Fractions: Adding, Subtracting, Comparing and Ordering, Study Guides, Projects, Research of Mathematics

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ADDING AND SUBTRACTING

FRACTIONS AND MIXED NUMBERS

Fraction- a number that names a part of a whole numerator- the part or top number in a fraction denominator- the bottom or the total number in a fraction

Mixed Number - a number that is made up of a whole number and a fraction

Improper Fraction - a number/fraction in which the numerator is larger than the denominator

Simplest form- the form of a fraction in which the numerator and denominator have only 1 as their common factor

Equivalent fractions- fractions that name the same amount or part

COMPARING AND ORDERING

• To compare fractions with the same denominators, compare the numerators - To compare fractions with the same numerators, compare the denominators. - Remember the smaller the denominators, the larger the piece, so the larger the fraction

When comparing only 2 fractions…

When you have only two fractions to be compared, you can cross multiply on an upward diagonal. When doing this, write your answer above the diagonal (two numbers you are multiplying). Then you can compare the two products to determine the larger fraction.

To order two or more fractions…

• You must get common denominators in order to compare the numerators.
• You get common denominators by finding a common multiple that all of the numbers go into evenly.
• There will be many common multiples, if you get stuck you can multiple the common denominators by each other.
• *However, if you change the denominator, you must change the numerator. - What ever you multiply the denominator by, you must multiple the numerator by the same number.

Comparing and Ordering

To REDUCE or simplify…

• To reduce a fraction you divide the numerator and the

denominator by the same number. *The number you

divide by must go into both the numerator and

denominator evenly.

*Sometimes, you may be able to reduce again.

• To reduce a fraction to lowest terms, divide the

numerator and denominator by their Greatest

Common Factor (GCF). This is also called simplifying

the fraction.

If a fraction is in simplest form, then the only common factor between the numerator and the denominator is 1

ADDING AND

SUBTRACTING FRACTIONS

There are 3 Simple Steps to add /subtract fractions : Step 1: Make sure the bottom numbers (the denominators) are the same. If not- make them the same (make equivalent fractions)

Step 2: Add/Subtract the top numbers (the numerators), put the answer over the denominator.

Step 3: Simplify the fraction (if needed)

EXAMPLES FOR YOU TO TRY:

ANSWERS:

Adding and Subtracting

Mixed Numbers:

Whole numbers & fractions… Improper fractions

• To add/subtract mixed numbers, you can add/subtract the numbers first by following the rules.
• Then you add/subtract the whole numbers
• Finally, we simplify if possible
• *Sometimes we may need to borrow or regroup - To add/subtract using improper fractions, change your mixed number to an improper fraction. - Then add/subtract your fractions using the rules - Finally, we simplify if possible

To make a MIXED NUMBER into

an IMPROPER FRACTION…

To change a mixed number into an improper fraction:

1. Multiply the denominator by the whole number
2. Add the numerator to your product—this is your new numerator
3. Keep your denominator