To simplify the expression 3 2/4 × 1 2/3, we can convert the mixed numbers into improper fractions.
First, let's convert 3 2/4 into an improper fraction. The whole number 3 can be written as 3/1. Adding the fraction part, we get 3/1 + 2/4.
To add these fractions, we need to find a common denominator. The common denominator of 1 and 4 is 4.
So, we rewrite 3/1 as 12/4. Adding 2/4, we get 12/4 + 2/4 = 14/4.
Now let's convert 1 2/3 into an improper fraction. The whole number 1 can be written as 1/1. Adding the fraction part, we get 1/1 + 2/3.
To add these fractions, we need to find a common denominator. The common denominator of 1 and 3 is 3.
So, we rewrite 1/1 as 3/3. Adding 2/3, we get 3/3 + 2/3 = 5/3.
Now we multiply the two improper fractions: (14/4) × (5/3).
To multiply fractions, we multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
So, (14/4) × (5/3) = (14 × 5) / (4 × 3) = 70/12.
To simplify this fraction, we can find the greatest common divisor (GCD) of the numerator and denominator, which is 2.
Dividing both the numerator and denominator by 2, we get 70/12 = (70 ÷ 2) / (12 ÷ 2) = 35/6.
Therefore, the simplified form of 3 2/4 × 1 2/3 is 35/6.