Download Unit 3 – Page 2

Lesson 3-6 and 3-7
Numerator- The number above the bar in a fraction; ex.
2
5
the 2 is the numerator
Denominator- the number below the bar in a fraction. This number tells how many parts the whole is divided
2
into. Ex. the 5 is the denominator
5
Adding and Subtracting fractions, mixed numbers, (with like and unlike denominators) and decimals.
Fractions
 If the denominators (bottom numbers) are the same add or subtract the top numbers and leave the
2
1
3
denominators the same. 5 + 5 = 5
If the denominators are different, find a common denominator and
3 1 3
x =
4 1 4
then add or subtract the numerators (top numbers), and keep the
same denominator.
1 2 2
x =
2 2 4
Comparing Fractions
_________
 Cross corner multiply from the bottom up. The side with the
1
15
12
larger product is the larger fraction.
4
3
3
3
is the larger fraction.
=
4

4
5
Decimals
 When adding and subtracting decimals, line up the decimals then add or subtract like normal.
Lesson 3-8
Adding and Subtracting Mixed Numbers with unlike denominators
2
1. Draw a line to divide the whole numbers from the fractions
2. Find a common denominator and convert the numerators
+3
3. Then add or subtract the whole numbers and the fractions as normal
1
6
x 5 = 30
5
3
5
x
6
6
5
=
18
30
23
23
5
= 530
30
Lesson 3-9
Least Common Multiple - The least (smallest) number that is a multiple of two or more numbers
5 and 6 Count by 5’s 5: 5, 10, 15, 20, 25, 30
Count by 6’s 6: 6, 18, 24, 30, 36, 42
Lesson 3-10
Multiplying Fractions
1. Multiply straight across
2. Reduce to simplest form
5
6
x 8 = 48
Multiplying a Whole Number by a Fraction
1. Put the whole number over 1
2. Multiply straight across
3. Reduce to simplest form
2
3
Ex.1
7
35
4x
Ex.2
4
1
2
3
x =
Multiply Mixed Numbers
1. Change mixed numbers to improper fractions
3
11
2. Multiply straight across
3
2
2x+4 = 4
24 x 3 3
3. Reduce to simplest form
8
3
2
4
3
6
2
3
x 5 = 20 ÷ 2 = 10
2_
3)8
-6_
2
2
11
3+3 = 3
x
2
3
2
11
4
x
11
3
=
121
12
10
12)121
121
0
1.6
+0.24
1.84
Lesson 3-11
Dividing with fractions and whole numbers
Reciprocal- the inverse or flip side of any fraction or whole number
Reciprocals
Ex. 1
3
4
→3
4
ex.2
1
2
→1
2
**When solving a division problem with fractions, only flip the second fraction.
1.
2.
3.
4.
5.
3
4
Keep the first fraction the same
Change the sign for ÷ to x
Invert the second fraction
Multiply straight across
Simplify your answer
2
3
4
÷1
2
3
1
2
3
3
4
3
2
÷ = x =
2
2
1
8) 9
-8
1
9
8
1
x 4 = 12 ÷ 2 = 6
**When dividing a whole number by a fraction always put the whole number over 1. Then follow the same steps.
Lesson 3-12
Multiply a number by a fraction less than 1, results in a smaller number
Dividing a number by a fraction less than 1, results in a greater number
1
3
1
3
1
3
2
6
1
3 x 2 = 1 x 2 = 2 = 12 ≤ 3
3÷2=1x1=1=6>3
Lesson 3-13 and 3-14
These lessons have students use what they’ve learned in lesson 3-8 through 3-12. Using unknown factors to add,
subtract, multiply, or divide.
Multiplication Equation
1. 3
9
3
3
5
2. 5
6
3. 4
9
x
= 20
x
9
4
= 20
4
20
20
5
6
x 7 = 42
24
4
9
x
x
= 42
x
= 63
Lesson 3-15, 3-16 and 3-17
These lessons reinforce the unit.
5
Related Division Equation
6
7
24
= 63
9
20
3
3
÷
=
÷5=4
÷
=
20
42
÷6=7
÷
=
24
63
÷9=7
5
4
4
6