Multiply. Write your answer in simplest form.
2 1/2 x 3 2/3
2 1/2 = 2 + 1 / 2 = 4 / 2 + 1 / 2 = 5 / 2
3 2/3 = 3 + 2 / 3 = 9 / 3 + 2 / 3 = 11 / 3
2 1/2 x 3 2/3 = 5 / 2 x 11 / 3 =
5 x 11 / 2 x 3 = 55 / 6 =
54 / 6 + 1 / 6 = 9 + 1 / 6 = 9 1/6
To multiply mixed numbers like 2 1/2 and 3 2/3, first convert them to improper fractions.
To convert 2 1/2 to an improper fraction, multiply the whole number (2) by the denominator (2) and add the numerator (1). Then place the sum over the denominator. In this case, it will be (2 x 2 + 1) / 2 = 5/2.
Similarly, convert 3 2/3 to an improper fraction. Multiply the whole number (3) by the denominator (3) and add the numerator (2). Place the sum over the denominator. So, (3 x 3 + 2) / 3 = 11/3.
Now, multiply the two fractions: (5/2) x (11/3). To multiply fractions, multiply the numerators (5 x 11 = 55) to get the new numerator, and multiply the denominators (2 x 3 = 6) to get the new denominator. So, the result is 55/6.
However, we need to simplify the fraction to its simplest form. Find the highest common factor (HCF) of the numerator and the denominator. In this case, the HCF of 55 and 6 is 1.
Divide both the numerator and the denominator by the HCF: 55 ÷ 1 / 6 ÷ 1 = 55/6.
So, the product of 2 1/2 and 3 2/3, in simplest form, is 55/6.
To multiply 2 1/2 by 3 2/3, first convert the mixed numbers into improper fractions.
2 1/2 can be written as (2 * 2 + 1) / 2 = 5/2.
3 2/3 can be written as (3 * 3 + 2) / 3 = 11/3.
Now, we can multiply these two fractions:
(5/2) x (11/3) = (5 x 11) / (2 x 3) = 55/6.
The answer, in simplest form, is 55/6.