Practical Problem: Finding Average Speed
Complex fractions often appear in formulas used to solve problems. A practical problem involving the rate, time, and distance formula illustrates working with complex fractions.
Subject: cancel
Transcript: IS THE DENOMINATOR OF THE COMPLEX FRACTION. NOW WE CAN REDUCE THE COMPLEX FRACTION. WE CAN CANCEL THE D'S IN THE NUMERATOR AND DENOMINATOR. NEXT
Practical Problem: Finding the Speed of the Wind
A practical problem involving two airplanes requires finding their true speed after factoring in wind speed. The rate, time, and distance formula is used to solve the problem.
Subject: cancel
Transcript: MINUS W TIMES 375 PLUS W. WE'LL MULTIPLY BOTH SIDES OF THE EQUATION BY THESE TWO BINOMIALS. N THE LEFT SIDE OF THE EQUATION, WE CAN CANCEL 400 MINUS W
Practical Problem: Finding Volume
A practical problem about volume is solved using division of a rational expression.
Subject: cancel
Transcript: 'S SEE WHAT WE CAN CANCEL. THE 3'S CANCEL, SO DOES PI, AND R CUBED. 32 AND 4 HAVE A COMMON FACTOR OF 4. AFTER CANCELING, WE GET 8. SO 8 IS THE ANSWER. THE
Multiplying by the Least Common Denominator to Get a Quadratic Equation
The steps involved in solving an equation by multiplying by the least common denominator to get a quadratic equation and checking the solution are detailed.
Subject: cancel
Transcript: 8. SO WE'LL MULTIPLY EACH SIDE OF THE EQUATION BY THESE FACTORS. N THE LEFT SIDE, WE'LL BEGIN BY MULTIPLYING THEM BY 3/X. THE X'S CANCEL. THAT LEAVES
Solving an Equation with the Least Common Denominator: Practice Problem
A problem is presented to practice solving an equation using the least common denominator to get a quadratic equation.
Subject: cancel
Transcript: 'S CANCEL. THE RESULT IS 18 TIMES X MINUS 4. NEXT, MULTIPLY THE LEAST COMMON DENOMINATOR BY 3 OVER X MINUS 4. THE X MINUS 4'S CANCEL. WE GET 27 TIMES X
Practical Problem: Machines Working at Different Speeds
The procedure for developing an equation to solve a practical work problem involving machines working at different speeds is detailed. The unknown is identified and an equation is written, solved, and checked.
Subject: cancel
Transcript: FACTORS. WE'LL START ON THE LEFT SIDE. WHEN WE MULTIPLY THE LEAST COMMON DENOMINATOR BY 1/X, WE CANCEL THESE X'S. THEN WE HAVE 8 TIMES X MINUS 3. WHEN WE
Dividing Rational Expressions: Two Practice Problems
Practice problems for dividing rational expressions.
Subject: cancel
Transcript: FACTORS OF THE DENOMINATOR ARE M AND M MINUS 5. NEXT WE'LL CANCEL. WE'LL CANCEL THE M MINUS 5'S. WE CAN ALSO CANCEL THE M PLUS 6'S. IN THE SECOND EXPRESSION
Dividing Rational Expressions
The procedure for dividing rational expressions is demonstrated.
Subject: cancel
Transcript: 'LL MULTIPLY 5/6 BY 2/15. NCE WE HAVE A MULTIPLICATION PROBLEM, WE CAN CANCEL. 5 AND 15 HAVE A COMMON FACTOR OF 5, SO WE CAN CANCEL HERE. 2 AND 6 HAVE A COMMON
Equation That Has No Solution, An
An equation is found to have no solution after using the least common denominator to get a quadratic equation.
Subject: cancel
Transcript: 'LL MULTIPLY BOTH SIDES OF THE EQUATION BY 5X SQUARED. N THE LEFT SIDE, WE'LL BEGIN BY MULTIPLYING 5X SQUARED BY 2/X. WE'LL CANCEL AN X HERE. 5X TIMES 2 IS 10X
Equation with Rational Expressions: Practice Problem
A problem to practice solving a equations with a rational expression.
Subject: cancel
Transcript: . MULTIPLY THE FIRST TERM ON THE LEFT SIDE OF THE EQUATION. THAT'S 2X TIMES 6, OR 12X. WE ALSO HAVE 2X TIMES 3 OVER 2X. THE 2X'S CANCEL. THE RESULT IS 3. SO