Turn this screenshot into a short video lesson.---**Extraction Content:**
**Title:**
Introduction
**Body Text:**
We can use fraction models to help us to add fractions and whole numbers.
For example, suppose that we want to find the value of $\frac{1}{2} + 1$ as an improper fraction. Let's solve this problem using a fraction model.
We cannot add these two fractions at the moment, because they are split into different numbers of parts (i.e., they have different denominators). So what do we do?
The first shape is split into 2 equal parts. So, we can split the whole number into 2 equal parts also:
Now, both shapes are split into 2 equal parts, and we have $1 + 2 = 3$ shaded parts in total.
Therefore,
$\frac{1}{2} + 1 = \frac{3}{2}$.
And that's our answer!
Learning to add fractions and whole numbers will give us vital clues on how to add fractions with unlike denominators, which is our ultimate goal.
**Mathematical Formulas/Equations:**
$\frac{1}{2} + 1$
$\frac{1}{2} + 1 = \frac{3}{2}$
**Chart/Diagram Description:**
**First Fraction Model Set:**
Type: Fraction model diagram.
Main Elements:
- Two rectangular shapes shown side-by-side.
- A '+' sign between the first and second rectangle.
- An '= ?' after the second rectangle.
- First rectangle: Divided vertically into two equal sections. The left section is shaded blue, the right section is not shaded.
- Annotation below first rectangle: A curved bracket enclosing the rectangle, labeled with "$\frac{1}{2}$". The denominator '2' is colored red.
- Second rectangle: A single solid blue rectangle.
- Annotation below second rectangle: A curved bracket enclosing the rectangle, labeled with "1".
**Second Fraction Model Set:**
Type: Fraction model diagram.
Main Elements:
- Two rectangular shapes shown side-by-side.
- A '+' sign between the first and second rectangle.
- An '= ?' after the second rectangle.
- First rectangle: Divided vertically into two equal sections. The left section is shaded blue, the right section is not shaded. This is the same as the first rectangle in the first set.
- Annotation below first rectangle: A curved bracket enclosing the rectangle, labeled with "$\frac{1}{2}$". The denominator '2' is colored red.
- Second rectangle: Divided vertically into two equal sections. Both the left and right sections are shaded blue.
- Annotation below second rectangle: A curved bracket enclosing the rectangle, labeled with "$\frac{2}{2}$". The denominator '2' is colored red.
视频信息
答案文本
视频字幕
We can use fraction models to help us add fractions and whole numbers. For example, let's find the value of one-half plus one as an improper fraction. Here we see one-half represented by a rectangle with one part shaded out of two, and the whole number one represented by a completely shaded rectangle.
We cannot add these two fractions at the moment, because they are split into different numbers of parts. In other words, they have different denominators. The first fraction has a denominator of 2, while the whole number can be thought of as having a denominator of 1. To add them, we need to express both numbers with the same denominator.
The first shape is split into 2 equal parts. So, we can split the whole number into 2 equal parts also. We divide the whole rectangle into 2 equal sections, both shaded blue. This shows us that 1 equals 2 over 2. Now both shapes are split into 2 equal parts, and they have the same denominator.
Now both shapes are split into 2 equal parts, and we can add them together. We have 1 shaded part from the first fraction plus 2 shaded parts from the second fraction, which gives us 3 shaded parts in total. Therefore, one-half plus two-halves equals three-halves. This gives us our final answer as an improper fraction.
Therefore, one-half plus one equals three-halves, and that's our answer! This visual method of using fraction models helps us understand how to add fractions and whole numbers. Learning to add fractions and whole numbers will give us vital clues on how to add fractions with unlike denominators, which is our ultimate goal in fraction arithmetic.