Transcript Warm-up Activity

Today’s Lesson
Ordering
Rational and
Irrational
Numbers
Warm-up Activity
Let’s warm up today
by practicing fractions
and mixed-number
equivalents.
1
4
I am baking a pie that requires 2
1
cups of flour, 4 3 cups of
1
blueberries, and 3 3 cups of sugar.
Convert each of the fractions
below into an equivalent fraction
using the denominator of 24.
2
1
4
4
1
3
3
1
3
Check your answers.
2
1
4
4
1
3
3
1
3
2
6
24
4
8
24
3
8
24
Now, convert each mixed number
into an improper fraction.
2
6
24
54
24
4
8
24
104
24
3
8
24
80
24
Finally, convert your improper
fraction into a decimal.
54
24
2.25
104
24
4.33
80
24
3.33
Note, you will arrive at the
same decimal whether you
start from a mixed number or
improper fraction.
Whole-Class Skills Lesson
Today, we will learn
ordering rational and
irrational numbers.
Look at the following fractions.
Which one is larger?
56
7
or
54
6
We can convert each of these fractions
into whole numbers to compare.
56
7
=8
54
6
=9
Therefore,
The larger number
56
7
<
54
6
.
Look at the following fractions.
Which one is larger?
27
4
or
39
6
We can find this answer multiple
ways.
Let’s first convert the fractions
to mixed numbers.
27
4
39
6
=6
1
4
=6
3
6
Can also be written as 6 12
The larger number
Next, let’s find the answer through
cross-multiplying.
27
4
39
6
Multiply the numerator by
the opposite denominator.
27
4
39
6
27 x 6 = 162
39 x 4 = 156
The larger number
Next, let’s find the answer through
least common denominators.
We can use the answers we
previously found from
turning the fractions into
mixed numbers.
The least common denominator is 4.
6
3
4
6
1
2
=
=
6
3
4
6
2
4
The larger number
Finally, let’s compare using
decimals.
6
3
4
=
6.75
6
1
2
=
6.50
The larger number
Through our various ways to
compare the fractions, it has been
27
39
proven that 4 < 6 .
Can you order the following
fractions from least to greatest
using the methods we just learned?
15
4
20
5
25
8
Check your answers.
25
8
<
15
4
<
20
5
Can you order the following
fractions from least to greatest
using the methods we just learned?
29
12
105
36
18
8
32
12
11
4
39
18
Check your answers.
39
18
<
18
8
<
29
12
<
32
12
<
11
4
<
105
36