1. Go over Homework

2. Write each mixed number as an improper fraction.
Warm Up
Write each mixed number as an improper fraction.
1. 1
3. 1 3 4 7 4 7 8 23 8
2. 2 5 6 11 6 1 12 97 12
4. 8

3. 2-7 Rational Numbers
Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

4. A fraction that does not have a zero on the bottom
Rational Number
a number that can be written as a fraction or quotient of two integers with a nonzero denominator.
A fraction that does not have a zero on the bottom
A terminating decimal
2 5
A repeating decimal
0.425
0.73

5. 7 9 2 9
Which is greater, or ?
To compare fractions with the same
denominator, just compare the numerators. 7 9 = 7 9 2 9
>
because 7 > 2. 2 9 =

6. Example 1A: Comparing Fractions
Compare the fractions. Write < or >. 7 9 5 8
The LCM of the denominators 9 and 8 is 72. 7 9
7  8
9  8 56 72 =
Write equivalent fractions with 72 as the denominator. = 5 8
5  9
8  9 45 72 = =
Compare the numerators. 56 72
> 45
, and so 7 9
> 5 8

7. Example 1B: Comparing Fractions
Compare the fractions. Write < or >. 2 5 3 7 – –
Both fractions can be written with a denominator of 35. 2 5
–2  7
5  7
–14 35
Write equivalent fractions with 35 as the denominator.
Put the negative signs
in the numerators. – = = 3 7
–3  5
7  5
–15 35 – = = 14 35 15 35 2 5 3 7 –
> –
, and so – > –

8. A fraction less than 0, such as - , can be
written as - , , or .
Helpful Hint!
2 5
-2 5

9. Check It Out! Example 2A
Compare the fractions. Write < or >. 5 6 7 8
The LCM of the denominators 6 and 8 is 24. 5 6 20 24
Write equivalent fractions with 48 as the denominator.
5  4
6  4 = = 7 8
7  3
8  3 21 24 = =
Compare the numerators. 20 24
< 21
, and so 5 6
< 7 8

10. Check It Out! Example 2B
Compare the fractions. Write < or >. 6 8 5 7 – –
Both fractions can be written with a denominator of 56. 6 8
–6  7
8  7
–42 56
Write equivalent fractions with 56 as the denominator.
Put the negative signs
in the numerators. – = = 5 7
–5  8
7  8
–40 56 – = = 42 56 40 56 6 8 5 7 –
< –
, and so – < –

11. Comparing Decimals
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.

12. Example 3A: Comparing Decimals
Compare the decimals. Write < or >.
0.427
0.425
0.427 7
Line up the decimal points.
The tenths and hundredths are
the same.
0.425 5
Compare the thousandths:
7 > 5.
Since > 0.005, >

13. Additional Example 3B: Comparing Decimals
Compare the decimals. Write < or >.
0.73
0.734
0.73 = _
0.733… 3
0.73 is a repeating decimal.
Line up the decimal points.
0.734 4
The tenths and hundredths are
the same.
Compare the thousandths:
3 < 4.
Since is < 0.004, 0.73 <

14. Check It Out! Example 4A
Compare the decimals. Write < or >.
0.535
0.538
0.535 5
Line up the decimal points.
The tenths and hundredths are
the same.
0.538 8
Compare the thousandths:
5 < 8.
Since < 0.008, <

15. Check It Out! Example 4B
Compare the decimals. Write < or >.
0.3
0.334
0.3 =
0.3333… 3
0.3 is a repeating decimal.
Line up the decimal points.
The tenths and hundredths are
the same.
0.334 4
Compare the thousandths:
3 < 4.
Since is < 0.004, 0.3 <

16. The values on a number line increase as you move from left to right.
Remember!

17. Or treat like money if possible: 80 cents, 90 cents, 93 cents
Additional Example 5: Ordering Fractions and Decimals 4 5
Order ,
0.93, and 0.9 from least to greatest.
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
0.80 < 0.90 < 0.93
Compare the decimals. 4 5
From least to greatest, the numbers are , 0.9, 0.93.
Or treat like money if possible: 80 cents, 90 cents, 93 cents

18. Or treat like money if possible: 60 cents, 70 cents, 84 cents
Check It Out! Example 6 3 5
Order , 0.84, and 0.7 from least to greatest.
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
0.60 < 0.70 < 0.84
Compare the decimals. 3 5
From least to greatest, the numbers are , 0.7, 0.84.
Or treat like money if possible: 60 cents, 70 cents, 84 cents

19. Homework
Pg 104 #2-36 evens only

20. Choose the greater number. 1.
Lesson Quiz
Choose the greater number. 1.
Place the numbers in order from least to greatest
3. 0.3, 0.32, 0.312 3 7 4 10 3 7 5 8 2 3 2 3 or 2. or
0.3, 0.312, 0.32 5 6 4.
0.8, 0.826, 5 6
, 0.8, 0.826
5. Dana’s 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