Question

Which statement about determining the quotient 1/8÷2 is true? Responses Because 1/4×2=18, 1/8 divided by 2 is ​1/4​. Because , 1 fourth times 2 equals 1 over 8, , , 1 over 8, divided by 2 is , ​, 1 fourth, ​, . Because 2/16×2=1/8, 1/8 divided by 2 is ​2/16​. Because , 2 over 16 end fraction times 2 equals 1 over 8, , , 1 over 8, divided by 2 is , ​, 2 over 16, ​, . ​1/16Because 1/2×2=18, 18 divided by 2 is ​12​. Because , 1 half times 2 equals 1 over 8, , , 1 over 8, divided by 2 is , ​, 1 half, ​, . Because 1/16×2=18, 18 divided by 2 is

Answer 1

None of the student-provided solutions are correct. The proper method is to multiply the fraction 1/8 by the reciprocal of 2, which results in the quotient of 1/16.

Dividing a fraction by a whole number involves multiplying the fraction by the reciprocal of the number. In this case, to calculate
`\( (1)/(8) / 2 \)`, you multiply
`\( (1)/(8) \)` by the reciprocal of 2, which is
`\( (1)/(2) \)`. The calculation is done as follows:

`\[ (1)/(8) / 2 = (1)/(8) * (1)/(2) \]`

When you multiply the numerators (1 × 1) and the denominators (8 × 2), you get:

`\[ (1)/(8) * (1)/(2) = (1 * 1)/(8 * 2) = (1)/(16) \]`

Therefore,
`\( (1)/(8) / 2 = (1)/(16) \)`. This means that if you have one-eighth and you divide it by 2, you end up with one-sixteenth. The quotient,
`\( (1)/(16) \)`, is the result of this division.

It's important to note that dividing by 2 is equivalent to multiplying by
`\( (1)/(2) \)`, and this process is a fundamental concept in fraction arithmetic. The simplified fraction
`\( (1)/(16) \)` is the final result of the division.