Solved on Feb 04, 2024

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) $? \times 8=2 \frac{1}{2}$

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:
$C: 8 \div 2 \frac{1}{2}$

Was this helpful?

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) $? \times 8=2 \frac{1}{2}$

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

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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​

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

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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 $2 \frac{1}{2}$ .