Envision Math 2.0: Grade 6, Volume 1
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2. Represent Rational Numbers on the Number Line
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Exercise 21 Page 75

The integer portion of a mixed number tells us how many whole units we will move away from 0 on the number line. The fractional portion expresses how much of the next whole unit will be included.

Practice makes perfect

We want to plot the numbers on a number line.

We can see that the unit is divided into 10 equal parts. Let's rewrite each number into the form of a mixed number that has the denominator equal to 10. Let's start with - 5 12.
- 5 12
- (5 + 1/2)
- (5 +1* 5/2* 5)
- (5 + 5/10)
- 5 510
Now, let's rewrite the decimal number - 6.3 as a mixed number.
- 6.3
- (6 + 0.3)
- (6 + 10* 0.3/10)
- (6 + 3/10)
- 6 310
We repeat the process for the rest of the numbers.
The Number The Mixed Number
A - 5 12 - 5 510
B - 6.3 - 6 310
C - 5.8 - 5 810
D - 6 710 - 6 710
E - 4.9 - 4 910
F - 6 910 - 6 910

Now, all numbers are mixed numbers. Let's plot the first number on the number line. A mixed number is an integer and a fraction combined. The integer part tells us how many whole units we will move away from 0 on the number line. The fractional part expresses how much of the next whole unit will be included. - 5 510 Since the given number is negative, we will first move to the left 5 whole units and 510 of a unit further. We can mark this point as A.

Let's consider the next number. - 6 310 This number is also negative. This means, we move to the left 6 whole units and 310 of a unit further. We can mark this point as B.

Now, we do the same for the rest of the numbers.