Which is the greatest of these fractions: 1/10,2/5,3/8,3/20,3/4?
To compare fractions with different denominators, we need to find a common denominator.
The least common multiple (LCM) of the denominators 10, 5, 8, 20, and 4 is 40.
Now we'll convert each fraction to have a denominator of 40:
1/10 = 4/40
2/5 = 16/40
3/8 = 15/40
3/20 = 6/40
3/4 = 30/40
So the fractions, in order from least to greatest, are:
4/40, 6/40, 15/40, 16/40, 30/40
Therefore, the greatest fraction is 30/40, which simplifies to 3/4.
To find the greatest fraction among 1/10, 2/5, 3/8, 3/20, and 3/4, we need to compare their values.
Let's convert all the fractions to a common denominator to make the comparison easier. The least common multiple (LCM) of 10, 5, 8, 20, and 4 is 40.
1/10 can be multiplied by 4/4 to have a denominator of 40: (1/10) * (4/4) = 4/40
2/5 can be multiplied by 8/8: (2/5) * (8/8) = 16/40
3/8 already has a denominator of 8, so we don't need to make any changes: 3/8
3/20 can be multiplied by 2/2: (3/20) * (2/2) = 6/40
3/4 can be multiplied by 10/10: (3/4) * (10/10) = 30/40
Now we can compare the fractions:
- 4/40
- 16/40
- 3/8
- 6/40
- 30/40
From the above fractions, 30/40 is the greatest fraction.
Therefore, the greatest fraction among 1/10, 2/5, 3/8, 3/20, and 3/4 is 30/40.
To determine which fraction is the greatest among 1/10, 2/5, 3/8, 3/20, and 3/4, you can compare them by converting them into a common denominator and then comparing the resulting numerators.
The common denominator you can use in this case is 40 because it is the smallest number that all the denominators divide into. To convert each fraction into a denominator of 40, you multiply the numerator and denominator by the same value.
1/10 can be converted to (1/10) * (4/4) = 4/40.
2/5 can be converted to (2/5) * (8/8) = 16/40.
3/8 remains the same since its denominator is already 8.
3/20 can be converted to (3/20) * (2/2) = 6/40.
3/4 can be converted to (3/4) * (10/10) = 30/40.
Now that all fractions have the same denominator of 40, you can compare the numerators to determine the greatest fraction:
4/40, 16/40, 3/8, 6/40, and 30/40.
From the numerators, you can see that the fraction 30/40 is the greatest since 30 is the largest value among 4, 16, 3, 6, and 30.
Therefore, the greatest fraction among 1/10, 2/5, 3/8, 3/20, and 3/4 is 30/40.