Math 020 – Fractions I
A fraction is used to describe part of a whole. In a fraction, the top number is called the numerator and
the bottom number is called the denominator.
*Label the numerator and denominator in the fraction:
Write a fraction to represent the shaded figure:
Mixed Numbers and Improper Fractions:
A proper fraction is a fraction that has a numerator smaller than the denominator.
Example: __________________________________________________________
An improper fraction has a numerator that is greater than or equal to the denominator.
Examples: _________________________________________________________
A mixed number contains a whole number and fraction together.
Examples: _________________________________________________________
Writing Mixed Numbers as Improper Fractions:
1. Multiply the whole number and the denominator of the fraction together.
2. Add the numerator to the product from step 1.
3. Place the sum from step 2 over the original denominator.
Example:___________________________________________________________
Practice: Write each mixed number as an improper fraction
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Writing Improper Fractions as Mixed Numbers:
1. Divide the numerator by the denominator, use division with remainders.
2. The quotient is the whole number part of the mixed number, the remainder is the numerator of the
new mixed number, and the denominator is the original denominator.
Think:
Example:
Practice: Write the improper fraction as a mixed number
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Factors:
Numbers that are multiplied together to find a product are called factors.
The factors of 20 are 1, 2, 4, 5, 10, and 20.
Find the factors of 24: _________________________________________________
Find the factors of 100:_________________________________________________
Find the factors of 19:__________________________________________________
Prime and composite numbers:
A prime number is a natural number that has exactly two factors, 1 and itself.
List the prime numbers between 1- 100 _________________________________
__________________________________________________________________
A composite number is any natural number that has factors other than 1 and itself.
Give some examples of composite numbers________________________________
Prime Factorization:
Prime factorization is the process of writing a number as a product using only prime numbers.
Find the prime factorization of 180:
Find the prime factorization of 945:
Find the prime factorization of 60:
Simplifying Fractions:
A fraction is written in simplest form when the numerator and denominator have no common factors
other than 1.
To simplify a fraction divide the numerator and denominator by a common factor. If the result does not
yield the fraction in simplest form, divide the fraction by a common factor again until the only common
factor left is 1.
Simplify the following fractions:
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Multiplying Fractions and Mixed Numbers:
To multiply two fractions, multiply the numerators and then multiply the denominators. Simplify if
needed.
Example:
Practice:
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To multiply mixed numbers, you must first turn all mixed numbers into improper fractions. Once mixed
numbers are converted to improper fractions, multiply numerators and then multiply denominators and
simplify if needed.
If you are multiplying a whole number by a fraction, make the whole number into a fraction by putting a
one as the denominator of the whole number.
Example:
Practice:
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Dividing Fractions and Mixed Numbers:
In order to divide fractions we will need to use reciprocals. Two numbers are reciprocals if their product
is 1. To find the reciprocal of a fraction, flip the numerator and denominator.
Examples:
Practice:
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Simplify if
needed.
Example:
Practice:
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In order to divide mixed numbers, all mixed numbers must be converted to improper fractions. Then
rewrite the division problem multiplying the first fraction by the reciprocal of the second fraction.
Example: 6
Practice:
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