Download comparing and ordering rational numbers 20151

Math 7/8 Warm-Up 11/17/15
Write each rational as a repeating or terminating decimal:
1
1) −7 20 =
1
2) 5 3 =
3)
−5
9
=
Write each repeating or terminating decimals as rationals:
4) 0. 8̅ =
5) 0.72 =
Content Standards
7.NS.2 – Apply and extend previous understandings of multiplication and division
of fractions to multiply and divide rational numbers.
7.NS.2b – Understand that integers can be divided provided that the divisor is not
zero and every quotient of integers is a rational number.
7. EE.3 – Convert between forms (whole numbers, fractions, and decimals) as
appropriate.
Mathematical Practices:
1: Make sense of problems and persevere in solving them.
3: Construct whole arguments and critique the reasoning of others.
4: Model with mathematics.
A rational number is a number that can be expressed as a ratio of two integers
written as a fraction p/q as long as the denominator q ≠ 0.
Common fractions, terminating or repeating decimals, percents, and integers are all
rational numbers.
Any number which is a whole number is also part of the integers and part of the
rational numbers.
Any number which does not terminate or repeat cannot be written as a decimal
and, therefore, cannot be rational. Example 𝜋, √7, √3
1) To compare rational numbers with unlike denominators, make a common
denominator or common multiple by finding the lowest common
denominator (LCD) or least common multiple (LCM) of the two
denominators.
*To find a LCM just multiply the two denominators together. Note, this will not
be the LCM unless the two numbers are relatively prime (have no common factors
other than 1 and itself).
Example 1: Compare
Example 2: Compare
7
8
12
18
5
7
6
9
using <, >, or =.
using <, >, or =.
Example 3: Compare
−9
−
16
7
10
using <, >, or =.
2) To compare rationals on a number line, mark off equal-size increments
between the two given values,
Example 4: Compare −3
Example 5: Compare −
3
8
5
7
Example 6: Compare −5
5
9
−3
7
8
using <, >, or =.
2
− 7 using <, >, or =.
−5
1
9
using <, >, or =.
3) To compare rational numbers in different forms, express each number as a
decimal and then compare.
Example 7: Compare 20% of students own roller shoes in Mr. Huang’s class to 5
out of 29 who own roller shoes in Mrs. Trevino’s class.
5
20% = __________________
Example 8: Order the set 23%, 0.21,
̅̅̅̅,
Example 9: Order the set 60%, 0.72
29
1 1
,
4 5
16
= _________________
from least to greatest.
7
1
, , from least to greatest.
25 10 5
Guided Practice:
Homework p. 275 – 276 (2, 4, 7, 8, 10, 11, 12, 13)