1. [tex]1,3 \times \frac{2}{4}[/tex]
2. [tex]5 \times \frac{1}{3}[/tex]
3. [tex]4 \times \frac{3}{5}[/tex]
4. [tex]4 \frac{3}{4} \times \frac{2}{3}[/tex]
5. [tex]5 \frac{2}{3} \times \frac{2}{4}[/tex]
Answer (1)
Multiply 3 × 4 2 to get 4 6 , which simplifies to 2 3 or 1.5 .
Multiply 5 × 3 1 to get 3 5 , approximately 1.67 .
Multiply 4 × 5 3 to get 5 12 , which equals 2.4 .
Multiply 4 4 3 × 3 2 by converting 4 4 3 to 4 19 , then multiply by 3 2 to get 12 38 , which simplifies to 6 19 or approximately 3.17 .
Multiply 5 3 2 × 4 2 by converting 5 3 2 to 3 17 , then multiply by 4 2 to get 12 34 , which simplifies to 6 17 or approximately 2.83 .
Explanation
Problem Analysis We are given six multiplication problems involving fractions and mixed numbers. Our goal is to calculate the result of each multiplication and simplify the fractions to their lowest terms.
Calculate 3 x 2/4 First, let's calculate 3 × 4 2 .
3 × 4 2 = 1 3 × 4 2 = 1 × 4 3 × 2 = 4 6 = 2 3 = 1 2 1 = 1.5
Calculate 5 x 1/3 Next, let's calculate 5 × 3 1 .
5 × 3 1 = 1 5 × 3 1 = 1 × 3 5 × 1 = 3 5 = 1 3 2 ≈ 1.67
Calculate 4 x 3/5 Now, let's calculate 4 × 5 3 .
4 × 5 3 = 1 4 × 5 3 = 1 × 5 4 × 3 = 5 12 = 2 5 2 = 2.4
Calculate 4 3/4 x 2/3 Now, let's calculate 4 4 3 × 3 2 . First, convert the mixed number to an improper fraction: 4 4 3 = 4 4 × 4 + 3 = 4 16 + 3 = 4 19 .
Then, multiply: 4 19 × 3 2 = 4 × 3 19 × 2 = 12 38 = 6 19 = 3 6 1 ≈ 3.17
Calculate 5 2/3 x 2/4 Finally, let's calculate 5 3 2 × 4 2 . First, convert the mixed number to an improper fraction: 5 3 2 = 3 5 × 3 + 2 = 3 15 + 2 = 3 17 .
Then, multiply: 3 17 × 4 2 = 3 × 4 17 × 2 = 12 34 = 6 17 = 2 6 5 ≈ 2.83
Final Results The results of the calculations are:
3 × 4 2 = 2 3 = 1.5
5 × 3 1 = 3 5 ≈ 1.67
4 × 5 3 = 5 12 = 2.4
4 4 3 × 3 2 = 6 19 ≈ 3.17
5 3 2 × 4 2 = 6 17 ≈ 2.83
Examples
Understanding fraction multiplication is crucial in many real-life scenarios. For instance, when baking, you might need to halve a recipe that calls for 3 2 cup of flour. Calculating 2 1 × 3 2 helps you determine the exact amount of flour needed. Similarly, in construction, if you need to use 4 3 of a wooden plank that is 5 meters long, multiplying 5 × 4 3 will give you the required length. These calculations ensure precision and efficiency in everyday tasks.
