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Fraction Reminders:
 Improper fraction = numerator > denominator
 Mixed number = whole number and a fraction [ 3½ ]
 Always reduce whenever possible.
 Any number on top of itself (the same number) = one whole [ 1 ]
2/2 = 1
23/23 = 1
234/234 = 1
x/x = 1
 When you subtract, you must rename 1 as a fraction.
1 = 2/2
1 = 3/3
1 = 4/4
1 = 5/5
1 = 6/6
1 = 7/7
 Borrowing: Break down whole numbers into smaller, equivalent mixed numbers.
4 = 32/2 or 39/9 etc.
9 = 86/6 or 824/24
Mixed Number ~> Improper Fraction
1. Multiply the denominator and the
whole number.
2. Add the numerator.
3. This answer is the new numerator.
4. Denominator remains the same.
Improper Fraction ~> Mixed Number
1. Divide the numerator by the
denominator (numerator under
2. The whole number is the quotient
(number on top of the bridge).
3. Numerator is the remainder.
4. Denominator is the divisor (number
outside the bridge).
Least Common Denominator (LCD)
1. List multiples of each denominator.
a. Circle the smallest number that appears on both lists. This is the
b. Write equivalent fractions, using the LCM as the denominator.
1. Use each denominator as a multiplier for the other fraction.*
a. Multiply the first fraction (numerator and denominator) with the
second fraction’s denominator.
b. Multiply the second fraction (numerator and denominator) with the
first fraction’s denominator.
*Using this method will cause you to reduce more often at the conclusion of
the problem.
1. Use prime factorization to find the LCM.
a. Find the prime factorization of each number.
b. Circle the greatest power of every prime factor that appear in any of
the prime factorizations.
c. Multiply the circled powers to find the LCM.
From the Classroom of Mr. Meisel
2. Write equivalent fractions.
(new denominator = original denominator x original denominator)
Add Fractions
1. Find the Least Common Denominator (LCD) and write the equivalent
2. Add the numerators.
3. Denominator stays the same.
4. Add the whole numbers.
5. Convert improper fraction into mixed number. Remember to add the whole
numbers together before you finished!
6. Simplify (reduce to lowest terms if possible).
Subtracting Fractions
1. Find the Least Common Denominator (LCD).
2. Subtract the numerators; if you cannot subtract rename the fraction
a. If the numerator is too small to subtract from the other numerator,
you must borrow from the whole number, then subtract the
i. Borrowing from a whole number
1. Change the whole number into an equivalent mixed
number. See “Fraction Reminders” above.
2. Add this fraction to your original fraction that you are
borrowing for (not the whole number; just add the
3. Denominator stays the same.
4. Subtract the whole numbers.
5. Simplify (reduce to lowest terms if possible).
Multiply Fractions
1. Put whole numbers on top of 1
2. Change mixed numbers into improper fractions.
3. Cross cancel (if possible).
*cross cancel in the beginning or REDUCE at the end!
4. Multiply across.
a) numerator x numerator
b) denominator x denominator
5. Change improper fraction to mixed number.
6. Reduce to simplest form.
From the Classroom of Mr. Meisel
Divide Fractions
1. Find the reciprocal
a. Re-write the first fraction
b. Flip the sign (  to  )
c. Flip the second fraction (numerator becomes denominator;
denominator becomes numerator)
2. Multiply (see steps above)
From the Classroom of Mr. Meisel