Practical Problem: How Fast Can Two Workers Mow a Lawn?
A practical problem compares the rate at which two park workers mow the lawn and asks how much lawn the two can mow in an hour. The question is answered by adding rational expressions.
Subject: fraction
Transcript: . NE IS A LONG TIME EMPLOYEE WHO WORKS QUICKLY. THE OTHER IS A NEW EMPLOYEE WHO TAKES ABOUT TWICE AS LONG TO GET THE JOB DONE. WHAT FRACTION OF THE LAWN
Practical Problem: Homes and Apartments on 100 Acres
is expressed in a system of equations involving fractions and solved using the least common denominator strategy.
Subject: fraction
Transcript: NARRATOR: SYSTEMS WITH FRACTIONS ARE NOT JUST TEXTBOOK PROBLEMS, MANY PRACTICAL PROBLEMS OFTEN INVOLVE FRACTIONS. HERE'S AN EXAMPLE. CITY DEVELOPERS
Practical Problem: How Long it Will Take to do Payroll
A work problem requires finding out how long it will take two workers with different work speeds to complete a task. The process of developing an equation and solving it are detailed.
Subject: fraction
Transcript: THE JOB ALONE. FOR ANGIE, THAT'S 5 HOURS. FOR PAM, IT'S UNKNOWN. SO WE'LL LET X STAND FOR PAM'S HOURS. NOW LET'S FIND THE FRACTION OF WORK EACH EMPLOYEE
Solving an Equation with a Fraction
Most people are more comfortable working with whole numbers than with fractions, so when an equation includes a fraction the first thing to do is get
Subject: fraction
Transcript: WORKING WITH WHOLE NUMBERS THAN WITH FRACTIONS, EVEN IF IT TAKES AN EXTRA STEP OR TWO. SO YOU'LL PROBABLY WANT TO GET RID OF THE DENOMINATOR FIRST THING
Examples of Simplifying Expressions
Expressions that include a negative exponent can be simplified by first rewriting the expression with positive exponents.
Subject: fraction
Transcript: , BOTH BASES HAVE NEGATIVE EXPONENTS. WE CAN MOVE EACH TO THE OPPOSITE PART OF THE FRACTION. WE CAN CHANGE THE SIGN OF THEIR EXPONENTS. IN STANDARD FORM
Some Problems are More Easily Solved Using Two Variables
A practical problem is presented that demonstrates a situation in which two variables and a system of equations is the easiest way to reach a solution.
Subject: fraction
Transcript: . TO SOLVE IT, WE'LL FIRST CLEAR THE FRACTIONS BY MULTIPLYING BOTH SIDES OF THE EQUATION BY 3. SIMPLIFY. SUBTRACT. X EQUALS 2.25. THAT'S THE PRICE OF A
Roots of Variables
Simplifying radicals with cube and other roots and variables.
Subject: fraction
Transcript: RATIO OF THE EXPONENT OVER THE INDEX TO AN INTEGER. WHEN THAT HAPPENS, WE CAN WRITE THE EXPONENT AS A FRACTION. FOR EXAMPLE, THE FOURTH ROOT OF M CUBED IS
Review of Equation-Solving Strategies
Review of three strategies for solving equations.
Subject: fraction
Transcript: OR SUBTRACTING, DO THE ADDING OR SUBTRACTING FIRST. IF THERE ARE ANY FRACTIONS, CLEAR THEM. AND SIMPLIFY EITHER SIDE OF THE EQUATION IF YOU CAN
Review of Ratios
A ratio is a direct comparison between two numbers. A batting average, which is the ratio of a player's hits to the number of times at bat, is calculated.
Subject: fraction
Transcript: DENOMINATOR, WE USUALLY JUST WRITE THE RATIO AS A WHOLE NUMBER, 30 MILES PER HOUR. IN ADDITION TO WRITING RATIOS AS FRACTIONS AND WHOLE NUMBERS, WE CAN ALSO
Practical Problem: Two Solutions for a Work Problem
A practical work problem that requires finding out how long it will take two workers with different work speeds to complete a task is solved using an equation with a rational expression. Two different approaches to finding the solution to this probl...
Subject: fraction
Transcript: IT FIRST BY THINKING ABOUT THE FRACTION OF THE WHOLE JOB EACH EMPLOYEE COMPLETES. WE'LL MAKE A TABLE TO KEEP TRACK OF THE INFORMATION. THERE ARE TWO