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If the numerator of a fraction is zero?
If the denominator is zero?
If the numerator of a fraction is zero, ␣that fraction equals zero.
If the denominator of a fraction is zero, that fraction is considered ‘undefined’. E.g. the fraction 03 = 0, but the fraction 30 = undefined.
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How do you divide fractions?
Flip and Multiply! – To divide two fractions, flip the second fraction, and multiply the two together.
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Simple vs. Complex fractions:
- 1. Terms can only be cancelled within simple fractions. Terms within complex fractions can never be cancelled!
- 2. It can be useful to remember that complex fractions contain a shortcut: the numerator of a complex fraction can always be split!
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What is a reciprocal?
Reciprocals – Any two numbers whose product equals 1 are known as reciprocals.
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What do i do with fractions within fractions?
To simplify any fraction that contains a fraction within its numerator and/or denominator, always multiply the numerator by the “flip” of the denominator!
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Properties of Fractions
1.Increasing the numerator increases the value of the fraction
2. while the increasing the denominator decreases the value of the fraction:
- 3. Increasing the numerator and the denominator by the same amount brings the value of a
- fraction closer to l
- 4. while decreasing the numerator and the denominator by the same amount
- moves the value of a fraction away from 1.
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Properties of Zero
– If the numerator of a fraction is zero, that fraction equals zero. If the denominator of a fraction is zero, that fraction is considered undefined.
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Proper Fractions
: 0 < xy < 1 – Any fraction whose numerator is smaller than its denominator is known as a proper fraction.
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If I multiply a proper fraction by a whole number?
always yields a product smaller than the original number.
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What if I square a fraction?
Squaring any whole number always yields a product equal to or larger than the original number.
Squaring any proper fraction, however, always yields a product smaller than the original number.
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When I divide a number by a fraction?
Dividing any number by a whole number always yields a quotient equal to or smaller than the original number.
Dividing any number by a proper fraction, however, always yields a quotient larger than the original number.
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If I take the square root of a fraction?
Taking the square root of any whole number always yields a root equal to or smaller than the original number.
Taking the square root of a proper fraction, however, always yields a root larger than the original number.
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How do I compare two fractions?
Cross-Multiplying • The easiest way to compare any two fractions is to cross-multiply their numerators and denominators. Multiply from the bottom up, and write each product over the corresponding numerator, as shown below: - • The fraction under the larger product will always be larger
- Approximating
- • If the numerators and denominators of a given fraction are too large to multiply easily, identify approximateequivalentsthatareeasytoworkwith,suchas 41, 13, 12, 23,and 43.
Converting to decimals
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Converting to decimals
Value of 1/3
= 1.333
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Converting to decimals
Value of 1/6
= .166666
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Converting to decimals
Value of 1/7
=~ .14
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Converting to decimals
Value of 1/8
=.125
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Converting to decimals
Value of 1/9
=.11111
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Converting to decimals
Value of 1/11
= 0.09999999
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Converting to decimals
Value of 1/99
= 0.011111
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