Perform the indicated operation. Write your answer as a simplified fraction.
1. 1/3 + 0.25 = 7/12
2. 0.3125 - 1/4 = 1/16
3. -7/10 + 0.2 = -9/10
3. -1/2
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To perform the indicated operations and write the answers as simplified fractions, follow these steps:
1. To add fractions with different denominators (like 1/3 and 0.25), find a common denominator. In this case, the common denominator is 12, which is the least common multiple of 3 and 4. Multiply the numerator and denominator of 1/3 by 4, and the numerator and denominator of 0.25 by 12.
(1/3) + (0.25) = (1/3 * 4/4) + (0.25 * 12/12)
= 4/12 + 3/12
= 7/12
2. To subtract fractions (like 0.3125 and 1/4), find a common denominator. In this case, the common denominator is 16, which is the least common multiple of 4 and 1. Multiply the numerator and denominator of 1/4 by 4, and the numerator and denominator of 0.3125 by 16.
(0.3125) - (1/4) = (0.3125 * 16/16) - (1/4 * 4/4)
= 5/16 - 4/16
= 1/16
3. To add fractions with different denominators (like -7/10 and 0.2), find a common denominator. In this case, the common denominator is 10. Multiply the numerator and denominator of -7/10 by 1, and the numerator and denominator of 0.2 by 10.
(-7/10) + (0.2) = (-7/10 * 1/1) + (0.2 * 10/10)
= -7/10 + 2/10
= -9/10
So, the simplified fractions for the given operations are:
1. 1/3 + 0.25 = 7/12
2. 0.3125 - 1/4 = 1/16
3. -7/10 + 0.2 = -9/10