3 x 1/2 in fraction form
The Correct answer and Explanation is:
To solve the expression 3×123 \times \frac{1}{2}3×21 and express the answer in fraction form, we start by converting the whole number into a fraction. The number 3 can be represented as 31\frac{3}{1}13. Therefore, the expression can be rewritten as:31×12\frac{3}{1} \times \frac{1}{2}13×21
When multiplying fractions, the general rule is to multiply the numerators together and multiply the denominators together. So, we proceed as follows:
- Multiply the numerators:3×1=33 \times 1 = 33×1=3
- Multiply the denominators:1×2=21 \times 2 = 21×2=2
Putting these together gives us:3×11×2=32\frac{3 \times 1}{1 \times 2} = \frac{3}{2}1×23×1=23
Now, we have 32\frac{3}{2}23 as our result. This fraction is an improper fraction because the numerator (3) is greater than the denominator (2).
Explanation of Improper Fractions
Improper fractions, such as 32\frac{3}{2}23, are common in mathematics. They indicate that the value represented is greater than one whole unit. To convert an improper fraction to a mixed number, you divide the numerator by the denominator:
- Division: 3÷2=13 \div 2 = 13÷2=1 remainder 111
This means 32\frac{3}{2}23 can also be expressed as:1121 \frac{1}{2}121
This mixed number representation provides an intuitive understanding of the fraction: it tells us that we have one whole and an additional half.
Summary
The multiplication 3×123 \times \frac{1}{2}3×21 results in 32\frac{3}{2}23 or 1121 \frac{1}{2}121. This process demonstrates the fundamental rules of multiplying fractions, emphasizing the conversion of whole numbers into fraction form for consistency in calculations. Such operations are crucial in various applications, including cooking, construction, and scientific measurements, where fractions frequently arise.