RECORDED CLASSESMATH 201 FRACTIONS Division unsolved for simplicity parts of a whole between integers can be expressed as decimals Fractions allow for more accuracy. Decimals round up or down. small values lost or gained Fractions don’t round small values. numerator number on top denominator number on bottom rational numbers Common denominator to add or subtract multiplicative inverses reciprocals a over b (a/b) and b over a (b/a) product of 1 The numerator switches with the denominator. |
INDEX MATH 201 1. Fractions 444 2. Adding Fractions 333 3. Subtracting Mixed Numbers 333 4. Multiplying Fractions 333 5. Dividing Fractions 333 multiply fractions top by top bottom by bottom cross cancel common factors divide fractions find the inverse and multiply Reduce top and
bottom by common factors When top and bottom have multiple terms Solve top and
bottom before you divide |
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ADDING FRACTIONS Meaning Clusters
only the numerators change
in value. Denominators must share a
common value. 1/5 + 2/5 = (1 + 2)/5 = 3/5 If the fractions have different denominators find the lowest common
denominator. 1/2 + 1/3 Often the lowest number divisible by both denominators will
be their product. 2 x 3 = 6 Express both numbers as fractions with 6 as
their denominator. Any number multiplied by 1 maintains
it’s value. 1/2 x 1 = 1/2 Any number divided by itself equals
1. 3/3 = 1 Multiply the denominator and the numerator by whatever number results in
a common denominator. 1/2 = 1/2 x 1 = 1/2 x 3/3 = (1 x 3)/(2 x 3) = 3/6 1/3 = 1/3 x 1 = 1/3 x 2/2 = (1 x 2)/(3 x 2) = 2/6 |
Add the numerators. 3/6 + 2/6 = (3 +2)/6 = 5/6 MEMORY
TRIGGERS TESTS ______adding_______________________ ___________________________________ Denominators_______________________
________fractions____________________ ___________________________________ ___________lowest___________________ ___________________________________ _______________divisible_____________ Speed Learning format by
Carl Peterson ©2005 |
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SUBTRACTING MIXED NUMBERS Meaning Clusters You bake 47 muffins and store them in
plastic bags. The bags hold 10 muffins each. Use mixed numbers to represent the amount of
muffin bags. 47 ÷ 10 = 47/10
= 4 7/10 You will completely fill
4 bags. Another bag will only have 7 muffins. You want to take 19 muffins to
school. How many bags will
you need? 19 ÷ 10 = 19/10
= 1 9/10 You need 2
bags. 1 will be
full. 1 will have 9 muffins. To find out how many bags you leave at
home change the
mixed numbers into improper fractions. Improper
fraction numerators
have greater
values than their denominators. 47/10
– 19/10 = 28/10 |
Convert the improper fraction into
a mixed number. 28/10 = 2 8/10 You
will need 3
bags. 2
will be full and
1 will have 8 muffins. MEMORY
TRIGGERS TESTS _______mixed numbers_______________ ___________________________________ ____________bag____________________
_________________muffins____________ ___________________________________ ________________need_______________ ___________________________________ __________________9________________ Speed Learning format by
Carl Peterson ©2005 |
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MULTIPLYING FRACTIONS Meaning Clusters Unlike adding and subtracting, multiplying fractions does not require a
common denominator. Multiply the terms in both numerators to calculate the numerator of
the product. 5/6
× 3/10 5 × 3 = 15 Multiply the terms in both denominators to calculate the denominator of
the product. 6 × 10 = 60 5/6
× 3/10 = (5 × 3)/(6 × 10) = 15/60 The numerator and denominator of the product divide
by 15. Reduce the fraction. (15/15)/(60/15)
= (1)/(4) = 1/4 You may also cross-cancel the terms at
the beginning. 5/6
× 3/10 The numerator of the first
term and the
denominator of the second
term divide by 5. 5/6
× 3/10 = 1/6 × 3/2 |
The denominator of the first term and the numerator of the second term divide
by 3. 1/6
× 3/2 = 1/2 × 1/2 Multiply the fraction 1/2
× 1/2 = (1 × 1)/(2 × 2) = 1/4
MEMORY
TRIGGERS TESTS Multiply____________________________ ___________________________________ _______________terms_______________
_______denominator_________________ ___________________________________ ____________________product________ ___________________________________ |
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DIVIDING FRACTIONS Meaning Clusters Divide the fractions 1/2
and 2/3. 1/2
÷ 2/3 Find the reciprocal of the fraction on the right side of
the division sign. When a term is multiplied by it’s reciprocal the product will equal
1. 2/3x
= 1 Multiply both sides by
3/2. 2/3(3/2)x
= 1(3/2) x = 3/2 You can also find a
reciprocal by switching
the terms in the
numerator and denominator. The reciprocal of 2/3
is 3/2. The 2 becomes
the
denominator and the 3
becomes the numerator. Division is the inverse
function of multiplication. Replace the
factor by which you
divide with it’s
reciprocal and multiply. 1/2
÷ 2/3 = 1/2 × 3/2
1/2
× 3/2 = (1 × 3)/(2 × 2)
= 3/4 |
MEMORY
TRIGGERS TESTS Divide______________________________ ___________________________________ _______________reciprocal____________
_________term______________________ ___________________________________ 2/3x________________________________ ___________________________________ ___________________________________ |