Section A Section A Checkpoint

Problem 1

Label the point on each number line with a fraction it represents.

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Solution

$\frac78$ . There are 8 equal parts in 1, and the point is on the 7th tick mark from 0 to show 7 parts.
$\frac85$ . There are 5 equal parts in each whole, and the point is on the 8th tick mark from 0 to show 8 parts.

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Sample Response

$\frac78$ . There are 8 equal parts in 1, and the point is on the 7th tick mark from 0 to show 7 parts.
$\frac85$ . There are 5 equal parts in each whole, and the point is on the 8th tick mark from 0 to show 8 parts.

Problem 2

Is $\frac{7}{12}$ greater than or less than $\frac{1}{2}$ ? Explain your reasoning. Use the number line if it is helpful.

Number Line. From 0 to 1, evenly spaced by twelfths.

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Solution

$\frac{7}{12}$ is greater than $\frac{1}{2}$ . Sample responses: $\frac{7}{12}$ is the 7th tick mark from 0 on this number line, and it’s more than halfway to 1. Half of 12 is 6 and $\frac{1}{2}$ is $\frac{6}{12}$ , so $\frac{7}{12}$ is greater.

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Sample Response

Problem 3

Explain why $\frac{4}{12}$ is equivalent to $\frac{1}{3}$ . Use the number line if it is helpful.

Number Line. From 0 to 1, evenly spaced by thirds.

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Solution

Sample response: If I divide each third into 4 equal pieces, each of those pieces is 1 twelfth, and $\frac{1}{3}$ is on the 4th tick mark from 0, showing it is equivalent to 4 twelfths.

Number Line. From 0 to 1, evenly spaced by twelfths. One third is labeled.

Show Sample Response

Sample Response

Sample response: If I divide each third into 4 equal pieces, each of those pieces is 1 twelfth, and $\frac{1}{3}$ is on the 4th tick mark from 0, showing it is equivalent to 4 twelfths.