Transcript Slide 1

Comparing and Ordering
2-11 Rational Numbers
Warm Up
Problem of the Day
Lesson Presentation
Course 2
Comparing and Ordering
2-11 Rational Numbers
Warm Up
Write each mixed number as an
improper fraction.
1. 1 3
7
4
2. 2 7
8
23
8
3. 1 5
6
11
6
1
4. 812
97
12
4
Course 2
Comparing and Ordering
2-11 Rational Numbers
Learn to compare and order fractions and
decimals.
Course 2
Comparing and Ordering
2-11 Rational
Insert Lesson
Title Here
Numbers
Vocabulary
rational number
Course 2
Comparing and Ordering
2-11 Rational Numbers
7
2
Which is greater, 9 or 9 ?
When two fractions have the same
denominator, just compare the numerators.
7 > 2 because 7 > 2.
9
9
=7
9
2
=9
Course 2
Comparing and Ordering
2-11 Rational Numbers
Additional Example 1A: Comparing Fractions
Compare the fractions. Write < or >.
7
9
5
8
The LCM of the denominators 9 and 8 is 72.
7 =7·8
56
=
9·8
9
72
5 =5·9
45
=
8·9
8
72
56
45 , and so 7
5.
>
>
72
72
9
8
Course 2
Write equivalent
fractions with 72 as
the denominator.
Compare the
numbers.
Comparing and Ordering
2-11 Rational Numbers
Additional Example 1B: Comparing Fractions
Compare the fractions. Write < or >.
– 2
5
– 3
7
Cross Multiply
3
2
= – 7
–
5
-14
-15
-14 > -15
So -2/5 > -3/7
Course 2
Cross Multiply the denominator
Of the first fraction by the
Numerator of the second fraction
Second, Cross multiply the
Denominator of the second fraction
By the numerator of the first fraction
Comparing and Ordering
2-11 Rational Numbers
Check It Out: Example 1A
Compare the fractions. Write < or >.
5
6
7
8
5 7
6.< 8
Course 2
Comparing and Ordering
2-11 Rational Numbers
Check It Out: Example 1B
Compare the fractions. Write < or >.
5
– 6
–
8
7
Both fractions can be written with a denominator of 56.
–6 · 7
–42
6
=
–
=
8
8·7
56
–40
5 = –5 · 8
– 7
=
7·8
56
Write equivalent fractions
with common denominators.
Put the negative signs
in the numerators.
5
– 42 < – 40 , and so – 6 < –
.
8
7
56
56
Course 2
Comparing and Ordering
2-11 Rational Numbers
To compare decimals, line up
the decimal points and compare
digits from left to right until you
find the place where the digits
are different.
Course 2
Comparing and Ordering
2-11 Rational Numbers
Additional Example 2A: Comparing Decimals
Compare the decimals. Write < or >.
0.427
0.427
7
0.425
5
0.425
Line up the decimal points.
The tenths and hundredths are
the same.
Compare the thousandths:
7 > 5.
Since 0.007 > 0.005, 0.427 > 0.425.
Course 2
Comparing and Ordering
2-11 Rational Numbers
Additional Example 2B: Comparing Decimals
Compare the decimals. Write < or >.
0.73
0.734
_
3
0.73 = 0.733…
0.734
4
Line up the decimal points.
The tenths and hundredths are
the same.
Compare the thousandths:
3 < 4.
_
Since 0.03 is < 0.04, 0.73 < 0.734.
Course 2
Comparing and Ordering
2-11 Rational Numbers
Check It Out: Example 2A
Compare the decimals. Write < or >.
0.535
0.535
5
0.538
8
0.538
Line up the decimal points.
The tenths and hundredths are
the same.
Compare the thousandths:
5 < 8.
Since 0.005 < 0.008, 0.535 < 0.538.
Course 2
Comparing and Ordering
2-11 Rational Numbers
Check It Out: Example 2B
Compare the decimals. Write < or >.
0.3
0.334
__
Line up the decimal points.
3
0.33 = 0.3333…
The tenths and hundredths are
the same.
0.334
4
Compare the thousandths:
3 < 4.
__
Since 0.003 is < 0.004, 0.33 < 0.334.
Course 2
Comparing and Ordering
2-11 Rational Numbers
A rational number is a number
that can be written as a fraction
with integers for its numerator and
denominator. When rational
numbers are written in a variety of
forms, you can compare the
numbers by writing them all in the
same form.
Course 2
Comparing and Ordering
2-11 Rational Numbers
Remember!
The values on a number line increase as you
move from left to right.
Course 2
Comparing and Ordering
2-11 Rational Numbers
Additional Example 3: Ordering Fractions and
Decimals
Order 4 , 0.93, and 0.9 from least to greatest.
5
Write as decimals with the same number of places.
4 = 0.80
0.93 = 0.93
0.9 = 0.90
5
Graph the numbers on a number line.
0.93
0
0.2
0.4
0.6
0.8
1
0.80 < 0.90 < 0.93 Compare the decimals in order.
From least to greatest, the numbers are 4 , 0.9, 0.93.
5
Course 2
Comparing and Ordering
2-11 Rational Numbers
Check It Out: Example 3
Order 3 , 0.84, and 0.7 from least to greatest.
5
Write as decimals with the same number of places.
3 = 0.60
5
0.84 = 0.84
0.7 = 0.70
Graph the numbers on a number line.
0.84
0
0.2
0.4
0.6
0.8
1
0.60 < 0.70 < 0.84 Compare the decimals in order.
From least to greatest, the numbers are 3 , 0.7, 0.84.
5
Course 2
Comparing and Ordering
2-11 Rational
Insert Lesson
Title Here
Numbers
Lesson Practice
Compare the fractions. Write > or <.
3 or 4
>
<
2. 5 or 2
1.
8
10
3
7
Compare the decimals. Write < or >.
3. 0.32 and 0.312
>
4. Order 5
6 , 0.8, 0.826 from least to greatest.
0.8, 0.826, 5
6
Course 2