2/(2/3)+3/4/(4/5)=
The answer key explains it like this:
2/(2/3)+3/(3/4)+4/(4/5)=2x3/2+3x4/3+4x5/4= 3+4+5=12
*I do not understand how the answer is 12.
If 2/5 of (2/3)/(5/6) is divided by 3/10, what is the resulting value?
The answer key explains it like this:
2/5((2/3)/(5/6))/3/10=2/5x2/3x6/5x10/3=8/15
I do not understAnd why the answer is 8/15.
Well, your original line of text is not the same as the answer key's explanation.
I assume you get 3+4+5=12
Now, 2/(2/3) = 2*(3/2) = 2
when you divide by a fraction, it's the same as multiplying by its reciprocal.
In fact, when you divide by anything, it's the same as multiplying by its reciprocal. 2/3 = 2(1/3)
1. 2/(2/3) + 3/4/(4/5).
2/(2/3) + (3/4)/(4/5) =
2*(3/2) + (3/4)*(5/4) =
6/2 + 15/16 =
48/16 + 15/16 = 63/16
2. (2/5)(2/3)/(5/6)/(3/10) =
(2/5)(2/3)(6/5)(10/3) = 240/225 = 48/45 = 16/15.
The answer cannot be less than one.
To understand how to get the answer to the first equation, let's break it down step by step:
First, we simplify the expression within the parentheses: (2/3) divided by (4/5).
Dividing fractions is the same as multiplying by the reciprocal of the second fraction, so we have: (2/3) x (5/4).
Next, we multiply the fractions: (2x5)/(3x4) = 10/12.
Now, we add this result to the first fraction: 2/(2/3) + 10/12.
Simplifying the first fraction in the expression, we multiply by the reciprocal: 2 x (3/2) = 3.
Finally, we add the two fractions together: 3 + 10/12.
To add fractions, we need a common denominator. In this case, the least common denominator is 12.
Converting the fraction 3 to have a denominator of 12, we get 36/12.
Now we can add the fractions: 36/12 + 10/12 = 46/12.
Simplifying the fraction, we divide the numerator and denominator by their greatest common divisor, which is 2: (46/2)/(12/2) = 23/6.
So, the final answer to the first equation is 23/6, not 12.
Now, let's move on to the second equation:
We have the fraction 2/5 of (2/3)/(5/6), divided by 3/10.
First, we simplify the expression within the parentheses: (2/3) divided by (5/6).
To divide fractions, we multiply by the reciprocal: (2/3) x (6/5).
Then, we multiply the fractions: (2x6) / (3x5) = 12/15.
Next, we multiply this result by 2/5: (2/5) x (12/15).
Multiplying the fractions gives us (2x12) / (5x15) = 24/75.
Finally, we divide this fraction by 3/10.
Dividing fractions is the same as multiplying by the reciprocal, so we have: (24/75) x (10/3).
Multiplying these fractions gives us (24x10) / (75x3) = 240/225.
To simplify the fraction, we divide the numerator and denominator by their greatest common divisor, which is 15: (240/15) / (225/15) = 16/15.
Therefore, the resulting value of the second equation is 16/15, not 8/15.
It seems there might be errors in the given answer key explanations.