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- https://math.libretexts.org/Courses/Highline_College/Math_081_091%3A_CAM_Aligned_Textbook/03%3A_Fractions_Decimals_and_Percentages/3.04%3A_Fraction_DivisionThe reciprocal of the fraction a/b is b/a, where a ≠ 0 and b ≠ 0. A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, we invert the fraction. This means that we pla...The reciprocal of the fraction a/b is b/a, where a ≠ 0 and b ≠ 0. A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator. To divide fractions, multiply the first fraction by the reciprocal of the second.
- https://math.libretexts.org/Courses/Highline_College/Math_081%3A_Introduction_to_Algebra/03%3A_Fractions/3.05%3A_Multiply_and_Divide_Fractions_(Part_2)The reciprocal of the fraction a/b is b/a, where a ≠ 0 and b ≠ 0. A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, we invert the fraction. This means that we pla...The reciprocal of the fraction a/b is b/a, where a ≠ 0 and b ≠ 0. A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator. To divide fractions, multiply the first fraction by the reciprocal of the second.
- https://math.libretexts.org/Workbench/Book-_Precalculus_I_for_Highline_College_w/Rational_Inequalities_and_Equations_of_Circles/1.07%3A_Trigonometric_Identities_and_Equations/1.7.02%3A_Solving_Trigonometric_Equations_with_IdentitiesIn this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions.
- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/07%3A_Trigonometric_Identities_and_Equations/7.02%3A_Solving_Trigonometric_Equations_with_IdentitiesIn this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions.
- https://math.libretexts.org/Courses/Santiago_Canyon_College/HiSet_Mathematica_(Lopez)/07%3A_Introduccion_a_las_Fracciones_y_Multiplicacion_y_Division_de_Fracciones/7.05%3A_Division_de_Fracciones\(\dfrac{\begin{array} {c} {^1} \\ {\cancel{7}} \end{array}}{\begin{array} {c} {\cancel{8}} \\ {^2} \end{array}} \cdot \dfrac{\begin{array} {c} {^{^1}} \\ {^{\cancel{5}}} \\ {\cancel{20}} \end{array}}...\(\dfrac{\begin{array} {c} {^1} \\ {\cancel{7}} \end{array}}{\begin{array} {c} {\cancel{8}} \\ {^2} \end{array}} \cdot \dfrac{\begin{array} {c} {^{^1}} \\ {^{\cancel{5}}} \\ {\cancel{20}} \end{array}}{\begin{array} {c} {\cancel{21}} \\ {^{\cancel{3}}} \\ {^{^1}} \end{array}} \dfrac{\begin{array} {c} {^1} \\ {\cancel{3}} \end{array}}{\begin{array} {c} {\cancel{35}} \\ {^7} \end{array}} = \dfrac{1 \cdot 1 \cdot 1}{2 \cdot 1 \cdot 7} = \dfrac{1}{14}\)
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/07%3A_Trigonometric_Identities_and_Equations/7.01%3A_Solving_Trigonometric_Equations_with_IdentitiesIn this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_165_College_Algebra_MTH_175_Precalculus/06%3A_Analytic_Trigonometry/6.03%3A_Verifying_Trigonometric_IdentitiesIn this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions.
- https://math.libretexts.org/Courses/Las_Positas_College/Foundational_Mathematics/04%3A_Fractions/4.05%3A_Multiply_and_Divide_Fractions_(Part_2)The reciprocal of the fraction a/b is b/a, where a ≠ 0 and b ≠ 0. A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, we invert the fraction. This means that we pla...The reciprocal of the fraction a/b is b/a, where a ≠ 0 and b ≠ 0. A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, we invert the fraction. This means that we place the numerator in the denominator and the denominator in the numerator. To divide fractions, multiply the first fraction by the reciprocal of the second.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/02%3A_Logic_and_Quantifiers/2.03%3A_Logical_EquivalencesSome logical statements are “the same.” For example, we discussed the fact that a conditional and its contrapositive have the same logical content. However, the equals sign (=) has already got a job...Some logical statements are “the same.” For example, we discussed the fact that a conditional and its contrapositive have the same logical content. However, the equals sign (=) has already got a job; it is used to indicate that two numerical quantities are the same. The formal definition of logical equivalence is two compound sentences are logically equivalent if in a truth table, the truth values of the two sentences are equal in every row. Thus, we use the symbol (≅) instead.
- https://math.libretexts.org/Courses/Barton_Community_College/Book%3A_Technical_Mathematics_(Turner)/02%3A_Fractions/2.04%3A_Dividing_Fractions\[ \begin{aligned} - \frac{6}{35} \div \frac{33}{55} = - \frac{6}{35} \cdot \frac{55}{33} ~ & \textcolor{red}{ \text{ Invert the divisor (second number).}} \\ = - \frac{6 \cdot 55}{35 \cdot 33} ~ & \t...\[ \begin{aligned} - \frac{6}{35} \div \frac{33}{55} = - \frac{6}{35} \cdot \frac{55}{33} ~ & \textcolor{red}{ \text{ Invert the divisor (second number).}} \\ = - \frac{6 \cdot 55}{35 \cdot 33} ~ & \textcolor{red}{ \text{ Multiply numerators; multiply denominators.}} \\ = - \frac{(2 \cdot 3) \cdot (5 \cdot 11)}{(5 \cdot 7) \cdot (3 \cdot 11)} ~ & \textcolor{red}{ \text{ Factor numerators and denominators.}} \\ = - \frac{2 \cdot \cancel{3} \cdot \cancel{5} \cdot \cancel{11}}{ \cancel{5} \cdot 7 …
- https://math.libretexts.org/Courses/Coastline_College/Math_C120%3A_Trigonometry_(Tran)/03%3A_Trigonometric_Identities_and_Equations/3.02%3A_Solving_Trigonometric_Equations_with_IdentitiesIn this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions.
