Exponents
Rational Expressions
Rules, Terms, & Concepts
Word Problems
Potpouri
100
(-3 x 5^-1)^-2
25 / 9
100
[x / (x - 1)] - [1 / (x + 1)]
(x^2 + 1) / (x-1)(x+1)
100
m x 10^n
Scientific Notation
100
12 is 3/5 of 10/21 of the number. Find the number
The number is 42.
100
0.560x10^-3
5.60x10^-4
200
(-5x3^-2)^-2
3.24
200
[(x-y)^-1] - [(x+y)^-1]
2y / (x+y)(x-y)
200
(p/q) / (r/s) = (p/q) x (s/r)
Division Rule for Fractions
200
The reciprocal of half a number increased by half the reciprocal of the number is 1/2. Find the number.
The number is -3.
200
7.50 x 10^-3
0.00750
300
4x^3y^-6 + (x^-1y^2)^-3
5x^3/y^6
300
ax+by-bx-ay/ax-by+bx-ay
(a-b)/(a+b)
300
(pr/qr) = (p/q)
Rule for Simplifying Fractions
300
Elvin drove halfway from Ashton to Dover at 40mph and the rest of the way at 60mph. What was his average speed for the whole trip. (HINT: Let the distance for the whole triple, say, 100 miles.)
Elvin's speed was 48 mph.
300
(y^2 - 4) / (y^2 + y - 6)
(y+2) / (y+3)
400
3x^2(3xy^-1)^-2
y^2 / 3
400
(r^2 - 5r + 4)(r - 4)^-2
(r-1) / (r-4)
400
(p/q) x (r/s) = (pr/qs)
Multiplication Rule for Fractions
400
The county's new asphalt paving machine can surface 1km of highway in 10hr. A much older machine can surface 1km of asphalt in 18hr. How long will it take them to surface 21km of highway if they start at opposite ends and work day and night?
It will take the machine 135 hours.
400
A town's old street sweeper can clean the streets in 60hr. The old sweeper together with the new sweeper can clean the streets in 15hr. How long would it take the new sweeper to do the job alone?
It would take the new sweeper 20 hours to do the job alone.
500
Show by counterexample that the given expressions are NOT equivalent. (HINT: let x=1 and y=2) (x+y)^-1 and (x^-1) + (y^-1)
1/3 DOES NOT EQUAL 3/2
500
(a^4 + 2a^2b^2 + b^4) / (a^4 - b^4) x (a - b)
(a^2 + b^2) / (a + b)
500
!!!!!DAILY DOUBLE!!!!! He introduced techniques for solving equations, finding sums of arithmetic series, and solving linear systems. His use of the zero symbol is a milestone in Chinese mathematics.
Ch'in Chiu-Shao (page 220)
500
A train averaged 120 km/hr for the first two thirds of a trip and 100 km/hr for the whole trip. Find its average speed for the last third of the trip.
The average speed was 75 km/hr.
500
The rail line between two cities consists of two segments, one is 96km longer than the other. A passenger train averages 60km/hr over the shorter segment, 120km/hr over the longer, and 100km/hr for the entire trip. How far apart are the cities?
The cities are 160 kilometers apart.
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