Question

Put these numbers in order from least to greatest. (3)/(12)-(2)/(40),5(12)/(16) Submit

Answer 1

To order the numbers from least to greatest, first simplify the expressions to common terms. After simplification, we find that 0.20 or 1/5 is the least and 5.75 or 23/4 is the greatest.

Step-by-step explanation:

The student's question involves ordering numbers from least to greatest, which is a basic concept in mathematics. The numbers given are in fraction and mixed number formats. To order these numbers, it's essential to convert all of them to common terms, either by converting to decimals or finding a common denominator. For the first part, (3/12)-(2/40), we can simplify the expression by finding a common denominator. For the mixed number, 5(12/16), we can simplify it by dividing the numerator by the denominator.

After simplifying:

(3/12)-(2/40) is equivalent to 0.25 - 0.05 which is 0.20, or 1/5 when expressed as a fraction.5(12/16) can be simplified to 5(3/4), as 12/16 can be reduced to 3/4, and then further to 5.75 or 23/4 as a mixed number.

Answer 2

First, simplify (3/12)-(2/40) to (1/4)-(1/20) which further simplifies to (1/5). The number 5(12/16) simplified to 5(3/4) which converts to (23/4). Comparing (1/5) to (23/4), the numbers in order from least to greatest are (3/12)-(2/40) then 5(12/16).

Step-by-step explanation:

To arrange the numbers (3/12)-(2/40) and 5(12/16) in order from least to greatest, we first need to simplify each expression. The fraction (3/12) can be reduced to (1/4) since 3 and 12 both divide by 3. For the second term, (2/40) can be reduced to (1/20) since 2 and 40 both divide by 2. The subtraction of these gives us (1/4) - (1/20), which we need to express with a common denominator. Multiplying both terms by 5, the expression becomes (5/20) - (1/20) = (4/20), and further reduction gives us (1/5).

Next, we look at the number 5(12/16) which can be simplified since 12 and 16 share a common factor of 4, resulting in 5(3/4). This expression is a mixed number and can be converted into an improper fraction: (5 × 4 + 3)/4 = 23/4.

Now, we compare (1/5) and (23/4). Converting (1/5) to have a common denominator with (23/4), we have (4/20) compared to (460/20). Clearly, (1/5) or (4/20) is less than (23/4). Therefore, the numbers in order from least to greatest are (3/12)-(2/40) then 5(12/16).