1. California
Standards
NS1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.
Also covered: NS2.4

2. VOCABULARY CARD
Rational Number

3. 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 =

4. One way to compare fractions with unlike denominators is to use models
One way to compare fractions with unlike denominators is to use models. For example,
the models show that < . 3 8 1 2 3 8 = 1 2 =
Another way to compare fractions with unlike denominators is to first write equivalent fractions with common denominators. Then compare the fractions.

5. Teacher 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

6. Teacher 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 – > –

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

8. Student Practice 1A:
Compare the fractions. Write < or >. 5 6 7 8
The LCM of the denominators 6 and 8 is 48. 5 6 40 48
Write equivalent fractions with 48 as the denominator.
5  8
6  8 = = 7 8
7  6
8  6 42 48 = =
Compare the numerators. 40 48
< 42
, and so 5 6
< 7 8

9. Student Practice 1B:
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 – < –

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. Teacher Example 2A: 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. Compare the decimals. Write < or >.
Teacher Example 2B:
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 <

13. Student Practice 2A:
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, <

14. Student Practice 2B:
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 <

15. A rational number is a number that can be written as a fraction or quotient of integers with a nonzero denominator. When rational numbers are written in a variety of forms, you can compare the numbers by writing them all in the same form.

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

17. Teacher 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. 4 5
From least to greatest, the numbers are , 0.9, 0.93.

18. Order , 0.84, and 0.7 from least to greatest.
Student Practice 3: 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.

19. Compare the fractions. Write > or <. 1. 2.
Lesson Quiz
Compare the fractions. Write > or <.
Compare the decimals. Write < or >.
and 0.312 3 7 4 10 5 8 2 3
and
>
<
and
> 5 6
4. Order , 0.8, from least to greatest.
Graph the numbers on a number line.
0.8, 0.826, 5 6 56
0.8
0.826