Representation of Rational Numbers

Henry used the table to describe some numbers. What correction does he need to make in the table?

• 6 should not be an integer

• –2/3 should also be an integer.

• –5 should also be a rational number.

• –5 should also be a whole number

Does the graphic organizer correctly group the numbers?

• Yes

• No

Explain the error

• The picture is labeled wrong.

• 3.4 isn't a rational number.

• -2 isn't a whole number and -1.2 isn't an integer.

• There are no errors.

How would 5/9 be classified?

• rational 

• whole and integer

• only integer

• only whole

Look at this diagram. What number would be placed where the red x is?

• -5

• 0

• 4.8

• 9

Which number on the number line is represented by 'P'?

• -1

• 1

• -1/6

• -1/3

Answer explanation

The distance on number line between 0 and -2 is divided into six equal parts hence each part must be representing -2/6 = -1/3. The denominator tells us the number of equal parts into which a unit is divided. Here, we can say that each unit on the number line is divided into three equal parts. P is the first part to the left of zero hence P must be representing number -1/3.

Tags

CCSS.6.NS.C.6C

Two rational numbers 3/2 and 9/6 are represented by letters E and F respectively. Which of the following is true with respect to E and F?

• E and F are located at the same place on the number line.

• E is located towards the right of F on the number line.

• E is located towards the left of F on the number line.

• E and F are located towards the left of 1 on the number line.

Answer explanation

3/2 and 9/6 are equivalent i.e. they have equal value, because 3/2 × 3/3 = 9/6. Also, the standard form of 9/6 is 3/2. The numbers with equal value are represented at the same position on the numberline. Hence option 3 is the right answer. Alternatively, If we plot 3/2 and 9/6 on number line we find that they are located at same position on the number line

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B

On a number line positive rational numbers lie ___

• To the left of zero

• to the right of zero

• between 0 and 1

• between 0 and -1

Answer explanation

Positive rational numbers are greater than 0. Hence, they lie to the right of zero on the number line. Negative rational numbers are smaller than 0. Hence, they lie to the left of zero on the number line. Hence option 2 is the correct answer.

Tags

CCSS.6.NS.C.6C

Which of the following is the correct representation of the rational number 5/4 on the number line?

• 
• 
• 
• 

Answer explanation

We see that each unit is divided into four equal parts. So, each part represents 1 out of 4 equal parts i.e. ¼. To represent 5/4 we should start from 0 and count 5 parts of ¼ each towards right. This gives us the result shown in option 3. Hence option 3 gives the correct representation of 5/4

Tags

CCSS.6.NS.C.6C

Which of the following statements is/are true? Statement A: On a number line 7/3 is located in the left of 2 Statement B: On a number line -7/3 is located in the left of -2

• Statement A only

• Statement B only

• Statements A and B

• Neither Statement A nor Statement B

Answer explanation

7/3 = 2 ⅓. Since 7/3 > 0, it will be plotted on the right side of 0. So, 7/3 can be plotted on the number line by dividing each unit into three equal parts and selecting the 7th part which will lie in the right of 2. As we can see 7/3 is in the right of 2 on the number line. Hence statement A is false. -7/3 = -2 ⅓. Since -7/3 < 0, it will be plotted on the left side of 0. So, -7/3 can be plotted on the number line by dividing each unit into three equal parts. Starting from 0 and moving towards left, select the 7th part which will lie in the left of -2. As we can see -7/3 is in the left of -2 on the number line. Hence statement B is true. Thus option 2 is the right answer for the given question.

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B