Simplifying Fractions

(5th Grade Mathematics)

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Simplifying A Proper Fraction

A proper fraction is said to be in lowest terms if the numerator and denominator do not have any factors in common.  For example: are all in lowest terms, but the fractions: are not.

Steps to simplifying a proper fraction

Example:

Step 1: Determine the factors of the numerator.

The factors of 12 are: 1, 2, 3, 4, 6 and 12.

Step 2: Determine the factors of the denominator.

The factors of 20 are: 1, 2, 4, 5, 10, 20.

Step 3: Find the greatest common factor.

The greatest common factor is 4

Step 4: Divide both the numerator and the denominator by the greatest common factor.

12 divided by 4 is 3.  20 divided 4 is 5.

Step 5: Write your answer.

With some practice you can often see the greatest common factor without having to list all the factors.  If you do this make sure that there are no common factors still remaining.

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Simplifying An Improper Fractions

An improper fraction is said to be in lowest terms if it is in mixed form and the fraction part is proper and in lowest terms. 

Steps to simplifying an improper fraction

Example:

Step 1: Divide the denominator into the numerator.  The quotient is the whole number in the mixed fraction.  The remainder is the new numerator.

The whole number is 5.  The new numerator is 2.  The denominator is 3

Step 2: Determine the factors of the new numerator.

The factors of 2 are 1, 2.

Step 3: Determine the factors of the denominator.

The factors of 3 are 1, 3.

Step 4: Find the greatest common divisor of the numerator and denominator.

The greatest common divisor is 1.

Step 5: Divide both the numerator and the denominator by the greatest common factor.

Dividing 2 and 3 by 1 does not change the fraction.

Step 6: Write your answer.

With some practice you can often see the greatest common factor without having to list all the factors.  If you do this make sure that there are no common factors still remaining.

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Simplifying A Mixed Fraction

A mixed fraction is said to be in lowest terms if the fraction part is proper and in lowest terms.

Steps to simplifying a mixed fraction

Example:

Step 1: Make sure the fraction part is in proper form.  If it is not use the improper fraction method above to put it in proper form.  Then add the whole numbers together. For this problem the fraction part is in proper form.
Step 2: Determine the factors of the numerator. The factors of the numerator 8 are 1, 2, 4, and 8.
Step 3: Determine the factors of the denominator. The factors of the denominator 12 are 1, 2, 3, 4, 6, and 12.
Step 4: Find the greatest common factor. The greatest common divisor is 4.
Step 5: Divide both the numerator and the denominator by the greatest common factor. 8 divided by 4 is 2.  12 divided by 4 is 3. 
Step 6: Write your answer.

With some practice you can often see the greatest common factor without having to list all the factors.  If you do this make sure that there are no common factors still remaining.

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Program Instructions

Instructions

 

Select the type of problem: There are three choices.

Delay: The motion of the basketball player is controlled by your computer processor speed.  If the player moves too fast make the number larger and click on Delay.  If too slow, enter a smaller number and click on Delay.

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Practice

For the proper fraction or mixed fraction problem:

  • Read the problem.

  • List the factors of the numerator and the denominator. 

  • Determine the greatest common factor (or the greatest common divisor (GCD)). 

  • Divide the numerator and denominator by the greatest common divisor.

  • Write your answer.

Note: The greatest common factor is at most 70.

For the improper fraction problem:

  • Read the problem.

  • Use the "Get Mixed Fraction" as a division tool to determine the whole number and the numerator.

  • List the factors of the numerator and the denominator.

  • Determine the greatest common factor.

  • Divide the numerator and denominator by the greatest common divisor.

  • Write your answer.

Practice fraction simplification

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