Add each of the following. Write answer as a simplified improper fraction.
1. 3/25 + 8/35 = 61/175
2. 5 1/4 + 3 5/12 = 26/3
3. -4 1/2 + 2 2/3 = -19/6
3. -11/6
the rest are correct.
Add −12/7+(3/14). Write your answer as a reduced improper fraction.
To add fractions, you need to have a common denominator. Follow these steps to solve each addition problem:
1. 3/25 + 8/35:
- Find the least common denominator (LCD) for 25 and 35. In this case, the LCD is 175.
- Rewrite each fraction with the LCD as its denominator:
3/25 becomes (3 * 7)/(25 * 7) = 21/175
8/35 becomes (8 * 5)/(35 * 5) = 40/175
- Now add the numerators:
21/175 + 40/175 = 61/175
So the answer is 61/175.
2. 5 1/4 + 3 5/12:
- Start by converting the mixed numbers into improper fractions:
5 1/4 becomes (5 * 4 + 1)/4 = 21/4
3 5/12 becomes (3 * 12 + 5)/12 = 41/12
- Find the LCD for 4 and 12, which is 12.
- Rewrite each fraction with the LCD as its denominator:
21/4 becomes (21 * 3)/(4 * 3) = 63/12
41/12 remains the same
- Now add the numerators:
63/12 + 41/12 = 104/12
- Simplify the fraction if possible. In this case, divide both the numerator and denominator by their greatest common divisor (which is 4). The simplified answer is:
104/12 = (104/4)/(12/4) = 26/3
So the answer is 26/3.
3. -4 1/2 + 2 2/3:
- Convert the mixed numbers into improper fractions:
-4 1/2 becomes (-4 * 2 + 1)/2 = -9/2
2 2/3 becomes (2 * 3 + 2)/3 = 8/3
- Find the LCD for 2 and 3, which is 6.
- Rewrite each fraction with the LCD as its denominator:
-9/2 becomes (-9 * 3)/(2 * 3) = -27/6
8/3 becomes (8 * 2)/(3 * 2) = 16/6
- Now add the numerators:
-27/6 + 16/6 = -11/6
So the answer is -11/6.