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• Norm Frankenberger
+
With Different Denominators
Norm Frankenberger
Summary Slide
Identifying the Parts of a Fraction
The Most Important Rule
What If the Fractions You’re Adding Have Different Denominators
Choosing a Common Denominator
Converting Fractions to Equivalents
Equivalent Fractions
• Why Adding Fractions Is Important?
In March 2008, a presidential panel reported after a two year study that “schools could improve students’ math scores by hammering home the basics, such as addition and multiplication, and then increasing the focus on fractions and geometry.
Norm Frankenberger
Norm Frankenberger
“Difficulty with fractions (including decimals and percents) is pervasive and is a major obstacle to further progress in mathematics, including algebra.”
Success in algebra is linked to higher graduation rates and college enrollment.
Let’s get started!
• Norm Frankenberger
Identifying the Parts of a Fraction
The top number is called the numerator.
The bottom number is called the denominator.
3
4
numerator
denominator
• Norm Frankenberger
The Most Important Rule
You CANNOT add (or subtract) fractions unless the denominators are the same!
1
3
+ 1
4
does not add up to 2
7
Norm Frankenberger
What If the Fractions You’re Adding Have Different Denominators
You must choose a new common denominator
You must change the fractions into their equivalent forms.
Norm Frankenberger
Choosing a Common Denominator
1
+ 3
1
4
Go through the list of multiples of the two denominators and pick out the first number that appears in both lists.
This is the common denominator!
Norm Frankenberger
Converting Fractions to Equivalents
• Put equal signs and the common denominator next to the original fractions
• Ask, “Three times what number equals twelve?”
• Now, whatever you do the bottom of the fraction, you must do to the top.
• Multiply the numerator times four
x 4 =
12
12
1
+ 3
1
4
4
=
=
x 4 =
x 3 =
3
x 3 =
Now repeat the same process with the second fraction.
Norm Frankenberger
Let’s take a closer look at equivalent fractions:
They are the mechanism by which we can change the original fractions into fractions with different denominators without losing the original value
If it wasn’t for equivalent fractions we could not add (or subtract) fractions.
• Norm Frankenberger
Equivalent Fractions
Equivalent fractions allow us to change a fraction to a fraction with a different denominator but with the same value.
For example:
==
½ ½ ½
In other words, ½ = 2/4= 4/8
2/4
4/8
• Norm Frankenberger
Now, Let’s Finish the Problem
Now, you add the numerators and put the total over the common denominator.
x 4 =
12
12
1
+ 3
1
4
4
=
=
x 4 =
x 3 =
3
x 3 =
7
12