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Visual Models for Fraction OperationsTRANSCRIPT
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