1/2 + 2/5
To add 1/2 and 2/5, we need to find a common denominator. The smallest number that both 2 and 5 can divide into is 10.
1/2 = 5/10
2/5 = 4/10
Now we can add the fractions:
5/10 + 4/10 = 9/10
Therefore, 1/2 + 2/5 = 9/10.
The partial table below shows the fraction of fish in Kathy's tank of different types.
Type of fish Fraction of total
Tetras
1
6
6
1
start fraction, 1, divided by, 6, end fraction
Guppies
2
5
5
2
start fraction, 2, divided by, 5, end fraction
Goldfish
1
4
4
1
start fraction, 1, divided by, 4, end fraction
…
…dots
…
…dots
What fraction of Kathy's fish are either tetras or guppies?
of the fish
To find the fraction of Kathy's fish that are either tetras or guppies, we need to add the fractions for each type of fish and then simplify.
Fraction of tetras: 1/6 + 1/6 = 2/6 = 1/3
Fraction of guppies: 2/5 + 2/5 = 4/5
To combine these fractions, we need to find a common denominator. The smallest number that both 3 and 5 can divide into is 15.
Fraction of tetras: 5/15
Fraction of guppies: 12/15
Now we can add the fractions:
5/15 + 12/15 = 17/15
This fraction is greater than 1, which means it needs to be simplified. We can divide the numerator and the denominator by the greatest common factor, which is 1.
17/15 = 1 and 2/15
Therefore, the fraction of Kathy's fish that are either tetras or guppies is 1 and 2/15.
To add fractions, you need to have a common denominator. The common denominator is the smallest number that both denominators can evenly divide into.
In this case, the denominators are 2 and 5. The smallest number that both 2 and 5 can divide into is 10.
To convert the fractions to have a denominator of 10, you need to adjust the numerators accordingly.
For the first fraction, 1/2, we need to multiply both the numerator and denominator by 5 to get a denominator of 10. This gives us (1*5)/(2*5) = 5/10.
For the second fraction, 2/5, we need to multiply both the numerator and denominator by 2 to get a denominator of 10. This gives us (2*2)/(5*2) = 4/10.
Now that both fractions have the same denominator, we can add them:
5/10 + 4/10 = (5+4)/10 = 9/10.
Therefore, the sum of 1/2 + 2/5 is 9/10.