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Unit 3: Fractions (Part 2)
Fractions in simplest form
 Fractions are in simplest form when the only common factor of the numerator
and denominator is 1.
 Divide the numerator and denominator by common factors
Improper Fractions and Mixed Numbers
 Improper fractions have a larger numerator than denominator
 Mixed Numbers have a whole number and a fraction
 Convert improper fractions to a mixed numbers by dividing and using DOWN
 Convert mixed numbers to improper fractions by multiplying whole number
and denominator and adding the numerator
Adding Fractions
 With like denominators:
o Add the numerators and keep the denominator the same
o Then simplify
 With unlike denominators:
o Use the butterfly method or equivalent fraction method to add.
o Be sure to simplify.
Subtracting Fractions
 With like denominators:
o Subtract the numerators and keep the denominator the same
o Then simplify
 With unlike denominators:
o Use the butterfly method or equivalent fraction method to subtract.
o Be sure to simplify.
Adding mixed numbers
 With like denominators:
o Add the numerators and keep the denominator the same.
o Then add the whole numbers.
o Be sure to change improper fractions into mixed numbers.
o Simplify.
 With unlike denominators:
o Use the butterfly method or equivalent fraction method to add.
o Then add the whole numbers.
o Be sure to change improper fractions into mixed numbers.
o Simplify your answer.
Subtracting mixed numbers
 Before subtracting mixed numbers: STOP: Compare the fractions, then
proceed
 With like denominators and a bigger starting fraction:
o Subtract the numerators and keep the denominator the same.
o Subtract the whole number.
o Simplify.
 With like denominators and a smaller starting fraction:
o Regroup one whole from the whole number to add to the fraction. This
will give you an improper fraction which is fine!
o Subtract the numerators and keep the denominator the same.
o Subtract the whole number.
o Simplify.
 With unlike denominators and a bigger starting fraction:
o Use the butterfly method or equivalent fraction method to subtract the
fractions
o Then subtract the whole numbers
o Be sure to simplify
 With unlike denominators and a smaller starting fraction:
o Regroup one whole from the whole number to add to the fraction. This
will give you an improper fraction which is fine!
o Use the butterfly method or equivalent fraction method to subtract the
fractions
o Then subtract the whole numbers
o Be sure to simplify
Multiplying Fractions
 Put your whole number over one if necessary
 Look across the fractions to see if there are any common factors and simplify
 Multiply your numerators
 Multiply your denominators
 Simplify
Dividing Fractions
 Put your whole number over one if necessary
 Follow KCF:
o Keep the first fraction
o Change the sign to a multiplication sign
o Flip your second fraction
 Then simplify, multiply, simplify
Multiplying and Dividing Mixed Numbers
 Change all mixed numbers into improper fractions
 Then follow the steps above to multiply or divide.
Estimating with fractions and mixed numbers
 Determine if the fraction is less than ½ or equal to or greater than ½
 If it is less than ½- round the fraction to 0
 If it is more than ½- round the fraction to 1
Problem solving key terms
 Addition: in all, altogether, joined, combined, added, total, both, more,
together, sum, increase
 Subtraction: difference, fewer, less than, how many more, how much more,
remains, left over, decreased, take away, minus, -er words (longer, shorter,
smaller, wider, etc.)
 Multiplication: of, twice, each, increased/decreased by a factor of, in all,
multiplied by, times, area, multiple
 Division: per, a, share, distribute, quotient, each, divide equally, equal
pieces, split, separate, cut up, half