Sonia had shells of three different sizes .4/9 of the shells were big and 2/5 of the remainder were medium sized .the rest of the shells were small .what fraction of the shells were small?
same old same old
no ideas?
See your last post.
To find the fraction of shells that were small, let's break down the problem step-by-step:
Step 1: Determine the fraction of shells that were big.
Given that 4/9 of the shells were big, this means that 4/9 of the total shells were big.
Step 2: Determine the remainder after the big shells.
To find the remainder after the big shells, we subtract the fraction of big shells (4/9) from 1 (whole). This can be expressed as 1 - 4/9.
1 - 4/9 = 9/9 - 4/9 = 5/9.
Therefore, the remainder after the big shells is 5/9.
Step 3: Determine the fraction of shells that were medium-sized.
Given that 2/5 of the remainder after the big shells were medium-sized, this means that 2/5 of 5/9 were medium-sized.
2/5 * 5/9 = 10/45.
Therefore, the fraction of shells that were medium-sized is 10/45.
Step 4: Determine the fraction of shells that were small.
To find the fraction of shells that were small, we subtract the fractions of big and medium-sized shells from 1 (whole). This can be expressed as:
1 - 4/9 - 10/45
To add and subtract fractions, we need a common denominator. The least common multiple (LCM) of 9 and 45 is 45.
Rewriting the fractions with the common denominator of 45:
(45/45) - (20/45) - (10/45) = 15/45.
Therefore, the fraction of shells that were small is 15/45, which can be simplified to 1/3.
In conclusion, 1/3 of the shells were small.
To find the fraction of shells that are small, let's break down the given information step by step.
First, we know that 4/9 of the shells are big. This means that 5/9 of the shells are not big (9/9 - 4/9 = 5/9).
Next, we are told that 2/5 of the remaining shells (5/9) are medium-sized. To calculate this, we multiply 5/9 by 2/5, which gives us (5/9) * (2/5) = 10/45. Therefore, 10/45 of the shells are medium-sized.
Now, let's calculate the fraction of shells that are small. To do this, we need to find the remaining portion of shells after accounting for the big and medium-sized shells.
We already determined that 4/9 of the shells are big and 10/45 are medium-sized. If we add these together, we get (4/9) + (10/45).
To calculate this sum, we need to find a common denominator for 9 and 45, which is 45. We can rewrite 4/9 as (4/9) * (5/5) to have the same denominator: (4/9) * (5/5) = 20/45.
Now we can add 20/45 (the big shells) to 10/45 (the medium-sized shells): (20/45) + (10/45) = 30/45.
Finally, we reduce the fraction 30/45 to its simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 15: (30÷15)/(45÷15) = 2/3.
Therefore, the fraction of shells that are small is 2/3.