Understanding expressions, brackets, terms & properties
An arithmetic expression is a mathematical phrase that combines numbers with operations. Think of it as a compact way to describe a calculation.
13 + 2 = 15
20 − 4 = 16
12 × 5 = 60
18 ÷ 3 = 6
Every expression has a value — the number it evaluates to. The = sign shows the relationship between an expression and its value.
Mallika spends ₹25 every day for lunch from Monday to Friday.
Expression: 5 × 25 = 125
So Mallika spends ₹125 on lunch in a week.
We can compare expressions using >, <, and = by finding their values first.
Raja has 1023 + 125 marbles. Joy has 1022 + 128 marbles. Who has more?
Raja: 1023 + 125 = 1148
Joy: 1022 + 128 = 1150
Joy has 2 more marbles! So: 1023 + 125 < 1022 + 128
Compare: 113 − 25 vs 112 − 24
113 − 25 = 88
112 − 24 = 88
They are equal! So: 113 − 25 = 112 − 24
(a) 13 + 4 = + 6
(b) 22 + = 6 × 5
(c) 8 × = 64 ÷ 2
(d) 34 − = 25
67 − 19, 67 − 20, 35 + 25, 5 × 11, 120 ÷ 3
Values: 48, 47, 60, 55, 40
When an expression has more than one operation, things can get confusing — just like ambiguity in language!
Expression: 30 + 5 × 4
Who is right? Mallesh is correct! By convention, multiplication is done before addition.
Rule: Always evaluate expressions inside brackets first!
Irfan buys biscuits for ₹15 and toor dal for ₹56. He pays ₹100.
Correct: Change = 100 − (15 + 56) = 100 − 71 = ₹29
Wrong way: 100 − 15 + 56 = 85 + 56 = 141 ✘ (Absurd! More than he paid!)
Terms are the parts of an expression separated by the + sign.
Subtracting is the same as adding the inverse:
83 − 14 = 83 + (−14)
So the terms of 83 − 14 are: 83 and −14
−18 − 3 = (−18) + (−3)
Terms: −18 and −3
6 × 5 + 3
Terms: 6×5 and 3
6×5 is a single term!
Click "Reveal" to see the terms for each expression:
| Expression | Terms | |
|---|---|---|
| 13 − 2 + 6 | 13, −2, 6 | |
| 5 + 6×3 | 5, 6×3 | |
| 4 + 15 − 9 | 4, 15, −9 | |
| 23 − 2×4 + 16 | 23, −2×4, 16 | |
| 28 + 19 − 8 | 28, 19, −8 |
Swapping terms doesn't change the sum.
A drone goes 6 m up and then 4 m down.
Expression: 6 + (−4) = 2
Swap the terms: (−4) + 6 = 2
Same result! ✔
Grouping terms differently doesn't change the sum.
Evaluate (−7) + 10 + (−11) in different ways:
Way 1: [(−7) + 10] + (−11) = 3 + (−11) = −8
Way 2: (−7) + [10 + (−11)] = (−7) + (−1) = −8
Way 3: [(−7) + (−11)] + 10 = (−18) + 10 = −8
All give −8!
When an expression has multiplication, evaluate each term first, then add.
Terms: 30 and 5×4
Step 1: Evaluate 5 × 4 = 20
Step 2: Add: 30 + 20 = 50
A family orders 4 dosas at ₹23 each and gives a ₹5 tip.
Expression: 4 × 23 + 5 = 92 + 5 = ₹97
33 students play "Fire in the Mountain, Run Run Run!" They form groups of 5.
Expression: 6 × 5 + 3 = 30 + 3 = 33
6 complete groups with 3 students left over.
Raghu has 4 packets. His mother gives half of 100 more.
Expression: 4 + 100 ÷ 2 = 4 + 50 = 54 packets
Kannan pays ₹432 using notes and coins:
Expression: 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1
= 400 + 20 + 10 + 2 = ₹432
Which grid matches 5 × 2 + 3?
We need a grid with 5 rows of 2, plus 3 extra = 13 cells
(a) 28 − 7 + 8 =
(b) 39 − 2×6 + 11 =
(c) 40 − 10 + 10 + 10 =
(d) 48 − 10×2 + 16÷2 =
(e) 6×3 − 4×8÷5 =
(a) 89 + 21 − 10
(b) 5 × 12 − 6
(c) 4 × 9 + 2 × 6
(a) A princess has 5 chests with 20 gold coins each, plus 13 loose coins. How many coins total?
Answer:
(b) A metro ticket costs ₹35. A family of 4 buys tickets but gets ₹10 discount. Total cost?
Answer:
(c) A window is at 12 m height. A ladder reaches 3 m above the window. Ladder length?
Answer: m
100 − (15 + 56)
= 100 − 15 − 56
= 29
500 − (250 − 100)
= 500 − 250 + 100 (the − flipped to +!)
= 350
NOT 500 − 250 − 100 = 150 ✘
28 + (35 − 10)
= 28 + 35 − 10 (signs stay the same!)
= 53
How does changing one term affect the value?
Answer:
Answer:
Answer:
(a) 38 − (−7) = 38 + =
(b) 17 + (−3) = 17 − =
(c) (−22) + 18 = 18 − =
(a) 13 − (6 + 3) =
(b) 13 − (6 − 3) =
(c) 13 + (6 + 3) =
(d) 13 + (6 − 3) =
(e) −(18 + 5) =
(f) −(18 − 5) =
(a) 43 − (12 + 9) vs 43 − 12 − 9 →
(b) 43 − (12 − 9) vs 43 − 12 − 9 →
(a) 16 − 4 + 2 = 10 → Write with brackets:
(b) 3 + 2 × 4 = 20 →
Try all combinations: 2+3+5, 2+3−5, 2−3+5, 2−3−5, etc.
Lhamo and Norbu each order a meal costing ₹43 for food + ₹24 for drink.
Expression: 2 × (43 + 24) = 2 × 67 = 134
OR: 2 × 43 + 2 × 24 = 86 + 48 = 134
Both ways give the same answer!
4 rows of soldiers + 3 rows of soldiers, each row has 5 soldiers.
4 × 5 + 3 × 5 = (4 + 3) × 5 = 7 × 5 = 35
Given that 53 × 18 = 954, find 63 × 18.
63 × 18 = (53 + 10) × 18 = 53×18 + 10×18 = 954 + 180 = 1134
Calculate 97 × 25 mentally:
97 × 25 = (100 − 3) × 25 = 100×25 − 3×25 = 2500 − 75 = 2425
(a) 102 × 7 =
(b) 98 × 12 =
(c) 999 × 4 =
(a) 3 × (5 + 2) =
(b) 7 × (8 − 3) =
(c) (10 + 4) × 6 =
(d) (20 − 3) × 5 =
(e) 6 × 12 + 6 × 8 = 6 ×
(f) 5 × 17 − 5 × 7 = 5 ×
(g) 101 × 13 =
(h) 99 × 15 =
(i) 48 × 9 =
(j) 52 × 11 =
(k) 4 × 63 + 4 × 37 =
(l) 7 × 84 − 7 × 34 =
(m) 997 × 5 =
(n) 1005 × 8 =
(o) 12 × 45 + 12 × 55 =
(p) 25 × 88 =
(a) 3×(4+5) vs 3×4+5 →
(b) 8×(7−2) vs 8×7−2 →
(c) 5×9+5×1 vs 5×(9+1) →
(d) 6×(10−3) vs 6×10−3 →
Answer:
A grid with 3 rows of 4 and 3 rows of 6:
Way 1: 3×4 + 3×6 = 12 + 18 = 30
Way 2: 3×(4+6) = 3×10 = 30
(a) A vendor has 5 baskets with 24 mangoes each, and gives away 18 mangoes. How many left?
Answer:
(b) Binu saves ₹15 daily. After 10 days, he spends ₹50. How much does he have?
Answer:
(c) A snail climbs 3 m up each day and slides 1 m down at night. After 5 days, how high is it?
Answer: m
(a) "I had 20 chocolates, gave 5 to each of 3 friends."
Expression:
(b) "4 packets of 6 pencils plus 2 loose pencils."
Expression:
Way 1: Group pairs: (1−2)+(3−4)+(5−6)+(7−8)+(9−10) = (−1)+(−1)+(−1)+(−1)+(−1) = −5
Way 2: Group differently: 1+(−2+3)+(−4+5)+(−6+7)+(−8+9)−10 = 1+1+1+1+1−10 = −5
Way 3: Positives: 1+3+5+7+9 = 25. Negatives: 2+4+6+8+10 = 30. Total: 25−30 = −5
(a) 28+32 vs 28+33 →
(b) 45−19 vs 45−20 →
(c) 7×8 vs 7×6+7×2 →
(d) 3×(5+2) vs 3×5+2 →
(e) 100−(30+20) vs 100−30+20 →
(f) 50−(25−10) vs 50−25−10 →
(g) 9×(8+3) vs 9×8+9×3 →
(h) 12×5−4 vs 12×(5−4) →
A: 8×6+8×4 • B: 8×(6+4) • C: 8×10 • D: 80 • E: 8×6+4
Put your expression skills to the ultimate test!
Using exactly three 3's and any operations (+, −, ×, ÷, brackets), make as many different values as possible.
Example: 3 + 3 + 3 = 9, 3 × 3 + 3 = 12, 3 × 3 × 3 = 27, 3 × 3 − 3 = 6, (3 + 3) × 3 = 18
Using exactly four 4's and any operations, try to make every number from 1 to 20.
Using digits 1, 2, 3, 4, 5 exactly once each with +, −, try to get every value from −10 to +10.
Using digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 exactly once each, make an expression that equals 100.