After interchanging the given two signs, what will be the value of the following expression? × and ÷ 20 + 5 ÷ 6 × 2 – 5
30
Understanding the Problem: Sign Interchange in Mathematical Expressions
The question asks us to evaluate a given mathematical expression after interchanging two specific signs: multiplication (×) and division (÷). We need to find the numerical value of the expression after performing this sign swap and then applying the correct order of operations.
The original expression is: 20 + 5 ÷ 6 × 2 – 5
We are required to interchange the '×' and '÷' signs.
Step-by-Step Evaluation After Interchanging Signs
First, let's rewrite the expression with the interchanged signs:
- Replace '÷' with '×'.
- Replace '×' with '÷'.
The new expression becomes: 20 + 5 × 6 ÷ 2 – 5
Now, we evaluate this new expression following the order of operations (BODMAS/PEMDAS).
BODMAS stands for:
- Brackets
- Orders (powers, square roots, etc.)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Applying the BODMAS rule to 20 + 5 × 6 ÷ 2 – 5:
- Division and Multiplication: We perform these operations from left to right.
- First, perform the multiplication: $\qquad 5 \times 6 = 30$
- The expression is now: $\qquad 20 + 30 \div 2 – 5$
- Next, perform the division: $\qquad 30 \div 2 = 15$
- The expression is now: $\qquad 20 + 15 – 5$
- Addition and Subtraction: We perform these operations from left to right.
- First, perform the addition: $\qquad 20 + 15 = 35$
- The expression is now: $\qquad 35 – 5$
- Finally, perform the subtraction: $\qquad 35 – 5 = 30$
The final value of the expression after interchanging the signs is 30.
Summary of Calculation
Original Expression: $20 + 5 \div 6 \times 2 – 5$
Signs to Interchange: $\times$ and $\div$
New Expression: $20 + 5 \times 6 \div 2 – 5$
Calculation:
$\qquad 20 + 5 \times 6 \div 2 – 5$
$\qquad 20 + 30 \div 2 – 5$ (Multiplication first)
$\qquad 20 + 15 – 5$ (Division next)
$\qquad 35 – 5$ (Addition next)
$\qquad 30$ (Subtraction last)
The value of the expression after interchanging the given two signs is 30.
Revision Table: Mathematical Operators and Order
| Operator | Description | Order (BODMAS/PEMDAS) |
|---|---|---|
| ( ) or [ ] | Brackets or Parentheses | 1st (Highest Priority) |
| ^ or ** | Orders (Exponents, Powers) | 2nd |
| × or * | Multiplication | 3rd (Same level as Division, done left to right) |
| ÷ or / | Division | 3rd (Same level as Multiplication, done left to right) |
| + | Addition | 4th (Same level as Subtraction, done left to right) |
| – | Subtraction | 4th (Same level as Addition, done left to right) |
Additional Information: Importance of Order of Operations
The order of operations is crucial in mathematics to ensure that expressions are evaluated consistently, leading to a unique result. If the operations are performed in a different order, the result would likely be incorrect. For example, in the expression $20 + 5 \times 3$, if we added first ($20+5=25$) and then multiplied ($25 \times 3 = 75$), we would get a different result than multiplying first ($5 \times 3 = 15$) and then adding ($20 + 15 = 35$). The BODMAS/PEMDAS rule provides a standard convention for this.
Problems involving interchanging signs test your understanding of both rewriting expressions based on specific rules and correctly applying the order of operations to the modified expression. Always remember to evaluate expressions step-by-step, dealing with operations according to their priority.
Important Questions from Logical Puzzle
Below is given a figure, in which a horse is placed on one of the boxes in a square grid of size $5 \times 5$. The horse can move in either of the following ways in a single move:
(i) two boxes to either left or right side and one box to either up or down side
(ii) two boxes to either up or down side and one box to either left or right side
(iii) the horse cannot step on a grey box. The horse has to stay within the grid and any move to out of the grid is NOT legal.
How many white boxes are there which cannot be covered by horse within 3 moves?
- Six persons Raj, Rohit, Rachit, Rajat, Rishu, and Rinku are working in an office. Each of them has a favorite car viz. P, Q, R, S, T, and U, but not necessarily in the same order. Each of them got a different salary - 1000, 2000, 2500, 3000, 3500, and 4000, but not necessarily in the same order. Rajat gets a salary of 2500 and his favorite car is U. The one who likes car Q gets a salary of 3000. Rachit likes car P and gets a salary of 3500. The one who gets a salary of 1000 does not like car R or S. Rinku does not like car Q or S but gets a salary of 2000. Rishu gets a salary of 4000 and does not like a car R. Rohit does not get a salary of 1000. Who gets a salary of 3000?
- Six friends P, Q, R, S, T, and U are sitting at different positions in a row of the company, and each of them get a different salary viz – 500, 800, 1000, 1500, 1800 & 2000, but not necessary in the same order. The friend who gets a salary of 2000 does not sit at the extreme end of the row. Q sits immediately before R and gets a salary of 800. T sits between U and S. Q is second to the left of S. P sits at the left end of the row and gets a salary of 1000. T gets a salary of 1500. R gets a salary neither of 2000 nor of 1800. How much salary does U get?
- Seven men A, B, C, D, E, F and G are standing in a queue, one behind the other in that order. That is, A is first in queue while G brings up the rear. Each of them is wearing a hat of a different colour of the rainbow - Violet, Indigo, Blue, Green, Yellow, Orange, and Red, but not necessarily in that order. It is also known that:
• D can see in front of him green and blue hats, but not the violet hat.
• E can see violet and yellow hats, but not the red hat.
• G can see hats of all the colours except Orange.
• E is wearing the Indigo coloured hat.
What colour hat is worn by F? - Who amongst the females arrived third?
