Final answer:
A story context for 2/3 divided by 5/6 can involve measuring ingredients, like determining how many 5/6 cups fit into 2/3 cup of sugar for a recipe.
Step-by-step explanation:
Creating a story context for the mathematical expression 2/3 divided by 5/6 can help students understand the concept better. Let's imagine that you are baking cookies and the recipe calls for 2/3 cup of sugar. However, you realize that your measuring cup measures sugar in units of 5/6 cup. To find out how many 5/6 cups are in 2/3 cup of sugar, you would divide 2/3 by 5/6. In essence, you are asking how many times can 5/6 fit into 2/3? To solve this, we flip the divisor and multiply: 2/3 × 6/5 = 4/5. Thus, 2/3 cup of sugar is equivalent to 4/5 of the 5/6 measuring cup.
To solve the division problem 2/3 divided by 5/6, we can convert it into a multiplication problem by finding the reciprocal of the divisor. The reciprocal of 5/6 is 6/5. So, 2/3 divided by 5/6 is the same as 2/3 multiplied by 6/5.
When we multiply fractions, we multiply the numerators and the denominators separately. Multiplying 2/3 by 6/5 gives us (2 * 6) / (3 * 5) = 12/15.
We can simplify the fraction 12/15 by dividing both the numerator and the denominator by their greatest common divisor, which is 3. Dividing 12 by 3 gives us 4, and dividing 15 by 3 gives us 5. Therefore, 2/3 divided by 5/6 is equal to 4/5.