Finding the Unknown | IT

Question 13

Context: It is known that $23 \times 41 \times 11 \times 8 \times 7 = 5,80,888$ . To find the value of the expression $23 \times 41 \times 11 \times 8$ , we can divide $5,80,888$ by $7$ .

Q. Is this the same as dividing both sides by 7, which removes the factor 7 and leaves only the expression to be evaluated on the LHS?

Solution

We can use equations to find the value of an unknown expression.

Step 1 — Write the given information

We are given a multiplication problem. The product of several numbers is known. Let us write this as an equation.

$23 \times 41 \times 11 \times 8 \times 7 = 5,80,888$

We want to find the value of $23 \times 41 \times 11 \times 8$ . Let us call this unknown expression $P$ . So, $P = 23 \times 41 \times 11 \times 8$ . Now, we can rewrite our main equation. We replace the expression with $P$ .

$P \times 7 = 5,80,888$

Diagram 1

Step 2 — Find the value of P

We need to find the value of $P$ . To do this, we must isolate $P$ . We can divide both sides of the equation by $7$ . This keeps the equation balanced.

$\frac{P \times 7}{7} = \frac{5,80,888}{7}$

The $7$ on the left side cancels out. So, $P$ is equal to the division result.

$P = \frac{5,80,888}{7}$

Let us perform the division.

$P = 82984$

$\boxed{P = 82,984}$

The question asks if dividing by $7$ is correct. Our steps show this is exactly what we did. So, the proposed method is correct.

Answer

(i) Yes, dividing $5,80,888$ by $7$ is correct. (ii) The expression's value is 82,984.

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Context: Finding the Unknown

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Context: Consider the equation $2n + 1 = 99$ .

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Q11

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Q12

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Q13

Context: It is known that $23 \times 41 \times 11 \times 8 \times 7 = 5,80,888$ . To find the value of the expression $23 \times 41 \times 11 \times 8$ , we can divide $5,80,888$ by $7$ .

Q. Is this the same as dividing both sides by 7, which removes the factor 7 and leaves only the expression to be evaluated on the LHS?

Q14

Ranjana creates a sequence of arrangements with square tiles as shown below. Can she extend the sequence and make an arrangement using 100 tiles? If yes, which step in the sequence will it be?

We have the expression $3k + 1$ which gives the number of tiles needed to make an arrangement in Step $k$ . To check whether an arrangement is possible using 100 tiles at some Step $k$ , we can solve the equation: $3k + 1 = 100$ . Find the value of $k$ .

Q15

We have the expression $3k + 1$ which gives the number of tiles needed to make an arrangement in Step $k$ .

To check whether an arrangement is possible using 100 tiles at some Step $k$ , we can solve the equation: $3k + 1 = 100$ . Find the value of $k$ .

Q16

Context: Example 11: Riyaz created a math trick, which he tries out on his friend Akash.

Riyaz asked Akash to perform the following steps without revealing the answer to any of the intermediate steps.

Think of a number.
Subtract 3 from the number.
Multiply the result by 4.
Add 8 to the product.
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Q17

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Q. Can you think of a simple rule that you can use to get the starting number from the final answer?

Q18

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Q19

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Q20

Can you form a chain going from the bottom equation to the top? Compare the operations used when going from the top to the bottom and from the bottom to the top.

Q21

Without calculating, can you find the value of the unknown in each equation in the chains above?

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Q22

7.3 Mind the Mistake, Mend the Mistake

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Q26

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Q27

Context: Brahmagupta's formula for solving equations of the form $Ax + B = Cx + D$ is $x = \frac{D - B}{A - C}$ .

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Q28

There are some children and donkeys on a beach. Together they have 28 heads and 80 feet. How many donkeys are there? How many children are there?