In previous grades, you used models to represent fractions. For example, you can use a fraction square to represent 4 over 5 4 5 . Remember that if the square represents one whole unit, the denominator tells you how many equal-sized parts that the square should be divided into. The numerator tells you how many of these equal-sized parts will be shaded.
The image below links you to an interactive that you can use to multiply fractions with fraction squares. Click on the image and the interactive will open in a new browser tab or window.
Use the interactive to model each pair of factors. Drag the model for the second factor on top of the first factor. The overlap model shows you the product of the two factors. Use your results to complete the table, as shown below, in your notes.
Factor 1 |
Factor 2 |
Number of Double-Shaded Parts (Overlap Model) |
Total Number of Parts (Overlap Model) |
Product |
2 over 5
2
5
|
3 over 4
3
4
|
|||
3 over 7
3
7
|
4 over 5
4
5
|
|||
2 over 3
2
3
|
7 over 8
7
8
|
|||
1 over 4
1
4
|
3 over 6
3
6
|
Interactive popup. Assistance may be required.
Factor 1 |
Factor 2 |
Number of Double-Shaded Parts (Overlap Model) |
Total Number of Parts (Overlap Model) |
Product |
2 over 5
2
5
|
3 over 4
3
4
|
6 |
20 |
3 over 20
6
20
|
3 over 7
3
7
|
4 over 5
4
5
|
12 |
35 |
12 over 35
12
35
|
2 over 3
2
3
|
7 over 8
7
8
|
14 |
24 |
14 over 24
14
24
|
1 over 4
1
4
|
3 over 6
3
6
|
3 |
24 |
3 over 24
3
24
|
Interactive popup. Assistance may be required.
The number of double-shaded parts is the same as the numerator of the product.
Interactive popup. Assistance may be required.
The number of double-shaded parts and the numerator of the product are the same as the product of the numerators of the two factors.
Interactive popup. Assistance may be required.
The total number of parts is the same as the denominator of the product.
Interactive popup. Assistance may be required.
The total number of parts and the denominator of the product are the same as the product of the denominators of the two factors.
In general, how do the numerators of the factors relate to the numerator of the product?
In general, how do the denominators of the factors relate to the denominator of the product?
Generalize a method that you could use to multiply two fractions.
Interactive popup. Assistance may be required.
What is the product of the numerators? Denominators?
Interactive popup. Assistance may be required.
The area of a rectangle is the product of the length and width of the rectangle.
Interactive popup. Assistance may be required.
To determine 7 over 10 7 10 of 5 over 8 5 8 multiply the two fractions together.
