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Write three different improper fractions that equal 4 1/2?

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3 Answers

An improper fraction is a fraction where the numerator is greater than the denominator, such as 35/6 or 9/2.
 
First, convert your mixed number to an improper fraction
 
4 1/2 = (4/1)(2/2) + (1/2) = 8/2 + 1/2 = 9/2
 
So 9/2 is one improper fraction that equals 4 1/2.
 
To get another one, multiply 9/2 by 2/2
 
(9/2)(2/2) = 18/4
 
So 18/4 is another improper fraction = 4 1/2
 
Can you find ta third one?
First thing to know - remember that any number over itself as a fraction equals "1"
Now you have to create an improper fraction from the mixed number 4 1/2. Let me know if you have difficulties with this.
 
What happens if you multiply this new improper fraction by "1"? It stays the same. This is true, even if the numbers change. When we multiply a fraction by 2/2, or 5/5, or 198/198, we are multiplying it by "1" each time. The result is an "equivalent fraction"
 
EX.- 16/7 * 3/3 = 48/21
        16/7 * 5/5 = 80/35
 
All of the equivalent fractions, 16/7, 48/21 and 80/35 are considered to be equivalent since they represent the exact same proportion, only divided into more sections.
 
Hopefully that helped!
Equivalent fractions have the same value, even if they look different.
 
Eg:  1/2=2/4=3/6=4/8...
 
In general, equivalent fractions are multiples of most reduced form of the fraction.
 
Now, to completely answer your question:  the mixed number becomes an improper fraction by:
 
4x2 = 8 + 1 = 9  --->  9/2
 
Therefore, the equivalent fractions:
 
9/2 x 2/2 = 18/4
9/2 x 3/3 = 27/6
9/2 x 4/4 = 36/8
9/2 x 5/5 = 45/10