Complete The Following Expression:${ \begin{array}{l} \frac{(2 \times 3) + 1}{} = \frac{12}{3} = \underline{6 + 1} \ \frac{12}{6} - 2 \frac{3}{6} = \ \end{array} }$(Note: The Expression Appears Incomplete. Please Verify The Initial Problem

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Introduction

The given expression appears to be incomplete, but we can attempt to solve it by filling in the missing parts. This problem involves basic arithmetic operations, including multiplication, addition, and subtraction. In this article, we will break down the expression, identify the missing parts, and provide a step-by-step solution.

Breaking Down the Expression

The given expression is:

{ \begin{array}{l} \frac{(2 \times 3) + 1}{} = \frac{12}{3} = \underline{6 + 1} \\ \frac{12}{6} - 2 \frac{3}{6} = \\ \end{array} \}

Let's analyze the first line of the expression:

(2×3)+1=123=6+1‾\frac{(2 \times 3) + 1}{} = \frac{12}{3} = \underline{6 + 1}

The expression starts with the product of 2 and 3, which equals 6. Then, 1 is added to the result, making it 7. However, the expression is incomplete, and the missing part is represented by the underscore.

Filling in the Missing Part

To fill in the missing part, we need to evaluate the expression 123\frac{12}{3}. This is a simple division problem, where 12 is divided by 3, resulting in 4. However, the expression is equal to 6+1‾\underline{6 + 1}, which also equals 7. This suggests that the missing part is actually 7, not 4.

Solving the Second Line of the Expression

Now that we have filled in the missing part, let's move on to the second line of the expression:

126−236\frac{12}{6} - 2 \frac{3}{6}

The first part of the expression, 126\frac{12}{6}, is a simple division problem, where 12 is divided by 6, resulting in 2. The second part of the expression, 2362 \frac{3}{6}, is a mixed number, where 2 is the whole number part, and 36\frac{3}{6} is the fractional part.

Evaluating the Mixed Number

To evaluate the mixed number 2362 \frac{3}{6}, we need to convert it to an improper fraction. This can be done by multiplying the whole number part by the denominator and then adding the numerator:

236=(2×6)+36=12+36=1562 \frac{3}{6} = \frac{(2 \times 6) + 3}{6} = \frac{12 + 3}{6} = \frac{15}{6}

Now that we have converted the mixed number to an improper fraction, we can simplify it by dividing the numerator and denominator by their greatest common divisor, which is 3:

156=52\frac{15}{6} = \frac{5}{2}

Subtracting the Two Fractions

Now that we have evaluated the two fractions, we can subtract them:

126−52\frac{12}{6} - \frac{5}{2}

To subtract these fractions, we need to find a common denominator, which is 6. We can then rewrite the fractions with the common denominator:

126=126\frac{12}{6} = \frac{12}{6}

52=156\frac{5}{2} = \frac{15}{6}

Now that the fractions have a common denominator, we can subtract them:

126−156=−36\frac{12}{6} - \frac{15}{6} = \frac{-3}{6}

Simplifying the Result

The result of the subtraction is −36\frac{-3}{6}. We can simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 3:

−36=−12\frac{-3}{6} = \frac{-1}{2}

Conclusion

In this article, we have solved the incomplete expression by filling in the missing parts and evaluating the arithmetic operations. We have broken down the expression into smaller parts, identified the missing parts, and provided a step-by-step solution. The final result is −12\frac{-1}{2}.

Final Answer

Q: What is the missing part in the expression (2×3)+1=123=6+1‾\frac{(2 \times 3) + 1}{} = \frac{12}{3} = \underline{6 + 1}?

A: The missing part is actually 7, not 4. This is because the expression 123\frac{12}{3} equals 4, but the expression 6+1‾\underline{6 + 1} also equals 7.

Q: How do you evaluate the mixed number 2362 \frac{3}{6}?

A: To evaluate the mixed number 2362 \frac{3}{6}, you need to convert it to an improper fraction. This can be done by multiplying the whole number part by the denominator and then adding the numerator:

236=(2×6)+36=12+36=1562 \frac{3}{6} = \frac{(2 \times 6) + 3}{6} = \frac{12 + 3}{6} = \frac{15}{6}

Q: How do you simplify the fraction 156\frac{15}{6}?

A: To simplify the fraction 156\frac{15}{6}, you need to divide the numerator and denominator by their greatest common divisor, which is 3:

156=52\frac{15}{6} = \frac{5}{2}

Q: How do you subtract the two fractions 126\frac{12}{6} and 52\frac{5}{2}?

A: To subtract the two fractions 126\frac{12}{6} and 52\frac{5}{2}, you need to find a common denominator, which is 6. You can then rewrite the fractions with the common denominator:

126=126\frac{12}{6} = \frac{12}{6}

52=156\frac{5}{2} = \frac{15}{6}

Now that the fractions have a common denominator, you can subtract them:

126−156=−36\frac{12}{6} - \frac{15}{6} = \frac{-3}{6}

Q: How do you simplify the result −36\frac{-3}{6}?

A: To simplify the result −36\frac{-3}{6}, you need to divide the numerator and denominator by their greatest common divisor, which is 3:

−36=−12\frac{-3}{6} = \frac{-1}{2}

Q: What is the final answer to the expression?

A: The final answer to the expression is −12\boxed{-\frac{1}{2}}.

Q: What is the purpose of finding a common denominator when subtracting fractions?

A: The purpose of finding a common denominator when subtracting fractions is to ensure that the fractions have the same unit of measurement. This allows you to compare the fractions and perform the subtraction.

Q: Can you provide an example of a real-world scenario where subtracting fractions is useful?

A: Yes, subtracting fractions is useful in a variety of real-world scenarios, such as:

  • Calculating the cost of a product after a discount
  • Determining the amount of time remaining after a certain amount of time has passed
  • Finding the area of a shape after a certain amount of area has been removed

For example, let's say you have a pizza that is 12 inches in diameter, and you eat 3 inches of it. To find the amount of pizza remaining, you would need to subtract the amount eaten from the total amount:

1212−312=912\frac{12}{12} - \frac{3}{12} = \frac{9}{12}

This means that 9/12 of the pizza remains.

Q: Can you provide an example of a real-world scenario where simplifying fractions is useful?

A: Yes, simplifying fractions is useful in a variety of real-world scenarios, such as:

  • Calculating the cost of a product after a discount
  • Determining the amount of time remaining after a certain amount of time has passed
  • Finding the area of a shape after a certain amount of area has been removed

For example, let's say you have a recipe that calls for 2/3 cup of sugar, but you only have a 1/2 cup measuring cup. To find the amount of sugar you need to measure, you would need to simplify the fraction:

23=46\frac{2}{3} = \frac{4}{6}

This means that you need to measure 4/6 of the cup, or 2/3 of the cup.

Q: Can you provide an example of a real-world scenario where converting mixed numbers to improper fractions is useful?

A: Yes, converting mixed numbers to improper fractions is useful in a variety of real-world scenarios, such as:

  • Calculating the cost of a product after a discount
  • Determining the amount of time remaining after a certain amount of time has passed
  • Finding the area of a shape after a certain amount of area has been removed

For example, let's say you have a recipe that calls for 2 1/2 cups of flour, but you only have a 1/4 cup measuring cup. To find the amount of flour you need to measure, you would need to convert the mixed number to an improper fraction:

212=(2×2)+12=522 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2}

This means that you need to measure 5/2 of the cup, or 2 1/2 cups.