1. 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 8
2. 2 5 6 1 12
4. 8

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

3. What are we doing today? Compare the fractions. Write > or <. 1.
Compare the decimals. Write < or >.
and 0.312 3 7 4 10 5 8 2 3
and 2.
and 5 6
4. Order , 0.8, from least to greatest.

4. Learn to compare and order fractions and decimals.
I will…
Learn to compare and order fractions and decimals.

5. Vocabulary
rational number

6. 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.

7. When two fractions have the same 7 9 2 9
Which is greater, or ?
When two fractions have the same
denominator, just compare the numerators. 7 9 2 9
>
because 7 > 2. 7 9 = 2 9 =

8. Example 1: 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
, so… 7 9
> 5 8

9. I try! Practice 1a. 1b. 1c. Compare the fractions. Write < or >.2 5 3 7 – – 5 6 7 8 6 8 5 7 – –

10. 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.

11. Example 2: 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, >

12. I try! Practice 2a. 2b. 2c. Compare the decimals. Write < or >.
0.73
0.734
0.535
0.538
0.3
0.334

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

14. Example 3: Ordering Fractions and Decimals4 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 in order. 4 5
From least to greatest, the numbers are , 0.9, 0.93.

15. Lesson
Quiz

16. Lesson Quiz
Compare the fractions. Write > or <. 1.
Compare the decimals. Write < or >.
and 0.312 3 7 4 10 5 8 2 3
and 2.
and 5 6
4. Order , 0.8, from least to greatest.

17. Lesson Quiz ANSWERS
Compare the fractions. Write > or <. 1.
Compare the decimals. Write < or >.
and 0.312 3 7 4 10 5 8 2 3
and
> 2.
and
<
> 5 6
4. Order , 0.8, from least to greatest.
0.8, 0.826, 5 6

18. Practice 1a
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 –
> –
, so… – > –

19. Practice 1b
Compare the fractions. Write < or >. 5 6 7 8
The LCM of the denominators 6 and 8 is 48. 5 6
5 · 8
6 · 8 40 48
Write equivalent fractions with 48 as the denominator. = = 7 8
7 · 6
8 · 6 42 48 = =
Compare the numerators. 40 48
< 42
, so… 5 6
< 7 8

20. Practice 1c
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 common denominators.
Put the negative signs
in the numerators. – = = 5 7
–5 · 8
7 · 8
–40 56 – = = 42 56 40 56 6 8 5 7 –
< –
, so… – < –

21. Compare the decimals. Write < or >.
Practice 2a
Compare the decimals. Write < or >.
0.73
0.734
0.73 = _
0.733… 3
Line up the decimal points.
The tenths and hundredths are
the same.
0.734 4
Compare the thousandths:
3 < 4.
Since is < 0.004, 0.73 <

22. Practice 2b
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, <

23. Practice 2c
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 <