A grid model provides a visual representation of fraction multiplication. It is just one of the ways that you can multiply fractions. Another way is to use the standard algorithm for the multiplication of fractions. You have seen and practiced this method before.
For Example
Chef Fractiona is catering a dinner party. There are 12 guests invited. Unfortunately, only \( \frac{2}{3} \) of the invited guests can attend.
How many guests will be at the dinner party?
Step 1: Express whole numbers as fractions. |
Write the whole number over 1: \[ \frac{12}{1} \] |
Step 2: Write the multiplication problem. |
You need to calculate the product of \( \frac{12}{1} \) and \( \frac{2}{3} \). \[ \frac{12}{1} \times \frac{2}{3} \] |
Step 3: Multiply the numerators. Then multiply the denominators. |
\[ \frac{2 \times 12}{3 \times 1} = \frac{24}{3} \] |
Step 4: Simplify the product if needed. |
The GCF of 24 and 3 is 3. Divide the numerator and denominator by 3. \[ \frac{24 \div 3}{3 \div 3} = \frac{8}{1} = 8 \] There will be 8 guests at the dinner party. |
Level Up
Now you can practice multiplying fractions using the standard algorithm. Answer the question you find on each tab. Then click the Answer button to check your work. Refer to the example above if you need help as you work.
Multiply: \( \frac{3}{4} \times \frac{8}{9} \)
\( \large \frac{2}{3} \)
If you need help arriving at this answer, click the Solution button.
Step 1: Express whole numbers as fractions. |
This problem does not contain whole numbers. You can skip this step. |
Step 2: Write the multiplication problem. |
This was given. \[ \frac{3}{4} \times \frac{8}{9} \] |
Step 3: Multiply the numerators. Then multiply the denominators. |
\[ \frac{3}{4} \times \frac{8}{9} = \frac{3 \times 8}{4 \times 9} = \frac{24}{36} \] |
Step 4: Simplify the product if needed. |
The GCF of 24 and 36 is 12. Divide the numerator and denominator by 12. \[ \frac{24 \div 12}{36 \div 12} = \frac{2}{3} \] |
Claudette is walking toward the beach. The beach is \( \frac{9}{10} \) of a mile from her house.
If she has walked \( \frac{2}{3} \) of the way to the beach, how far has Claudette walked?
\( \large \frac{3}{5} \) of a mile
If you need help arriving at this answer, click the Solution button.
Step 1: Express whole numbers as fractions. |
This problem does not contain whole numbers. You can skip this step. |
Step 2: Write the multiplication problem. |
You need to calculate the product of \( \frac{9}{10} \) and \( \frac{2}{3} \). \[ \frac{9}{10} \times \frac{2}{3} \] |
Step 3: Multiply the numerators. Then multiply the denominators. |
\[ \frac{9}{10} \times \frac{2}{3} = \frac{9 \times 2}{10 \times 3} = \frac{18}{30} \] |
Step 4: Simplify the product if needed. |
The GCF of 18 and 30 is 6. Divide the numerator and denominator by 6. \[ \frac{18 \div 6}{30 \div 6} = \frac{3}{5} \] |
What is the product when \( \frac{1}{4} \) is multiplied by 2?
\( \large \frac{1}{2} \)
If you need help arriving at this answer, click the Solution button.
Step 1: Express whole numbers as fractions. |
Write the whole number over 1: \[ \frac{2}{1} \] |
Step 2: Write the multiplication problem. |
You need to calculate the product of \( \frac{2}{1} \) and \( \frac{1}{4} \). \[ \frac{2}{1} \times \frac{1}{4} \] |
Step 3: Multiply the numerators. Then multiply the denominators. |
\[ \frac{2}{1} \times \frac{1}{4} = \frac{2 \times 1}{1 \times 4} = \frac{2}{4} \] |
Step 4: Simplify the product if needed. |
The GCF of 2 and 4 is 2. Divide the numerator and denominator by 2. \[ \frac{2 \div 2}{4 \div 2} = \frac{1}{2} \] |
After a pizza party, \( \frac{15}{4} \) pizzas were left over.
If you eat \( \frac{1}{5} \) of the remaining amount pizza the next day, how much of the leftover pizza did you eat?
\( \large \frac{3}{4} \) of the leftover pizza
If you need help arriving at this answer, click the Solution button.
Step 1: Express whole numbers as fractions. |
This problem does not contain whole numbers. You can skip this step. |
Step 2: Write the multiplication problem. |
You need to calculate the product of \( \frac{15}{4} \) and \( \frac{1}{5} \). \[ \frac{15}{4} \times \frac{1}{5} \] |
Step 3: Multiply the numerators. Then multiply the denominators. |
\[ \frac{15}{4} \times \frac{1}{5} = \frac{15 \times 1}{4 \times 5} = \frac{15}{20} \] |
Step 4: Simplify the product if needed. |
The GCF of 15 and 20 is 5. Divide the numerator and denominator by 5. \[ \frac{15 \div 5}{20 \div 5} = \frac{3}{4} \] |
What is the product of \( \frac{5}{18} \) and \( \frac{4}{7} \)?
\( \large \frac{10}{63} \)
If you need help arriving at this answer, click the Solution button.
Step 1: Express whole numbers as fractions. |
This problem does not contain whole numbers. You can skip this step. |
Step 2: Write the multiplication problem. |
You need to calculate the product of \( \frac{5}{18} \) and \( \frac{4}{7} \). \[ \frac{5}{18} \times \frac{4}{7} \] |
Step 3: Multiply the numerators. Then multiply the denominators. |
\[ \frac{5}{18} \times \frac{4}{7} = \frac{5 \times 4}{18 \times 7} = \frac{20}{126} \] |
Step 4: Simplify the product if needed. |
The GCF of 20 and 126 is 2. Divide the numerator and denominator by 2. \[ \frac{20 \div 2}{126 \div 2} = \frac{10}{63} \] |
Question
Create a grid model to show that \( \frac{3}{4} \times \frac{8}{9} = \frac{24}{36} \).
One possible grid model is shown. Notice that the grid is divided into 36 smaller, equally sized rectangles, and 24 of those rectangles are shaded with the overlapping color.
A rectangle that is vertically divided into 9 equal columns and horizontally divided into 4 equal rows. There are 36 total sections. Of the 36 total sections, 24 are shaded green, 3 are shaded blue, and 8 are shaded yellow. The green shading represents the overlap.
