In a classroom there are 6/3 graders students and 10/6 graders students express the ratio of third graders to the entry number of students as a fraction
To find the ratio of third graders to the whole number of students in the class, we need to add the number of third graders and sixth graders together.
The number of third graders is 6/3 = 2 (since 6 divided by 3 equals 2).
The number of sixth graders is 10/6 (since 10 divided by 6 equals 1 and a remainder of 4, or 1 and 4/6).
To find the least common multiple of 3 and 6, we can see that 6 is already a multiple of 3. Therefore, the least common multiple is 6.
Multiplying the numerator and denominator of the third graders' fraction by 2 gives us 4/6 instead of 2/6.
So, the number of third graders is 4/6 when expressed with the same denominator as the number of sixth graders.
Adding the number of third graders and sixth graders together gives us 4/6 + 10/6 = (4 + 10)/6 = 14/6.
Therefore, the ratio of third graders to the total number of students is 14/6.
To express the ratio of third graders to the total number of students in the classroom as a fraction, you would need to find the common denominator for 6/3 and 10/6.
The common denominator for 6/3 and 10/6 is 6. To convert 6/3 to have a denominator of 6, you multiply the numerator and denominator by 2, resulting in 12/6. The fraction 10/6 is already in terms of the common denominator.
Now, you can add the fractions together to get the total number of third graders out of the total number of students:
12/6 + 10/6 = 22/6
Therefore, the ratio of third graders to the total number of students in the classroom is 22/6.
To express the ratio of third graders to the total number of students as a fraction, you need to add the number of third graders and the number of sixth graders together to get the total number of students. Then, you can write the ratio of third graders to the total as a fraction by simplifying the fraction if possible.
In this case, let's first add the number of third graders and sixth graders. The classroom has 6/3 graders and 10/6 graders students. To add these fractions, we need to find a common denominator. In this case, the common denominator is 6 because both fractions can be divided evenly by 3.
The fraction 6/3 is equivalent to 2 because 6 divided by 3 equals 2. Similarly, the fraction 10/6 is equivalent to 5/3 because if we multiply the numerator (10) and the denominator (6) by 5, we get 50/30. Simplifying 50/30 gives us 5/3.
Now, let's add these two fractions:
2 + 5/3 = (2 * 3 + 5) / 3 = 11/3
So, the total number of students in the classroom is 11/3.
To express the ratio of third graders to the total number of students, we'll write it as a fraction:
2 / (11/3) = 2 * (3/11) = 6/11
Therefore, the ratio of third graders to the total number of students is 6/11.