Question

These circles are the same size and each is divided into equal parts. They model the expression

2 3/10 +1 9/10

Answer 1

The student's question pertains to the addition of the mixed numbers 2 3/10 and 1 9/10. This mathematical problem requires the addition of whole numbers and fractions with a common denominator.

Step-by-step explanation:

The student's question involves modeling the expression 2 3/10 + 1 9/10 using divided circles. This is a mathematical exercise that blends concepts of fractions and addition. To understand this representation, we can consider a few mathematical principles that underpin operations with fractions.

Fractions can be considered parts of a whole and in the context of arithmetic, adding fractions requires a common denominator. In the given expression, we are adding the whole numbers 2 and 1; and then the fractions 3/10 and 9/10. Since the fractions already have a common denominator (10), they can be easily added together.

Let's break down the arithmetic:

1. Combine the whole numbers: 2 + 1 = 3
2. Add the fractions: 3/10 + 9/10 = (3+9)/10 = 12/10
3. Since 12/10 is the same as 1 and 2/10, we can simplify it by adding 1 to our whole number and taking the 2/10 as a remaining fraction.
4. The final sum becomes 3 + 1 and 2/10, which is equal to 4 and 2/10.

In terms of circle representation, we can think of this as each whole number representing a full circle, and the fractional parts representing slices of that circle. Therefore, our solution is essentially equivalent to having four full circles and an additional slice that is two-tenths of another circle.

In general, when dealing with fractions and arithmetic operations like addition, it's essential to understand that maintaining equivalence through the same operation on both numerators when denominators are equal leads to an accurate sum.

Understanding Fractions and Addition

Understanding the concept of fractions and their relation to division and multiplication aids in such problems. The process of adding fractions is analogous to combining partial pieces into a whole, as long as their denominators are common. Various strategies, like representing fractions with physical shapes such as circles or pie slices, help visualize this process and strengthen comprehension of arithmetic operations involving fractions.