Equivalent fractions on the area model. Draw two 4 by 5 units on the grid paper. Show the fraction as a second model divided into 20ths and determine the fractional amount shaded. Therefore, draw two 4 by 3 units on the grid paper. Show the fraction as a partition of the second model to show a fraction equivalent to . Name the new modeled fraction and write an equivalency statement. Draw a 4 by 6 unit and model %. Now draw additional units and partition so that three equivalent fractions can be found. Model each fraction and write the equivalency statement.
The Correct Answer and Explanation is:
Part 1: Draw two 4 by 5 units (grids)
Draw two rectangles that are 4 units tall and 5 units wide. This gives each rectangle a total of:4×5=20 units4 \times 5 = 20 \text{ units}4×5=20 units
Shade a portion of the first rectangle, for example, 10 squares out of 20. This shows the fraction:1020\frac{10}{20}2010
Now, in the second 4 by 5 rectangle, divide each square in half vertically. Now, each original square becomes 2 smaller parts. You now have:20×2=40 parts20 \times 2 = 40 \text{ parts}20×2=40 parts
If you shade the same area as before (10 squares), now it becomes:10×2=20 shaded parts out of 4010 \times 2 = 20 \text{ shaded parts out of 40}10×2=20 shaded parts out of 40
The new fraction is:2040\frac{20}{40}4020
So, we have:1020=2040\frac{10}{20} = \frac{20}{40}2010=4020
Part 2: Draw two 4 by 3 units
Draw two rectangles of size 4 by 3, each having:4×3=12 units4 \times 3 = 12 \text{ units}4×3=12 units
Shade, for instance, 6 squares to show:612\frac{6}{12}126
Now in the second rectangle, divide each unit into 2 smaller parts horizontally. Now there are:12×2=24 parts12 \times 2 = 24 \text{ parts}12×2=24 parts
If you shade the same area, it becomes:6×2=12 parts6 \times 2 = 12 \text{ parts}6×2=12 parts
So the new fraction is:1224\frac{12}{24}2412
Equivalency statement:612=1224\frac{6}{12} = \frac{12}{24}126=2412
Part 3: Draw a 4 by 6 unit and model a percent
Let’s say we want to model 50%. A 4 by 6 rectangle has:4×6=24 units4 \times 6 = 24 \text{ units}4×6=24 units
Shade half of it:1224\frac{12}{24}2412
Now let’s draw additional models:
- Divide each square into 2 parts → 48 parts → shade 24 → 2448\frac{24}{48}4824
- Divide each square into 3 parts → 72 parts → shade 36 → 3672\frac{36}{72}7236
- Divide each square into 4 parts → 96 parts → shade 48 → 4896\frac{48}{96}9648
Equivalency statements:1224=2448=3672=4896\frac{12}{24} = \frac{24}{48} = \frac{36}{72} = \frac{48}{96}2412=4824=7236=9648
These area models show that different fractions can represent the same value.
