Expressions Using Letter-Numbers | IT

Question 5

Now, find the values of the other arithmetic expressions:

$23 - 10 \times 2$
$83 + 28 - 13 + 32$
$34 - 14 + 20$
$42 + 15 - (8 - 7)$
$68 - (18 + 13)$
$7 \times 4 + 9 \times 6$
$20 + 8 \times (16 - 6)$

Solution

We will solve each expression using the order of operations.

Step 1 — First expression

Let us calculate the first expression. We do multiplication before subtraction. First, multiply 10 by 2.

$10 \times 2 = 20$

Then, subtract 20 from 23.

$23 - 20$

$\boxed{3}$

Step 2 — Second expression

Let us calculate the second expression. We do operations from left to right. First, add 83 and 28.

$83 + 28 = 111$

Then, subtract 13 from 111.

$111 - 13 = 98$

Finally, add 32 to 98.

$98 + 32$

$\boxed{130}$

Step 3 — Third expression

Let us calculate the third expression. We do operations from left to right. First, subtract 14 from 34.

$34 - 14 = 20$

Then, add 20 to 20.

$20 + 20$

$\boxed{40}$

Step 4 — Fourth expression

Let us calculate the fourth expression. We solve inside the parentheses first. Subtract 7 from 8.

$8 - 7 = 1$

Now, the expression is $42 + 15 - 1$ . We do operations from left to right. Add 42 and 15.

$42 + 15 = 57$

Then, subtract 1 from 57.

$57 - 1$

$\boxed{56}$

Step 5 — Fifth expression

Let us calculate the fifth expression. We solve inside the parentheses first. Add 18 and 13.

$18 + 13 = 31$

Now, the expression is $68 - 31$ . Subtract 31 from 68.

$68 - 31$

$\boxed{37}$

Step 6 — Sixth expression

Let us calculate the sixth expression. We do multiplication before addition. First, multiply 7 by 4.

$7 \times 4 = 28$

Next, multiply 9 by 6.

$9 \times 6 = 54$

Finally, add 28 and 54.

$28 + 54$

$\boxed{82}$

Step 7 — Seventh expression

Let us calculate the seventh expression. We solve inside the parentheses first. Subtract 6 from 16.

$16 - 6 = 10$

Now, the expression is $20 + 8 \times 10$ . We do multiplication before addition. Multiply 8 by 10.

$8 \times 10 = 80$

Finally, add 20 and 80.

$20 + 80$

$\boxed{100}$

Answer

(1) 3 (2) 130 (3) 40 (4) 56 (5) 37 (6) 82 (7) 100

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Q12

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Q13

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Q14

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Q15

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Q16

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Q. Simplify this expression further.

Q17

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Q18

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Q19

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Observe each of them and see if there is a mistake.
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Q21

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Q22

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Q23

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Q24

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Q26

Verify this expression for diagonal sums by considering any $2 \times 2$ square and taking its top left number to be 'a'.

Q27

Context: Consider a set of numbers from the calendar (having endless rows) forming under the following shape:

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Q28

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Q29

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Q30

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Q31

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Q32

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Q33

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Q34

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Q35

Numbers are written in a particular sequence in this endless 4-column grid.

(a) Give expressions to generate all the numbers in a given column (1, 2, 3, 4).

(b) In which row and column will the following numbers appear:

(i) 124

(ii) 147

(iii) 201

(d) Observe the positions of multiples of 3.

Do you see any pattern in it? List other patterns that you see.