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Fractions can be written in proper, improper and mixed forms. In this handout we will define each form and describe how to convert between them.
Part A โ Proper Fractions
Exercise 1: Express the left over pizza slices as a fraction of the whole.
Definition: In a proper fraction, the numerator is smaller than the denominator.
Part B โ Improper Fractions
Exercise 2: Express the left over pizza slices as a fraction of the whole.
Improper Fractions
Definition: An improper fraction is when the numerator is equal to or larger than the denominator.
This happens when we have at least one whole AND a part of a whole.
Part C โ Mixed Numbers
In Exercise 2 we counted and described the left over pizza as an improper fraction. In this next part we will see that we are also able to count and describe the left over pizza
How to create an IMPROPER FRACTION:
Numerator Denominator =^
Total Number of Slices Number of Slices in 1 Whole =^
๐ ๐
1
There are 4 slices left over and each whole pizza contains 6 slices. Thus, our fraction looks like
There are 11 slices left over and each whole pizza contains 6 slices. Thus, our fraction looks like
2
3 4
5 6
7
as a mixed number.
Mixed Numbers
Definition: A mixed number is when we have a whole number AND a proper fraction combined.
Note: Whether working with improper fractions of mixed numbers, the denominator of a fraction is ALWAYS equal to the number of slices in 1 whole.
Part D โ Converting Between Improper Fractions and Mixed Numbers
To convert from an improper fraction to a mixed number follow the steps below:
Step 1: Rewrite the fraction as a division problem between the numerator and denominator. Step 2: Perform long division. Step 3: Rewrite the long division problem as a mixed number by:
a) setting the quotient equal to the whole number, b) the remainder equal to the numerator of the proper fraction, and c) the divisor equal to its denominator.
divisor ) dividend
Exercise 3: Convert the improper fraction, into a mixed number.
Step 1: Rewrite the fraction as a division problem.
Proper Whole Number (^) Fraction How to create a MIXED NUMBER:
Number of Wholes Proper Fraction
quotient (^) remainder quotient divisor remainder
Exercise 4: Convert into a mixed fraction.
Step 1: To find the new numerator, multiply the denominator of the fraction by the number of wholes and add it to the numerator.
Step 2: The denominator stays the same.
Step 3: Rewrite as an improper fraction.
Simplifying Before Beginning the Question Sometimes it is helpful to reduce fractions into their lowest terms before converting them between forms.
Exercise 5: Convert 1 into a mixed number.
Step 1: Find the Greatest Common Factor (GCF) between 32 and 8.
Step 2: Divide the numerator and denominator by the GCF.
: Convert the improper fraction into a mixed number by performing long division.
Exercises:
- Convert the following improper fractions into mixed numbers: 1 1
11 1
1 1
1
- Convert the following mixed numbers into improper fractions: 1 1
1
- Convert the following mixed numbers into improper fractions and vice versa: (Hint: Simplify before beginning the question.)
1 1 1
- Are the following fractions equal? Justify your answers using diagrams, words, or numbers. 1 1 1
- Explain using words and pictures, why you can never divide by 0?
- Simplify the following fraction,.
