Transcript Lesson 4.3

Lesson 4.3
Core Focus on Decimals
& Fractions
Adding and Subtracting Mixed
Numbers
Warm-Up
1. Find the value of 3 × 4 + 1.
2. Find the value of 5 × 3 + 3.
13
18
3. Find the value of 12 × 4 + 2.
50
4. Rewrite
as an improper fraction.
27
8
3 83
5. Rewrite
as an improper fraction.
2 74
18
7
Lesson 4.3
Adding and Subtracting Mixed
Numbers
Find sums and differences of expressions
that include mixed numbers.
Explore!
Mixing Paint
Kazi painted his bedroom. He mixed different colors of paint together to make new and exciting
shades.
Step 1
Kazi purchased two small cans of paint for the ceiling. The can of red paint contained
2 34 pints. The can of blue paint contained 1 85 pints. He mixed the two cans of paint
together. How much paint does he have for the ceiling?
a. Write the problem as a mathematical expression.
b. Write each mixed number as an improper fraction.
c. Rewrite the fractions using the least common denominator.
d. Find the sum or difference. Simplify your answer and
convert it to a mixed number, if needed.
Step 2
Kazi bought 1 16 gallons of yellow and 4 13 gallons of green paint for
the walls. He mixed the two colors of paint together. How much
paint does he have available for the walls?
a. Write the problem as a mathematical expression.
b. Write each mixed number as an improper fraction.
c. Rewrite the fractions using the least common denominator.
d. Find the sum or difference. Simplify your answer and convert it to a mixed
number, if needed.
Explore!
Mixing Paint
Kazi painted his bedroom. He mixed different colors of paint together to make new and exciting
shades.
Step 3
Kazi bought 2 15 pints of white paint for the trip. When he finished painting he still had
7
10 pint of white paint left. How much paint did Kazi use?
a. Write the problem as a mathematical expression.
b. Write each mixed number as an improper fraction.
c. Rewrite the fractions using the least common denominator.
d. Find the sum or difference. Simplify your answer and
convert it to a mixed number, if needed.
Step 4
Explain in your own words how to add or subtract mixed numbers
using the method in this Explore!.
Adding or Subtracting Mixed
Numbers Using Improper Fractions
1. Write the mixed numbers as improper fractions.
2. If the denominators are different, rewrite the
fractions using the least common denominator
(LCD).
3. Add or subtract the numerators.
4. Write the sum or difference over the common
denominator.
5. Simplify the fraction.
Example 1
Find the value of 3 14  1 32 .
Change each mixed number
to an improper fractions.
13
5
2
3 
and 1 3 
4
3
1
4
Write equivalent fractions with the
least common denominator, 12.
and
Add the numerators.
39 20 39  20 59



12 12
12
12
Write as a mixed number.
59
11
 4 12
12
11
3 14  1 23  4 12
Example 2
Seth ran a mile around the track. It took him 6 56 minutes to run a mile.
His friend, Tremaine, also ran a mile on the track. It took Tremaine 7 13
minutes to run the mile. How much faster did Seth run than Tremaine?
Write the problem.
7 13  6 56
Write the mixed numbers
as improper fractions.
22
41
5
7 
and 6 6 
3
6
Write equivalent fractions with
the LCD of 6.
22 44

3
6
Subtract the numerators.
44 41 44  41 3 1
 
 
6
6
6
6 2
1
3
Write the fraction in simplest form.
1
Seth ran the mile minute faster than Tremaine.
2
Communication Prompt
What is the process for adding 3 14 and 4 15 ?
Exit Problems
1. Find the value of 7 16  2 13 .
9 12
2. Jacob collected 2 14 bags of aluminum cans to recycle on
Monday. He collected 3 12 bags of aluminum cans to recycle
on Tuesday. How many bags did he collect in the two days?
5 43 bags
3. Find the value of 9 85  4 14 .
5 83
4. Carmen bought 10 pounds of flour. She used 2 15 pounds of
flour for baking one week. How many pounds of flour did
she have left?
7 45 pounds of flour left