Answer:
3/5 has the smallest denominator
Step-by-step explanation:
Question:
There exist infinitely many common fractions a/b , where a > 0 and b > 0 and for which 3/5 < a/b< 2/3. Of these common fractions, which has the smallest denominator? Express your answer as a common fraction.
Solution
A Common fraction is a rational number written in the form: a/b. Where a and b are both integers.
The denominator and numerator in this case are greater than zero. That is, they are non zeros.
The least common denominator (LCD) of two non- zero denominators is the smallest whole number that is divisible by each of the denominators.
To find the smallest denominator between 3/5 and 2/3, we would convert the fractions to equivalent fractions with a common denominator by finding their LCM (lowest common multiple).
When comparing two fractions with like denominators, the larger fraction is the one with the greater numerator and the smaller fraction is one with the smaller numerator.
In our solution after comparing, the smaller fraction would have the smallest denominator.
Find attached the solution.
Answer:
Step-by-step explanation:e equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. ... Another method for solving quadratics is the square root property. The variable is squared.
Answer: the old price for 1 liter is $0.3
Step-by-step explanation:
Let x represent the old price for 1 liter of petrol.
Last week a man bought 20 liters at the old price. This means that the total amount that the man paid for 20 liters is 20x.
The cost of petrol rises by 2 cents a liter. This means that the new price per liter is x + 2/100 = x + 0.02
This week he bought 10 liters at the new price. This means that the total amount that the man paid for 10 liters is
10(x + 0.02)
= 10x + 0.2
Altogether, the petrol costs $9.20. This means that
20x + 10x + 0.2 = 9.2
30x + 0.2 = 9.2
30x = 9.2 - 0.2
30x = 9
x = 9/30
x = 0.3
Answer:
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
(a-b)(a+b) = a^2 - b^2
Step-by-step explanation:
They differ because you can either add the property or multiply
Answer:
X= 5, -9
Step-by-step explanation:
(X+2)² =49
Expand the bracket,
(X+2) (X+2)= 49
Apply the distributive property;
X(X+2) +2 (X+2) =49
X²+2X+2X+4=49
X²+4X+4=49
Move 49 to the left side of the equation;
X²+4X+4-49=0
X²+4X-45=0
Apply Factorisation method;
Consider the form
a²+bx+c=0
Find two numbers whose sum is equal to b and whose product is equal to c.
Comparing with our equation;
B =4 and C =45
We can use 9 and -5, this is because ;
9+(-5)=4 and 9*(-5)= 45.
Replace X +4X-45=0 with (X-5) (X+9)=0
Therefore;
X-5=0
X+9=0
Moving to the left side of the equation;
Therefore X= 5 and -9
