a. To evaluate (1/2 + 1/3) * 2/5, add the fractions, then multiply. b. The result is 1/3. In the expression (5/16 - 11/10 ÷ 22/5), divide the fractions, then subtract. The result is -1/16.
To evaluate the expression (1/2 + 1/3) * 2/5, we need to follow the order of operations, also known as BEDMAS.
BEDMAS stands for Brackets, Exponents, Division and Multiplication, Addition and Subtraction.
In this case, we start by adding the fractions 1/2 and 1/3. We need to find a common denominator. The common denominator is 6, so we can rewrite the fractions as 3/6 and 2/6. Adding these fractions gives us 5/6.
Next, we multiply 5/6 by 2/5. To do this, we multiply the numerators together (5 * 2 = 10) and multiply the denominators together (6 * 5 = 30). The result is 10/30, which can be simplified to 1/3.
Therefore, the value of (1/2 + 1/3) * 2/5 is 1/3.
In the expression (5/16 - 11/10 ÷ 22/5), we again need to follow the order of operations. First, we divide 11/10 by 22/5. When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction. So, 11/10 ÷ 22/5 is the same as 11/10 * 5/22. This gives us 55/220, which can be simplified to 1/4.
Next, we subtract 5/16 from 1/4. To do this, we need to find a common denominator. The common denominator is 16, so we can rewrite 1/4 as 4/16. Subtracting 5/16 from 4/16 gives us -1/16.
Therefore, the value of (5/16 - 11/10 ÷ 22/5) is -1/16.