y varies directly as the reciprocal of x
The reciprocal of x is written as:
1/x
The phrase varies directly means there exists a constant k such that
y = k/x
product of a number and its reciprocal is increased by 7
The phrase a number means an arbitrary variable, let's call it x:
x
Its reciprocal means we take the reciprocal of x:
1/x
product of a number and its reciprocal:
x * 1/x
x/x
The x's cancel giving us:
1
is increased by 7 means we add...
How many 1/4 sheets are there in 5 sheets
We divide 5 sheets by 1/4 sheets:
5/1/4
However, when we divide by a fraction, it's the same as multiplying by the reciprocal of the fraction:
The reciprocal of 1/4 is 4/1, so we have:
5 * 4/1 = 20/1 = 20
Ande has 8 pints of milk. If he drinks 1/4 of a pint of milk each day, how long will the 8 pints of milk last him?
Milk Days = Total Pints of Milk / pints drank per day
Milk Days = 8 / 1/4
Dividing by a fraction is the same as multiplying by it's reciprocal.
The reciprocal of 1/4 is 4/1, so...
M is the sum of a and its reciprocal
The reciprocal of a variable is 1 divided by the variable
1/a
The sum of a and its reciprocal means we add:
a + 1/a
The phrase is means an equation, so we set M equal to the sum of a + 1/a:
M = 1 + 1/a
How many one-fifths are there in 200?
Using the rule of dividing by a fraction is the same as multiplying by the reciprocal, we have:
200 / 1/5 = 200 * 5 = 1000
the sum of the reciprocal of x and the reciprocal of y
Reciprocal of x means 1 over x:
1/x
Reciprocal of y means 1 over y:
1/y
The sum means we add the two reciprocals together:
1/x + 1/y
The sum of the reciprocals of x and y
The reciprocal of a variable is found by taking 1 over the variable.
Reciprocal of x = 1/x
Reciprocal of y = 1/y
The sum means we add the reciprocals together
1/x + 1/y
The square of a number added to its reciprocal
The phrase a number means an arbitrary variable, let's call it x.
the square of x mean we raise x to the power of 2. It's written as:
x^2
The reciprocal of x is 1/x
We add these together to get our final algebraic expression:
x^2 + 1/x
the reciprocal of the product a and b
Take this algebraic expression in pieces:
The product a and b means we multiply a times b
ab
The reciprocal means we take 1 over ab
1/ab
5 more than the reciprocal of a number
Take this algebraic expression in pieces:
The phrase a number means an arbitrary variable, let's call it x.
x
The reciprocal of this number means we divide 1 over x:
1/x
5 more means we add 5 to 1/x
1/x + 5