Final answer:
The example of using the distributive property with fractions is 1/2×(3+4)=1/2×3+1/2×4, illustrating the multiplication of 1/2 to both 3 and 4 inside the parentheses.
Step-by-step explanation:
The statement that is an example of using the distributive property of operations with fractions is: 1/2×(3+4)=1/2×3+1/2×4.
This demonstrates the distributive property because the number 1/2 is being multiplied by each term inside the parentheses individually. According to the property, multiplying a number by a sum of two others is equal to the sum of the product of that number with each term. It’s important to remember that when you're dividing by 8, it is the same as multiplying by its reciprocal, which is 1/8. Similarly, dividing by 2 is equivalent to multiplying by 1/2. Also, when you are adding fractions or working with them, they may need to have a common denominator, which often involves multiplication.
Remember that the sign rules for multiplication apply equally to whole numbers and fractions. When two positive numbers multiply, like in the given problem (1/2 is positive and so are 3 and 4), the result is also positive.