Question

Which expression does the model represent?

A number line going from 0 to 1 in increments of one-eighths.
StartFraction 7 Over 8 EndFraction divided by StartFraction 1 Over 8 EndFraction
StartFraction 1 Over 8 EndFraction divided by StartFraction 7 Over 8 EndFraction
StartFraction 1 Over 8 EndFraction divided by 7
7 divided by StartFraction 7 Over 8 EndFraction

Answer 1

The expression that the model represents is
`\((7)/(8) / (1)/(8)\)`, which amounts to 7 when we multiply the fraction
`\((7)/(8)\)` by the reciprocal of
`\((1)/(8)\)`, demonstrating how multiplication and division of fractions are related.

Step-by-step explanation:

The student's question pertains to interpreting a fraction operation given a number line divided into one-eighth increments.

The correct expression represented by a number line going from 0 to 1 in increments of one-eighth is Start-Fraction 7 Over 8 End-Fraction divided by Start-Fraction 1 Over 8 End-Fraction.

This is because dividing a fraction by another fraction is the same as multiplying the first fraction by the reciprocal of the second. In this case, multiplying
`\((7)/(8)\)` by the reciprocal of
`\((1)/(8)\)`, which is 8, gives us 7.

Hence, the operation results in 7 equal parts, each of which is
`\((1)/(8)\)` of the whole, filling the entire number line up to 1.