Arithmetic Expressions

Fill in the blanks to make the expressions equal on both sides of the = sign: (a) 13 + 4 = ___ + 6 (b) 22 + ___ = $6 \times 5$ (c) 8 × ___ = 64 ÷ 2 (d) 34 - ___ = 25

Arrange the following expressions in ascending (increasing) order of their values. (a) 67 - 19 (b) 67 - 20 (c) 35 + 25 (d) $5 \times 11$ (e) 120 ÷ 3

Find the values of the following expressions by writing the terms in each case. (a) 28 - 7 + 8 (b) 39 - $2 \times 6$ + 11 (c) 40 - 10 + 10 + 10 (d) 48 - $10 \times 2$ + 16 ÷ 2 (e) $6 \times 3$ - $4 \times 8$ × 5

Write a story/situation for each of the following expressions and find their values. (a) 89 + 21 - 10 (b) $5 \times 12$ - 6 (c) $4 \times 9$ + $2 \times 6$

Fill in the blanks with numbers, and boxes with operation signs such that the expressions on both sides are equal. (a) 24 + (6 - 4) = 24 + 6 ☐ ___ (b) 38 + () = 38 + 9 - 4 (c) 24 - (6 + 4) = 24 - 6 ☐ ___ (d) 24 - 6 - 4 = 24 - 6 ☐ ___ (e) 27 - (8 + 3) = 27 - 8 - 3 (f) 27 - () = 27 - 8 + 3

Remove the brackets and write the expression having the same value. (a) 14 + (12 + 10) (b) 14 - (12 + 10) (c) 14 + (12 - 10) (d) 14 - (12 - 10) (e) -14 + 12 - 10 (f) 14 - (-12 - 10)

Find the values of the following expressions. For each pair, first try to guess whether they have the same value. When are the two expressions equal? (a) (6 + 10) - 2 and 6 + (10 - 2) (b) 16 - (8 - 3) and (16 - 8) - 3 (c) 27 - (18 + 4) and 27 + (-18 - 4)

Using only reasoning of how terms change their values, fill the blanks to make the expressions on either side of the equality (=) equal. (a) 423 + ___ = 419 + ___ (b) 207 - 68 = 210 - ___

Using the numbers 2, 3 and 5, and the operators '+' and '-', and brackets, as necessary, generate expressions to give as many different values as possible. For example, 2 - 3 + 5 = 4 and 3 - (5 - 2) = 0.

Whenever Jasoda has to subtract 9 from a number, she subtracts 10 and adds 1 to it. For example, 36 - 9 = 26 + 1. (a) Do you think she always gets the correct answer? Why? (b) Can you think of other similar strategies? Give some examples.

Consider the two expressions: a) 73 - 14 + 1, b) 73 - 14 - 1. For each of these expressions, identify the expressions from the following collection that are equal to it. (a) 73 - (14 + 1) (b) 73 - (14 - 1) (c) 73 + (-14 + 1) (d) 73 + (-14 - 1)

Fill in the blanks with numbers, and boxes by signs, so that the expressions on both sides are equal. (a) 3 × (6 + 7) = $3 \times 6$ ☐ $3 \times 7$ (b) (8 + 3) × 4 = $8 \times 4$ ☐ $3 \times 4$ (c) 3 × (5 + 8) = $3 \times 5$ ☐ ___ (d) (9 + 2) × 4 = $9 \times 4$ ☐ ___ (e) 3 × (___ + 4) = 3 × ___ + ___ (f) (___ + 6) × 4 = $13 \times 4$ + ___ (g) 3 × (___ + ) = $3 \times 5$ + $3 \times 2$ (h) ( + ___) × ___ = $2 \times 4$ + $3 \times 4$ (i) 5 × (9 - 2) = $5 \times 9$ ☐ 5 × ___ (j) (5 - 2) × 7 = $5 \times 7$ ☐ 2 × ___ (k) 5 × (8 - 3) = $5 \times 8$ ☐ ___ (l) (8 - 3) × 7 = $8 \times 7$ ☐ $3 \times 7$ (m) 5 × (12 - ___) = ___ ☐ 5 × ___ (n) (15 - ) × 7 = ___ ☐ $6 \times 7$ (o) 5 × ( - ) = $5 \times 9$ - $5 \times 4$ (p) ( - ___) × ___ = $17 \times 7$ - $9 \times 7$

In the boxes below, fill '<', '>' or '=' after analysing the expressions on the LHS and RHS. Use reasoning and understanding of terms and brackets to figure this out and not by evaluating the expressions. (a) (8 - 3) × 29 ☐ (3 - 8) × 29 (b) 15 + $9 \times 18$ ☐ (15 + 9) × 18 (c) 23 × (17 - 9) ☐ $23 \times 17$ + $23 \times 9$ (d) (34 - 28) × 42 ☐ $34 \times 42$ - $28 \times 42$

Here is one way to make 14: 2 × (1 + 6) = 14. Are there other ways of getting 14? Fill them out below: (a) ___ × (___ + ) = 14 (b) ___ × ( + ) = 14 (c) ___ × ( + ) = 14 (d) ___ × ( + ___) = 14

Find different ways of evaluating the following expressions: (a) 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 (b) 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1

Compare the following pairs of expressions using '<', '>' or '=' or by reasoning. (a) 49 - 7 + 8 ☐ 49 - 7 + 8 (b) $83 \times 42$ - 18 ☐ $83 \times 40$ - 18 (c) 145 - $17 \times 8$ ☐ 145 - $17 \times 6$ (d) $23 \times 48$ - 35 ☐ 23 × (48 - 35) (e) (16 - 11) × 12 ☐ -$11 \times 12$ + $16 \times 12$ (f) (76 - 53) × 88 ☐ 88 × (53 - 76) (g) 25 × (42 + 16) ☐ 25 × (43 + 15) (h) 36 × (28 - 16) ☐ 35 × (27 - 15)

Identify which of the following expressions are equal to the given expression without computation. You may rewrite the expressions using terms or removing brackets. There can be more than one expression which is equal to the given expression. (a) 83 - 37 - 12 (i) 84 - 38 - 12 (ii) 84 - (37 + 12) (iii) 83 - 38 - 13 (iv) -37 + 83 - 12 (b) 93 + $37 \times 44$ + 76 (i) 37 + $93 \times 44$ + 76 (ii) 93 + $37 \times 76$ + 44 (iii) (93 + 37) × (44 + 76) (iv) $37 \times 44$ + 93 + 76

Choose a number and create ten different expressions having that value.

Using four 4's, create expressions to get all values from 1 to 20.

Using the numbers 1, 2, 3, 4, and 5 exactly once in any order get as many values as possible between –10 and +10.