Question

10 - 15/8 × (3/2 ÷ 4 ½) ÷ (-¼)

Answer 1

To simplify the expression, follow the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division - from left to right, Addition and Subtraction - from left to right):

Start with the innermost parentheses:

3/2 ÷ 4 ½ = (1.5 ÷ 4.5) = 1/3

Now, the expression becomes:

10 - 15/8 × (1/3) ÷ (-¼)

Next, perform the multiplications and divisions:

15/8 × (1/3) = (15/8) * (1/3) = 5/8

Also, remember that dividing by a negative number flips the sign:

(-¼) = -(1/4)

Now, the expression becomes:

10 - 5/8 ÷ -(1/4)

Perform the division:

5/8 ÷ -(1/4) = (5/8) / -(1/4)

To divide fractions, multiply by the reciprocal of the second fraction:

(5/8) * (-4/1) = -20/8 = -5/2

Finally, subtract:

10 - (-5/2)

To subtract a negative number, you can think of it as adding the positive:

10 + 5/2 = 20/2 + 5/2 = 25/2

So, the simplified result is 25/2, which can also be expressed as 12.5.

Answer 2

`\sf 12 (1)/(2) \textsf{ or } (25)/(2)`

Explanation:

Definition:

Order of operations: A set of rules that determine the order in which mathematical operations are performed.

PEMDAS: A mnemonic device that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

In this case:

`\sf 10-(15)/(8) * ((3)/(2) / 4 (1)/(2)) / -(1)/(4)`

In order to solve the expression, we need to follow the order of operations, which is PEMDAS:

Parentheses: Evaluate all expressions within parentheses first.

Exponents: Evaluate all exponents next.

Multiplication and Division: Perform multiplication and division from left to right.

Addition and Subtraction: Perform addition and subtraction from left to right.

Following the order of operations, we get the following steps:

`\sf 10-(15)/(8) * ((3)/(2) / 4 (1)/(2)) / -(1)/(4)`

`\sf 10-(15)/(8) * ((3)/(2) / (9)/(2)) / -(1)/(4)`

`\sf 10-(15)/(8) * ((3)/(2) * (2)/(9)) / -(1)/(4)`

`\sf 10-(15)/(8) * (1)/(3) / -(1)/(4)`

`\sf 10-(5)/(8) / -(1)/(4)`

`\sf 10+(5)/(8) * -(4)/(1)`

`\sf 10+(5)/(2)`

`\sf 10+2(1)/(2)`

`\sf 12(1)/(2)`

So, the answer is:

`\sf 12 (1)/(2) \textsf{ or } (25)/(2)`