Chapter 2
2.5: Operations with Rational Numbers
Objective…
Part A: Add Rational Numbers
Page 98
Sum of two rational numbers with
SAME Denominator
Sum of two rational numbers with
DIFFERENT Denominators
Math terminology
Math terminology
Rule
Rule
Example
Example
4 ⎛ 3⎞
+⎜− ⎟
5 ⎝ 5⎠
1 ⎛ 2⎞
+⎜− ⎟
5 ⎝ 3⎠
Practice… Evaluate each expression
⎛ −2 ⎞ ⎛ 3 ⎞
⎜⎝ ⎟⎠ + ⎜⎝ ⎟⎠
7
−5
⎛ 1⎞ ⎛ 1⎞
⎜⎝ 1 ⎟⎠ + ⎜⎝ −2 ⎟⎠
3
3
⎛ −1⎞ ⎛ 2 ⎞
⎜⎝ ⎟⎠ + ⎜⎝ ⎟⎠
9
−5
⎛ 1⎞ ⎛ 4⎞
⎜⎝ −1 ⎟⎠ + ⎜⎝ 3 ⎟⎠
6
9
Chapter 2
2.5: Operations with Rational Numbers
⎛ 2 ⎞ ⎛ −4 ⎞ ⎛ 1 ⎞
⎜⎝ ⎟⎠ + ⎜⎝ ⎟⎠ + ⎜⎝ ⎟⎠
5
15
10
⎛ 1 ⎞ ⎛ −5 ⎞ ⎛ −1⎞
⎜⎝ ⎟⎠ + ⎜⎝ ⎟⎠ + ⎜⎝ ⎟⎠
6
9
3
Part B: Subtract Rational Numbers
Page 102
Difference of two rational numbers
with SAME Denominator
Difference of two rational numbers
with DIFFERENT Denominators
Math terminology
Math terminology
Rule
Rule
Example
Example
⎛ 2⎞ ⎛ 4⎞
⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠
7
7
⎛ 2⎞ ⎛ 1⎞
⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠
5
2
Practice… Evaluate each expression
⎛ 1⎞ ⎛ 3⎞
⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠
6
4
⎛ 1⎞ ⎛ 2⎞
⎜⎝ 2 ⎟⎠ − ⎜⎝ 4 ⎟⎠
4
3
⎛ 1 ⎞ ⎛ 11 ⎞
⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠
3
12
⎛ 1⎞ ⎛ 3 ⎞
⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠
4
10
Chapter 2
2.5: Operations with Rational Numbers
⎛ 1 ⎞ ⎛ 5⎞
⎜⎝ 3 ⎟⎠ − ⎜⎝ 7 ⎟⎠
4
6
⎛ 7⎞ ⎛ 9 ⎞
⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠
8
10
⎛ 3 ⎞ ⎛ 27 ⎞ ⎛ 3 ⎞
⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠
7
28
14
⎛ 5⎞ ⎛ 1⎞ ⎛ 5 ⎞
⎜⎝ 1 ⎟⎠ − ⎜⎝ ⎟⎠ − ⎜⎝ ⎟⎠
6
3
12
1)
Mr. Dawson has a partial roll of wire 18 ¼ feet long. He needs 25 ½
feet of write for a remodeling project. How many feet of wire is
he short?
2)
Philadelphia suffered a severe snowstorm in 1996 that left 30 and
seven-tenths inches of snow on the ground. Another severe
snowstorm occurred in 2010, when 28 ½ inches of snow fell?
a. Write a subtraction expression for the difference in depth of
these two record snowfalls.
b. Rewrite the expression as an addition expression.
c. Find the difference in these two record snowfalls.
Chapter 2
2.5: Operations with Rational Numbers
Part C: Multiply Rational Numbers
Math Notes...multiplying positive and negative rational numbers
Two signs are the SAME
Two signs are DIFFERENT
Example…
−1 ⎛ −3 ⎞
•⎜ ⎟
2 ⎝ 4⎠
Example…
1 ⎛ −3 ⎞
•⎜ ⎟
2 ⎝ 4⎠
Practice… Evaluate each product
−3 8
•
7 15
−4 20
•
5 21
3 ⎛ 1⎞
−2 • ⎜ −1 ⎟
5 ⎝ 4⎠
1 ⎛ 2⎞
−3 • ⎜ −2 ⎟
4 ⎝ 3⎠
Part D: Divide Rational Numbers
Math Notes...dividing positive and negative rational numbers
Two signs are the SAME
Two signs are DIFFERENT
Example…
⎛ 2⎞
⎜⎝ ⎟⎠
7
8
Practice… Evaluate each quotient
−5 1
÷
6 24
Example…
⎛ 5⎞
3÷⎜− ⎟
⎝ 2⎠
1 ⎛ 2⎞
−5 ÷ ⎜ −2 ⎟
3 ⎝ 5⎠
Chapter 2
2.5: Operations with Rational Numbers
⎛ −1 ⎞
⎜⎝ ⎟⎠
4
⎛ 1⎞
⎜⎝ ⎟⎠
2
⎛ 1⎞
⎜⎝ ⎟⎠
4
⎛ −3 ⎞
⎜⎝ ⎟⎠
8
3 −6
÷
20 35
1 ⎛ 1⎞
−3 ÷ ⎜ −1 ⎟
3 ⎝ 4⎠
1)
2
A pancake recipe requires 1 cups of flour to make 20 pancakes
3
and you have 9 cups of flour.
a. How many pancakes can you make with 1 cup of flour?
b. How many pancakes can you make with 9 cups of flour?
c. Do you have enough to make 100 pancakes?