Grade 6

End-of-Unit Assessment

Unit 7 Assessment - Rational Numbers

Points J, K, L, and M are plotted on the number line shown below.

A number line from negative 2 to 1. Points labeled J and K are between negative 2 and negative 1. Point L is at negative 1. Point M is between negative 1 and 0.

What point represents the location of the value $-1\frac{3}{4}$ ?

A. point J
B. point K
C. point L
D. point M

Which expression represents the opposite of the number $-2\frac{1}{2}$ ?

A. $-(2\frac{1}{2})$
B. $-(-2\frac{1}{2})$
C. $-2(\frac{1}{2})$
D. $2(-\frac{1}{2})$

The lowest recorded temperatures for each of two states are listed below:

$-27°F$
$-35°F$

Write a statement using $<$ , $>$ , $\leq$ , or $\geq$ to compare the recorded temperatures of the two states.

Points W, X, Y, and Z are plotted on the coordinate plane shown below.

A four-quadrant coordinate plane with axes from negative 3 to 3. Point W is in Quadrant II, Point X is in Quadrant III, Point Y is in Quadrant IV, and Point Z is in Quadrant I.

Which point is located at $(-2, 3)$ ?

A. point W
B. point X
C. point Y
D. point Z

A coordinate plane can be used to show the distance, in units, between two locations. The location of Jack's house and a store are listed below.

Jack's house is located at $(-7, -8)$ .
The store is located at $(-7, 4)$ .

What is the distance, in units, between Jack's house and the store?

A. 4
B. 8
C. 12
D. 14

Paige uses the coordinate plane to represent the locations of vegetable patches in her garden. Broccoli is at $(-2, -3)$ . Cabbage is at $(5, -3)$ .

What is the shortest distance, in feet, from the cabbage patch to the broccoli patch? Be sure to include the coordinates.

A student claims that 4 is the greatest common factor of 24 and 40, because the two numbers are both multiples of 4. Is the student's claim correct?

Explain how you determined your answer.

Answer Key

Solution:

$-1\frac{3}{4}$ is between $-2$ and $-1$ , located $\frac{3}{4}$ of the way from $-1$ toward $-2$ . This places it closer to $-2$ , which is point J.

Solution:

The opposite of $-2\frac{1}{2}$ is $+2\frac{1}{2}$ . The expression $-(-2\frac{1}{2})$ applies negation to $-2\frac{1}{2}$ , yielding $+2\frac{1}{2}$ .

$-27°F > -35°F$ (or equivalently $-35°F < -27°F$ )

Solution:

On the number line, $-27$ is to the right of $-35$ (closer to zero), so $-27 > -35$ . In context: $-27°F$ is the warmer temperature.

Solution:

$(-2, 3)$ means $x = -2$ (2 units left of origin) and $y = 3$ (3 units up). This is Quadrant II. Point W is at $(-2, 3)$ .

Solution:

Both points share $x = -7$ , so the distance is vertical: $|4 - (-8)| = |4 + 8| = 12$ .

7 feet

Solution:

Both points share $y = -3$ , so the distance is horizontal: $|5 - (-2)| = |5 + 2| = 7$ .

No. The GCF of 24 and 40 is 8, not 4.

Solution:

While 4 is a common factor of 24 and 40, both numbers are also divisible by 8: $24 \div 8 = 3$ and $40 \div 8 = 5$ . Since $8 > 4$ and 8 is a common factor, 4 is not the greatest common factor. The GCF is 8.