page ?? #?-?? answers student learning goal chart lesson reflection
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Page ?? #?-?? ANSWERS
Student Learning Goal Chart
Lesson Reflection
Pre-Algebra Learning Goal
Student will understand rational and real numbers.
Students will understand BLAH BLAH BLAH by being able to do the following:
• Learn to write rational numbers in equivalent forms (3.1)• Learn to add and subtract decimals and rational numbers
with like denominators (3.2)• Learn to add and subtract fractions with unlike
denominators (3.5)
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Today’s Learning Goal Assignment
Learn to add and subtract fractions with unlike denominators.
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
least common denominator (LCD)
Vocabulary
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
To solve this problem, add and subtract rational numbers with unlike denominators. First find a common denominator using one of the following methods:
Method 1 Find a common denominator by multiplying one denominator by the other denominator.
Method 2 Find the least common denominator (LCD); the least common multiple of the denominators.
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Add or subtract.
1. +5 14
1 7
13 16
2.
12
2 38 1– 7
1 6
3. –2+ 3 5
2 3
4. Evaluate – n for n = . 138 9 16
Lesson Quiz: Part 1
–2 1 15
12
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Lesson Quiz: Part 2
Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy?
5.3 4
12
2 in.3 4
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Are you ready for the FAST Track?
If YES, prepare for Ch. 3 Section 3 YES, BACK to Ch. 3 Section 3!
If NO, continue with the Ch. 3 Section 5 lesson!
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Pre-Algebra HW: page 7?? #?-??
(3-1, 3-2, 3-5)
Page ??#?-??
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators3-5 Adding and Subtracting with Unlike
Denominators
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Warm UpAdd or subtract.
1 + – 1 5 11. 2
5
2. 7 123 – 2
3. 6.5 + –1.2
4. 3.4 – 0.9
5.3
2.5
3 5
11 12
1 3 1
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Problem of the Day
A school installed a new phone system with four-digit extensions. How many extensions are possible?all numbers from 0000 to 9999, or 10,000
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Today’s Learning Goal Assignment
Learn to add and subtract fractions with unlike denominators.
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
least common denominator (LCD)
Vocabulary
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
A pattern for a double-circle skirt requires 9 yards of 45-inch-wide material. To add a ruffle takes another 2 yards. If the total amount of material for the skirt and ruffle are cut from a bolt of fabric 15 yards long, how much fabric is left?
1 3
2 5
1 2
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
To solve this problem, add and subtract rational numbers with unlike denominators. First find a common denominator using one of the following methods:
Method 1 Find a common denominator by multiplying one denominator by the other denominator.
Method 2 Find the least common denominator (LCD); the least common multiple of the denominators.
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Find a common denominator: 8(7)=56.
2 7
+1 8
Multiply by fractions equal to 1.
Rewrite with a common denominator.Simplify
Additional Example 1A: Adding and Subtracting Fractions with Unlike Denominators
2 7
+1 8
7 7
8 8
23 56
=16 56
+7 56
A.
Add or Subtract. Method 1:
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
The least common multiple of two numbers is the smallest number other than zero that is a multiple of the two numbers.
Remember!
1 61 +
5 8 List the multiples of each
denominator and find the LCD
Write as an improper fraction.
Multiples of 6: 6; 12; 24; 30
Multiples of 8: 8; 16; 24; 32
Rewrite with a common denominator.
5 8+
7 6
4 4
3 3
43 24=
15 24+
28 24
19 24= 1
Multiply by fractions equal to 1.
Simplify.
5 8+
7 6
B.
Additional Example 1B: Adding and Subtracting Fractions with Unlike Denominators
Add or Subtract. Method 2:
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Find a common denominator 3(8)=24.
5 8
+1 3
Multiply by fractions equal to 1.
Rewrite with a common denominator.
23 24
Try This: Example 1A
Add or Subtract. Method 1:
=15 24
+8 24
A.
5 8
+1 3
8 8
3 3
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
1 62 +
3 4 List the multiples of each
denominator and find the LCD
Write as an improper fraction.
Multiples of 6: 6; 12; 24; 30
Multiples of 4: 4; 8; 12; 16
Rewrite with a common denominator.
Multiply by fractions equal to 1.
Simplify.
3 4+
13 6
3 4+
13 6
2 2
33
B.
11 12
= 235 12=9
12+26 12
Try This: Example 1B
Add or Subtract. Method 2:
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Evaluate t – for t = .
Additional Example 2: Evaluating Expressions with Rational Numbers
4 5
–5 6
24 30
–25 30
1 30
=
Multiply by fractions equal to 1.
4 5
5 6
Substitute for n.5 6
Rewrite with a common denominator: 6(5) = 30.
4 5
–5 6
5 5
6 6
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Evaluate – h for h = .
Try This: Example 2
Multiply by fractions equal to 1.
5 9
–7 12
Substitute for h.–7 12
Rewrite with lowest common denominator (36).
–7 12–
5 9
7 12+5
9=
Simplify.41 36 or 1 5
36
21 36+20
36
–7 12–5
9
7 12+5
9
7 12+5
94 4
3 3
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Additional Example 3: Consumer Application
Subtract both amounts from 36 to find the amount of ribbon left.Write as improper fractions. The LCD is 8.
36 – 12 – 13 7 8
3 4
Rewrite with a common denominator. Simplify.
, or 9 3 8
75 8 There will be 9 inches left.
3 8
103 8
288 8
– – 110 8
103 8
55 4
288 8 – –
Two dancers are making necklaces from ribbon for their costumes. They need pieces measuring 13 inches and 12 inches. How much ribbon will be left over after the pieces are cut from a 36-inch length?
7 8
3 4
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Try This: Example 3
Subtract both amounts from 12 to find the amount of board left.Write as improper fractions. The LCD is 12.
12 – 6 – 4 3 4
5 12
Rewrite with a common denominator. Simplify.
, or 5 6
10 12 There will be inches left.
5 6
81 4144 12
– – 53 12
27 4 53 12
144 12 – –
Fred and Jose are building a tree house. They need to cut a 6 foot piece of wood and a 4 foot piece of wood from a 12 foot board. How much of the board will be left?
5 12
3 4
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Add or subtract.
1. +5 14
1 7
13 16
2.
12
2 38 1– 7
1 6
3. –2+ 3 5
2 3
4. Evaluate – n for n = . 138 9 16
Lesson Quiz: Part 1
–2 1 15
12
Pre-Algebra
3-5 Adding and Subtracting with Unlike Denominators
Lesson Quiz: Part 2
Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy?
5.3 4
12
2 in.3 4