Addition of Fractions: For any fractions a/b and c/d,

a + c = ad + bc = ad + bcb d bd bd bd

Approximating Method when Adding Fractions

_1_ 3

_1_ 2

_3_ 4

When the two shaded amounts are combined, the total is approximately . _3_

4

Finding the sum of two fractions is easy when they have the same

denominator.

4_ 6

3_ 6

4_ 6

+ 3_ 6

= 1 7_ 6

1_ 6

OR

Addition of fractions can also be illustrated using a number line:

¼ + ⅓

Adding Unlike Denominators

= ?

First, find the smallest common denominator of ¼ and ⅓.

1 × 3 = _3_ 4 3 12

1 × 4 = _4_3 4 12

So…

1 = _3_4 12

1 = _4_3 12

1 + 1 = _7_4 3 12

1 + 14 3=

_3_ + _4_ 12 12

=_7_ 12

_

Subtraction of Fractions: For any fractions a/b and c/d,

a _ c = ad _ bc = ad – bcb d bd bd bd

Using a Number Line:

Using Fraction Bars:

1_ 2

_1_ 6

_1_ 3

_1_ _1_ _2_ _1_ 2 6 6 3

_ = OR

_5_ 6

_1_ 4

This is what’s left over.

Subtracting Unlike Denominators:

_5_ _1_ 6 4

_ = ?

…

• 5 × 2 = 10 1 × 3 = 3 6 2 12 4 3 12

• 10 - 3 = 7 12 12 12

The smallest common denominator of ⅚ and ¼ is 12.

1012

312

712

…

×

Whole Number Times a Fraction: For any whole number k and fraction a/b,

k × a = ka b b

Multiplication of a fraction and a whole number can be illustrated

in a couple of different ways.

Whole Number Times a Fraction

1 Whole Bar

3 × 1 = 1 + 1 + 1 = 3 or 1 1_ 2 2 2 2 2 2

Fraction Times a Whole Number

A B C

1 × 4 = 1 + 1 + 1 + 1 = 4_ 3 3 3 3 3 3

1

⅓

Fraction Times a Whole Number

1 1 3 3

1× 4 =

Multiplication of Fractions: For any fractions a/b and c/d,

a × c = acb d bd

Fraction Times a Fraction

1 × 1 = 1_ OR 1 of 1 = 1_ 3 5 15 3 5 15

1_15

1_15

1_ 5

1_ 3

×

Fraction Times a Fraction

2 × 4 = 8_ OR 2 of 4 = 8_ 3 5 15 3 5 15

8_15

8_15

4_ 5 ×

2_ 3

÷

Division of Fractions: For any fractions a/b and c/d, with c/d ≠ 0,

a ÷ c = a × d = adb d b c bc

5 ÷ 1_ 6 12

= 10

…

_1_ 12

goes into 10 times.

_5_ 6

5 ÷ 1_ _1_ 6 3 2

= 2

Remainder

Divisor

TRIPLE BOTH AMOUNTS

Inverting the Divisor and Multiplying

1 1 1 3 3 1_ 2 3 2 1 2 2

÷ = = 1= ×

1 1 1_ 1_ 3_ 3_ 2 3 2 3 2 2

÷ = ( × 3)÷ ( × 3) = ÷ 1 =

Simplified Version of Equation Above