Transcript Fractions on the Number Line

Comparing &
Ordering Rational
Numbers
MCC6.NS.7.a
MCC6.NS.7.b
MCC6.NS.7.d
Comparing Rational
Numbers
To compare rational numbers, we use the
symbols:
> (greater than)
< (less than)
= (equal to)
> (greater than or equal to)
< (less than or equal to)
Using the Number Line
The expression a > b means
a is to the right of b on the number line.
b
a
The expression a < b means
a is the left of b on the number line.
a
b
Using the Number Line
The expression -1 > -3 means
-1 is to the right of -3 on the number line.
-3 -1
The expression -3 < -1 means
-3 is the left of -1 on the number line.
-3 -1
Common Misconception
with Comparing Numbers
Some students think the greatest number
is the number closest to zero.
NOPE!  Because that rule is not always true.
-5
-2
0
10
-2 is closer to 0 than -5 and is greater than -5… but
-2 is closer to 0 than 10 but is less than 10.
Example 1:
Order the following numbers from greatest to least.
Use the number line to justify the order.
7, -3, 5, -5, 10, -10, 4, 0
Example 2:
Which symbol makes this sentence true?
Use >, <, or =
Step 1:
Step 2:
Step 3:
Step 4:
3½
3¼
Compare the whole-number parts.
3=3
Find a common denominator for the fraction parts.
2: 2, 4, 6
4: 4, 8, 12
Rewrite the fractions with a common denominator.
𝟏 𝟐
=
𝟐 𝟒
Compare the fractions.
𝟐 𝟏
>
𝟒 𝟒
Example 3:
Which symbol makes this sentence true?
Use >, <, or =
15.36
15.391
Step 1: Align the numbers on the decimal point.
Compare the whole numbers first.
15 = 15
15.36
Step 2: Compare the tenths place.
15.391
.3 = .3
Step 3: Compare the hundredths place.
._9 > ._6
Stop when one place value is larger than the other.
Comparing
Rational Numbers
Rational numbers are written in different forms.
1. Change them into the same form.
2. Use the number line to help compare the numbers.
1.5,
𝟏
1 ,
𝟐
-.5, 50%
1, 1.5, -1.5, .5
-2 -1
0
1 2
Converting Fractions
into Decimals
To convert a fraction into a decimal,
divide the numerator by the denominator.
1
2
0.5
2| 1.0
-10
0
Converting Fractions
into Decimals
Let’s practice!
3
4
1
5
Converting Mixed
Numbers into Decimals
Temporarily ignore the whole number.
Convert the fraction into a decimal.
Place the whole number in front of the decimal.
3
2
4
2
1
-3
5
-3.2
Review
A.
1
4
.25
B.
2
5
.4
C.
1
2
8
2.125
D.
1
−
2
-.5
Fractions &
Mixed Numbers
on the
Number Line
Remember when...
You created boxes to represent fractions?
1
3
First, you drew a rectangular box.
Then you used the denominator to split the box.
Then you used the numerator to shade the box.
Do You Remember Now?
3
4
First, you drew a rectangular box.
Then you used the denominator to split the box.
Then you used the numerator to shade the box.
Let’s Take It to the Next
Level!
1
Place on the number line.
3
Do the same thing as before!
Just put the box on the line!
Where you stop is
First, draw a box from 0 to 1.
where the fraction is
Then use the denominator to split the box.
on the number line!
Then use the numerator to shade the box.
Let’s Try It Again!
3
Place on the number line.
4
Do the same thing as before!
Just putyou
thestop
box on
Where
is the line!
First,the
draw
a box from
where
fraction
is 0 to 1.
Then use the denominator to split the box.
on the number line!
Then use the numerator to shade the box.
Remember…
ALWAYS start shading at zero!
What About Negative
Fractions?
1
Place - on the number line.
3
Do the same thing as before!
Just put the box on the line!
Where
youdraw
stop
is from 0 to -1.
This time,
a box
where
the
is to split the box.
Then use
thefraction
denominator
on
the
line!to shade the box.
Then
usenumber
the numerator
Remember…
ALWAYS start shading at zero!
Let’s Try Another Negative
Fraction!
3
Place − on the number line.
4
Do the same thing as before!
Just put the
box on
the
line!is
Where
you
stop
This time, where
draw a box
0 to -1. is
thefrom
fraction
Then use the denominator to split the box.
on the number line!
Then use the numerator to shade the box.
Let’s Take It to the Next
Level!
1
Place1 on the number line.
3
Start at the whole number
on the number line.
Put the box on the line between
the whole numberWhere
& the next
youinteger.
stop is
First, draw a box from 1 to 2.
wheretothe
is
Then use the denominator
split fraction
the box.
Then use the numerator
to shade
the box.line!
on the
number
Let’s Try It Again!
3
Place on the number line.
4
Do the same thing as before!
Just putyou
thestop
box on
Where
is the line!
First,the
draw
a box from
where
fraction
is 0 to 1.
Then use the denominator to split the box.
on the number line!
Then use the numerator to shade the box.
Remember…
ALWAYS start shading at zero!
What About
Mixed Numbers?
1
Place -3 on the number line.
3
Do the same thing as before!
Just put the box on the line!
Where
youdraw
stop
is from -3 to -4.
This time,
a box
where
the
is to split the box.
Then use
thefraction
denominator
on
the
line!to shade the box.
Then
usenumber
the numerator
Remember…
ALWAYS start shading at zero!
But…
What If I Have to
Name the Fraction?
Name That Fraction!
What rational number does A represent?
Just use the lines that are there!
Draw the box from 0 to 1.
Count
how manymany
spaces are in the box for the
However
denominator.
spaces
you
shade
is
Then starting at 0, shade each space until you reach the
the numerator!
letter for the numerator.
Remember…
ALWAYS start shading at zero!
Name That Fraction!
What rational number does A represent?
Just use the lines that are there!
Draw the box from 0 to 1.
Count
how manymany
spaces are in the box for the
However
denominator.
spaces
you
shaded
Then starting at 0, shade each space until you reach the
is the numerator!
letter for the numerator.
Remember…
ALWAYS start shading at zero!
Name That Negative
Fraction!
What rational number does A represent?
Just use the lines that are there!
Draw the box from 0 to -1.
Count
how manymany
spaces are in the box for the
However
denominator.
spaces
you
shade
is
Then starting at 0, shade each space until you reach the
the numerator!
letter for the numerator.
Remember…
ALWAYS start shading at zero!
Try Again!
What rational number does A represent?
Just use the lines that are there!
Draw the box from 0 to -1.
Count
how manymany
spaces are in the box for the
However
denominator.
spaces
you
shaded
Then starting at 0, shade each space until you reach the
is the numerator!
letter for the numerator.