frac{16}{5} = 3 \frac{1}{5}C=8×52​=516​=351​Option C represents the number of times 2122 \frac{1}{2}221​ fits into 8, not the fraction of 8 that is 2122 \frac{1}{2}221​.

STEP 11

Evaluate option D: ? ×8=212\times 8=2 \frac{1}{2}×8=221​This equation is asking us to find the number that, when multiplied by 8, gives 2122 \frac{1}{2}221​.

STEP 12

To solve for the unknown number in option D, we need to divide 2122 \frac{1}{2}221​ by 8.D=52÷8D = \frac{5}{2} \div 8D=25​÷8

STEP 13

This is the same operation we performed in STEP_4 and STEP_5, so option D also represents the fraction of 8 that is 2122 \frac{1}{2}221​.

STEP 14

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Question Find the expression that does not answer "What fraction of 8 is $2 \frac{1}{2}$ ?". A) $2 \frac{1}{2} \div 8$ B) $\frac{5}{2} \times \frac{1}{8}$ C) $8 \div 2 \frac{1}{2}$ D) $? \times 8=2 \frac{1}{2}$

Understand the question being asked. The question "What fraction of 8 is $2 \frac{1}{2}$ ?" is asking us to find the fraction that represents the part of 8 that equals $2 \frac{1}{2}$ .

Convert the mixed number $2 \frac{1}{2}$ to an improper fraction to make calculations easier.
$2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$

Evaluate option A: $2 \frac{1}{2} \div 8$
Convert the mixed number to an improper fraction and then divide by 8.
$A = \frac{5}{2} \div 8$

When dividing by a whole number, we can multiply by its reciprocal.
$A = \frac{5}{2} \times \frac{1}{8}$

Calculate the result for option A.
$A = \frac{5}{2} \times \frac{1}{8} = \frac{5}{16}$
Option A represents the fraction of 8 that is $2 \frac{1}{2}$ .

Evaluate option B: $\frac{5}{2} \times \frac{1}{8}$
This is the same expression we obtained in STEP_6, so it also represents the fraction of 8 that is $2 \frac{1}{2}$ .

Evaluate option C: $8 \div 2 \frac{1}{2}$
Convert the mixed number to an improper fraction and then divide 8 by this fraction.
$C = 8 \div \frac{5}{2}$

When dividing by a fraction, we multiply by its reciprocal.
$C = 8 \times \frac{2}{5}$

Calculate the result for option C.
$C = 8 \times \frac{2}{5} = \frac{16}{5} = 3 \frac{1}{5}$
Option C represents the number of times $2 \frac{1}{2}$ fits into 8, not the fraction of 8 that is $2 \frac{1}{2}$ .

Evaluate option D: ? $\times 8=2 \frac{1}{2}$
This equation is asking us to find the number that, when multiplied by 8, gives $2 \frac{1}{2}$ .

To solve for the unknown number in option D, we need to divide $2 \frac{1}{2}$ by 8.
$D = \frac{5}{2} \div 8$

This is the same operation we performed in STEP_4 and STEP_5, so option D also represents the fraction of 8 that is $2 \frac{1}{2}$ .