Fractions

Reducing Fractions multiplying Fractions

All fractions must be reduced to lowest terms. Fractions are in lowest terms if the only whole number you can divide both num erator and denominator by is 1 (one). Divide num erator and denominator by the same factor until you have it reduc ed to lowest terms.

Change all mixed numbers to improper fractions. ADDING Fractions Add the whole num bers: if you are working with mixed num bers, add the whole number amounts.

Get a c ommon denominator: Find the LCM of the denominators in the problem.

Reduc e top to bottom or diagonally (it is called CROSS CANCELING).

Multiply num erators, then denominator s.

Reduc e. DIVIDING Fractions

Add the numerators.

Change all fractions to im proper fractions.

Find the reciproc al of the SECOND fraction, which means flip it upside down. What was in the num erator, will now be the denominator, and what was in the denom inator will now be the numer ator.

Reduc e: reduc e your answer, converting to a mixed num ber if nec essary. Converting improper fractions to mixed numbers No answer may be left as a mixed number with an improper fr action -these MUST be conver ted to proper mixed numbers.

Divide the num erator by the denominator.

Multiply the fir st fraction and the new (flipped) second fr action.

The remainder becom es the fraction part of your mixed number.

If nec essary, turn the im proper fraction into a mixed number.

Som etim es when adding fractions, you might get a mixed num ber/ improper fraction com bo. You must change the im proper fraction to a mixed number and combine the whole number am ounts.

If nec essary, reduce the frac tion.

subtracting Fractions GREATEST common factor If you divide both the numer ator and the denominator by the same number, the fraction will not change. You will reduce the fr action by creating an equivalent fraction.

Greatest Common Factor is the number that the numerator and the denominator of the sam e fraction “have in common” - they are both divisible by it. The largest number that both the denominator and the num erator can be divided by is called the Greatest Comm on Factor. Factor

Borr owing: If the sec ond fraction is larger than the first, borrow the amount of the denominator.

Subtract the whole numbers: if you are working with mixed numbers, subtract the whole number amounts. Write that whole number in the answer.

Get a c ommon denominator: Find the LCM of the denominators in the problem

Subtract the num erators. Use the GCF to reduce fr actions! Reduce: reduce your answer, converting to a mixed num ber if nec essary.

LEAST common multiple If you multiply both the numer ator and the denominator by the same num ber, the fraction will not change. You will create an equivalent fraction.

Least Comm on Multiple is the num ber that the denominators of the two frac tions (that you are adding or subtracting) “have in common” it is the product of their multiplication by other numbers. You will find it by looking at the multiplication table. Look at the multiplication table, find all the multiples of each of the denominators. The smallest number that occurs in each line is the L east Comm on Multiple. Multiple

Use the L CM to find a comm on denominator for adding and subtracting fractions!!

Converting mixed numbers to improper fractions Multiply the whole number by the denominator.

Add this to the numerator.

Write the new fraction using the original denominator and new numerator.