Comparing and Ordering Rational Numbers

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Write each mixed number as an improper
fraction. 1. 1 3. 1
23 8
7 4
3 4
7 8
2. 2
5 6
1 12
11 6
97 12
4. 8
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Problem of the Day Hot dogs are sold in packs of
6. Buns are sold in bags of 8. What is the least
number of hot dog packages and the least number
of bun packages you would need to buy in order to
have the same number of hot dogs and buns?
4 packages of hot dogs and 3 packages of buns
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Learn to compare and order fractions and
decimals.
5
7 9
2 9
Which is greater, or ?
When two fractions have the same denominator,
just compare the numerators.
7 9
2 9
gt
because 7 gt 2.
7 9

2 9

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Additional Example 1A Comparing Fractions
Compare the fractions. Write lt or gt.
A.
Both fractions can be written with a denominator
of 72.
Write as fractions with common denominators.




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Additional Example 1B Comparing Fractions
Compare the fractions. Write lt or gt.
B.


Both fractions can be written with a denominator
of 35.
Write as fractions with common denominators. Put
the negative signs in the numerators.
2 7 5 7
14 35



3 5 7 5
15 35



3 7
14 35
15 35


gt

, and so gt .
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Try This Example 1A
Compare the fractions. Write lt or gt.
A.
Both fractions can be written with a denominator
of 48.
Write as fractions with common denominators.




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Try This Example 1B
Compare the fractions. Write lt or gt.
B.


Both fractions can be written with a denominator
of 56.
Write as fractions with common denominators. Put
the negative signs in the numerators.
6 7 8 7
42 56



5 8 7 8
40 56



5 7
42 56
40 56


lt

, and so lt .
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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.
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Additional Example 2 Comparing Decimals
Compare the decimals. Write lt or gt.
0.427
0.425
0.427
Line up the decimal points.
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The tenths and hundredths are the same.
0.425
5
Compare the thousandths
7 gt 5.
0.427 gt 0.425
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Try This Example 2
Compare the decimals. Write lt or gt.
0.535
0.538
0.535
Line up the decimal points.
5
The tenths and hundredths are the same.
0.538
8
Compare the thousandths
5 lt 8.
0.535 lt 0.538
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Additional Example 3 Ordering Fractions and
Decimals
Order the numbers from least to greatest.
4 5
0.93, and 0.9
,
Write as decimals with the same number of places.
4 5
0.80
0.93 0.93
0.9 0.90
Graph the numbers on a number line.
0.93
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Additional Example 3 Continued
Order the numbers from least to greatest.
4 5
0.93, and 0.9
,
The values on a number line increase as we move
from left to right.
0.80 lt 0.90 lt 0.93
Place the decimals in order.
4 5
, 0.9, 0.93
0.93
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Try This Example 3
Order the numbers from least to greatest.
3 5
0.84, and 0.7
,
Write as decimals with the same number of places.
3 5
0.60
0.84 0.84
0.7 0.70
Graph the numbers on a number line.
0.84
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Try This Example 3 Continued
Order the numbers from least to greatest.
3 5
0.84, and 0.7
,
The values on a number line increase as we move
from left to right.
0.60 lt 0.70 lt 0.84
Place the decimals in order.
3 5
, 0.7, 0.84
0.84
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Insert Lesson Title Here
Lesson Quiz Part 1
Choose the greater number. 1. Place the
numbers in order from least to greatest 3. 0.3,
0.32, 0.312
4 10
3 7
5 8
2 3
or
2.
or
0.3, 0.312, 0.32
5 6
4.
, 0.8, 0.826
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Insert Lesson Title Here
Lesson Quiz Part 2
5. Danas cross-country team is getting ready for
a big meet. On Monday they ran 3.7 miles, on
Tuesday they ran 3 miles, and on Wednesday
they ran miles. On which day did they run the
greatest distance?
3 8
11 4
Monday