Adding Fractions and Mixed Numbers

1
Adding Fractions and Mixed Numbers

• Objective 9

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Adding Fractions and Mixed Numbers

A fraction is made from two numbers. The
Numerator and the Denominator. Numerator Denomina
tor The Denominator shows the number of divisions
in the whole unit. The Denominator divides the
whole.
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Adding Fractions and Mixed Numbers

The Numerator is the number of divisions in the
fraction. Before we can add fractions the
denominators of the two fractions must be
equal. We can add 1/4 and 3/4 1 but we cannot
add 2/5 and 3/4 because the denominators are not
equal.
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Adding Fractions and Mixed Numbers

To add 2/5 and 1/4 we can make the denominators
in the two fractions equal by making the
denominator a multiple 4 and 5
4 4
1 4
X

X

13 20
5 20

We can now add
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Adding Fractions and Mixed Numbers
Finding the Least Common Multiple of the two
fractions. We find the prime factors of both
denominators. 4 2, 2 5 5 The
Least Common Multiple is 2 X 2 X 5 20
Factors
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Adding Fractions and Mixed s

• To add fractions one must have common
  denominators. For example 1/4 and 2/5 must be
  placed over the same denominator. To calculate
  that denominator we find the smallest factors of
  each of the denominators.
• The multiples of 1/4 are 2x2.
• The multiples of 5 are 1x5

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Adding Fractions and Mixed s

• The lowest common multiple is found by
  multiplying the multiples of the two fractions.
• 2 X 2 X 5 4 X 5 20
• 20 is the lowest common multiple of 4 and 5.
• We now put both fractions over the Lowest Common
  Multiple (LCM) we just found.

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Adding Fractions and Mixed s

• We put the fractions over the LCM by multiplying
  each fraction by a special form of 1 and add
  them.

X
X




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Adding Fractions and Mixed s

• Simplify

Denominators Factors

15
3
5
5
5
L C M
X
3
5

15


X


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Adding Fractions and Mixed s

• Simplify

Denominators Factors
8
2
2
2

6
3
2
L C M
X
3

24
X
2
2
2
X

X
X

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Adding Fractions and Mixed s

• Adding Mixed Numbers
• Convert the Mixed Number to a regular fraction
  and then add as fractions.
• Multiply the whole number by the denominator to
  form regular fraction.

2

2


Then add as regular fractions .
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Adding Fractions and Mixed s

• The End