Simplification — Extra Practice — Number System & Simplification Notes (English Medium)

NoteThis is the Extra Practice set: lots of questions. To learn the methods first, read the main chapter of the same topic (the one without “Extra Practice” in its name), then practise here.

Bank, SSC and railway papers open with 5–10 simplification questions. There is no hard theory in them — only the right order and a quick hand. The same expression $12 + 8 \times 3$ gets 60 from one student and 36 from another, only because one ignored the order. This chapter fixes that order (VBODMAS), the identities worth knowing and the tricks that save time.

1

The VBODMAS rule

What first, what next

The order of operations, kinds of brackets, “of”, absolute value, and expressions with powers and roots.

The order of operations

V · B · O · D · M · A · S

What each letter means, the order of opening brackets and the left-to-right rule.

Letter	Meaning	Example
V	Vinculum — the bar drawn over terms	$\overline{8 - 3} \times 2 = 5 \times 2$
B	Brackets	( ) { } [ ]
O	Of — multiplication, but done early	$\frac{1}{2}$ of 40
D	Division	÷
M	Multiplication	×
A	Addition	+
S	Subtraction	−

Order of brackets: first the small ( ), then the curly { }, then the big [ ] — from the inside out.
D and M have equal priority, and so do A and S — when operations of the same rank meet, go left to right. $48 \div 6 \times 2 = 8 \times 2 = 16$ , not $48 \div 12 = 4$ .
“Of” always comes before division and multiplication: $\frac{2}{5}$ of $50 + 10$ gives 20 first, then 30.
The part under a bar (V) is done first like a bracket: $20 - \overline{7 + 3} = 20 - 10 = 10$ .

Example 1 · Basic

Simplify 12 + 8 × 3 − 20 ÷ 4.

Solution, step by step

11) 12 + 24 − 20 ÷ 4
22) 12 + 24 − 5
33) 36 − 5
44) 31

Answer 31

Multiplication and division first, then addition and subtraction.

Example 2 · Standard

Simplify {36 ÷ (4 + 2) × 3} − [15 − (6 + 3)].

Solution, step by step

11) {36 ÷ 6 × 3} − [15 − (6 + 3)]
22) 18 − [15 − (6 + 3)]
33) 18 − [15 − 9]
44) 18 − 6
55) 12

Answer 12

Start with the innermost bracket.

Example 3 · Standard

Simplify 3/5 of 250 + 40 ÷ 8.

Solution, step by step

11) 150 + 40 ÷ 8
22) 150 + 5
33) 155

Answer 155

“Of” comes even before division.

BasicTry it yourself first

What is the value of 18 + 6 × 4 − 10?

BasicTry it yourself first

What is the value of 56 ÷ 7 + 3 × 5?

BasicTry it yourself first

What is the value of (14 + 6) × 3 − 25?

StandardTry it yourself first

What is the value of 72 ÷ 9 × 4 − 3 × 5 + 2?

StandardTry it yourself first

What is the value of 90 − [45 ÷ (7 + 2) + 6 × 3]?

StandardTry it yourself first

What is the value of {48 − (12 + 8) ÷ 4} × 2?

AdvancedTry it yourself first

What is the value of 216 ÷ {18 + [30 − (4 × 5 − 8)] × 2} + 11?

Absolute value

Distance from zero — never negative

What $∣ x ∣$ means and how to simplify with it.

∑ Formula

∣ x ∣ = {x - x x \geq 0 x < 0

Definition of absolute value

$∣ x ∣$ says how far $x$ is from zero. $∣5∣ = 5$ and $∣ - 5∣ = 5$ . So $∣3 - 9∣ = ∣ - 6∣ = 6$ , and $- ∣3 - 9∣ = - 6$ (the outer minus sign stays). Do the working inside the modulus first, then make it non-negative.

Example 4 · Standard

Evaluate

∣7 - 12∣ + ∣15 - 9∣ - ∣4 - 4∣

.

Solution, step by step

1 $∣7 - 12∣ = ∣ - 5∣ = 5$ , $∣15 - 9∣ = 6$ , $∣4 - 4∣ = 0$ .
2 $5 + 6 - 0 = 11$

Answer 11

BasicTry it yourself first

What is

∣6 - 13∣ + ∣20 - 9∣

?

StandardTry it yourself first

What is

∣8 - 25∣ - ∣7 - 19∣ + ∣4 - 4∣

?

StandardTry it yourself first

What is

∣3 - 17∣ + ∣21 - 6∣ - ∣9 - 30∣

?

AdvancedTry it yourself first

What is

∣15 - 48∣ - ∣22 - 5∣ + ∣31 - 40∣ - ∣6 - 6∣

?

Expressions with powers, roots and fractions

Powers first, then VBODMAS

When an expression has $x^{2}$ , $x$ or fractions, turn them into values first.

Powers and roots are “single units” just like brackets: in $3 + 2^{3} \times 2$ first $2^{3} = 8$ , then $8 \times 2 = 16$ , then $3 + 16 = 19$ . With fractions, convert to decimals or keep proper fractions, and simplify only at the end.

Example 5 · Standard

Evaluate

\frac{3 ^{2} + 4 ^{2}}{25} - 81 \div 3

.

Solution, step by step

1 $3^{2} + 4^{2} = 9 + 16 = 25$ , $25 = 5$ ⟹ the first part is $5$ .
2 $81 \div 3 = 9 \div 3 = 3$ ⟹ $5 - 3 = 2$

Answer 2

StandardTry it yourself first

What is the value of 2/3 of 90 + 4/5 of 55 − 30?

StandardTry it yourself first

What is the value of 5/8 of 640 ÷ 25 + 14?

AdvancedTry it yourself first

What is the value of 3/4 of 480 ÷ {6 + (36 ÷ 9) × 3} − 5?

StandardTry it yourself first

What is

144 + 3216 \div 2^{2}

?

AdvancedTry it yourself first

What is

(0.2)^{2} + (0.3)^{2} + 2 \times 0.2 \times 0.3

?

2

Algebraic identities

Shrinking a big calculation with a pattern

The patterns for squares, cubes and the difference of two squares, and questions built on them.

Identities for squares and cubes

Eight formulas worth knowing

The list of formulas and big-number calculations done in seconds.

Formula	When it helps
$(a + b)^{2} = a^{2} + 2 ab + b^{2}$	a perfect square of round or decimal numbers
$(a - b)^{2} = a^{2} - 2 ab + b^{2}$	a number near 100 or 1000
$a^{2} - b^{2} = (a + b) (a - b)$	difference of squares / simplifying fractions
$(a + b)^{2} + (a - b)^{2} = 2 (a^{2} + b^{2})$	sum of two squares
$(a + b)^{2} - (a - b)^{2} = 4 ab$	difference of two squares, from the product
$(a + b)^{3} = a^{3} + b^{3} + 3 ab (a + b)$	sum of cubes
$(a - b)^{3} = a^{3} - b^{3} - 3 ab (a - b)$	difference of cubes
$a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2})$	factorising a sum of cubes

Example 6 · Standard

Evaluate

(4.7)^{2} + 2 \times 4.7 \times 5.3 + (5.3)^{2}

.

Solution, step by step

1This is the pattern of $(a + b)^{2}$ .
2 $(4.7 + 5.3)^{2} = 1 0^{2} = 100$

Answer 100

Example 7 · Standard

Evaluate

\frac{8 7 ^{2} - 1 3 ^{2}}{74}

.

Solution, step by step

1 $8 7^{2} - 1 3^{2} = (87 + 13) (87 - 13) = 100 \times 74$ .
274 cancels: the value is $100$ .

Answer 100

Example 8 · Advanced

Evaluate

(0.75)^{3} - (0.25)^{3} - 3 \times 0.75 \times 0.25 \times 0.5

.

Solution, step by step

1With $a = 0.75, b = 0.25$ and $a - b = 0.5$ this is the form of $(a - b)^{3}$ .
2 $(0.75 - 0.25)^{3} = 0. 5^{3} = 0.125$

Answer 0.125

BasicTry it yourself first

What is 3.6² + 2 × 3.6 × 6.4 + 6.4²?

StandardTry it yourself first

What is 12.5² + 2 × 12.5 × 7.5 + 7.5²?

StandardTry it yourself first

What is 0.35² + 2 × 0.35 × 0.65 + 0.65²?

BasicTry it yourself first

What is

\frac{6 3 ^{2} - 3 7 ^{2}}{63 - 37}

?

StandardTry it yourself first

What is

\frac{14 8 ^{2} - 5 2 ^{2}}{148 - 52}

?

StandardTry it yourself first

What is

\frac{14 0 ^{2} - 2 4 ^{2}}{140 - 24}

?

BasicTry it yourself first

What is

(8 + 5)^{2} - (8 - 5)^{2}

?

StandardTry it yourself first

What is

(25 + 14)^{2} - (25 - 14)^{2}

?

Finding a value from given relations

From a sum and a product

When $x + y$ and $x y$ are given, find $x^{2} + y^{2}$ or $x^{3} + y^{3}$ without finding $x$ and $y$ .

∑ Formula

x^{2} + y^{2} = (x + y)^{2} - 2 x y, x^{3} + y^{3} = (x + y)^{3} - 3 x y (x + y)

The two big formulas

Method: square (or cube) the sum (or difference) you are given and fill the middle term from the product. You never need $x$ and $y$ separately.

Example 9 · Standard

If

x + y = 9

and

x y = 14

, find

x^{2} + y^{2}

and

x^{3} + y^{3}

.

Solution, step by step

1 $x^{2} + y^{2} = 81 - 28 = 53$ .
2 $x^{3} + y^{3} = 9^{3} - 3 \times 14 \times 9 = 729 - 378 = 351$ .

Answer $53$ and $351$

Example 10 · Advanced

If

3 x + 2 y = 12

and

x y = 6

, what is

9 x^{2} + 4 y^{2}

?

Solution, step by step

1 $(3 x + 2 y)^{2} = 9 x^{2} + 4 y^{2} + 2 \times 3 \times 2 \times x y$ .
2 $144 = 9 x^{2} + 4 y^{2} + 72$ ⟹ $9 x^{2} + 4 y^{2} = 72$

Answer 72

StandardTry it yourself first

If

2 x + 3 y = 13

and

x y = 5

, what is

4 x^{2} + 9 y^{2}

?

StandardTry it yourself first

If

4 x + 1 y = 14

and

x y = 6

, what is

16 x^{2} + 1 y^{2}

?

AdvancedTry it yourself first

If

5 x + 2 y = 19

and

x y = 9

, what is

25 x^{2} + 4 y^{2}

?

StandardTry it yourself first

If

a + b = 7

and

ab = 10

, what is

a^{3} + b^{3}

?

AdvancedTry it yourself first

If

a + b = 11

and

ab = 28

, what is

a^{3} + b^{3}

?

3

Speed methods

Multiplication tricks · series sums · find ?

Time-saving tricks, series formulas and the method for fill-in-the-blank questions.

Multiplication tricks

Go to the round number nearby

Multiplying by 5, 25, 125, 99, 101, 11 and fractions “of” a number.

Multiplier	Trick	Example
×5	×10 then ÷2	86 × 5 = 860 ÷ 2 = 430
×25	×100 then ÷4	48 × 25 = 4800 ÷ 4 = 1200
×125	×1000 then ÷8	64 × 125 = 64000 ÷ 8 = 8000
×99	×100 − the number	37 × 99 = 3700 − 37 = 3663
×101	×100 + the number	37 × 101 = 3700 + 37 = 3737
×11	×10 + the number	53 × 11 = 530 + 53 = 583

Fractions “of” a number: $\frac{3}{8}$ of 640 = $640 \div 8 \times 3 = 80 \times 3 = 240$ . Divide first, then multiply — it keeps the numbers small. Pairing with percent: $\frac{1}{8} = 12.5%$ , $\frac{3}{8} = 37.5%$ , $\frac{1}{6} = 16. \overline{6} %$ — remember these.

Example 11 · Basic

Find

68 \times 25

and

53 \times 99

.

Solution, step by step

1 $68 \times 25 = 6800 \div 4 = 1700$ .
2 $53 \times 99 = 5300 - 53 = 5247$ .

Answer $1700$ and $5247$

BasicTry it yourself first

What is 36 × 25?

BasicTry it yourself first

What is 74 × 5?

StandardTry it yourself first

What is 88 × 125?

StandardTry it yourself first

What is 47 × 99?

StandardTry it yourself first

What is 63 × 101?

StandardTry it yourself first

What is 85 × 11?

BasicTry it yourself first

What is 3/8 of 640?

StandardTry it yourself first

What is 7/12 of 1,260?

StandardTry it yourself first

What is 5/9 of 810?

AdvancedTry it yourself first

What is 11/16 of 2,400?

Sums of series

Four formulas

Sums of natural numbers, squares, cubes and odd numbers.

Series	Sum
$1 + 2 + 3 + \dots + n$	$\frac{n ( n + 1 )}{2}$
$1^{2} + 2^{2} + \dots + n^{2}$	$\frac{n ( n + 1 ) ( 2 n + 1 )}{6}$
$1^{3} + 2^{3} + \dots + n^{3}$	$[\frac{n ( n + 1 )}{2}]^{2}$
$1 + 3 + 5 + \dots + (2 n - 1)$	$n^{2}$
$2 + 4 + 6 + \dots + 2 n$	$n (n + 1)$

Example 12 · Standard

Find

1 + 2 + 3 + \dots + 60

and

1^{2} + 2^{2} + \dots + 1 0^{2}

.

Solution, step by step

1 $\frac{60 \times 61}{2} = 1830$ .
2 $\frac{10 \times 11 \times 21}{6} = 385$ .

Answer $1830$ and $385$

Example 13 · Standard

What is the sum of the first 20 even numbers?

Solution, step by step

1By $2 + 4 + \dots + 2 n = n (n + 1)$ it is $20 \times 21$ .
2 $= 420$

Answer 420

BasicTry it yourself first

What is

1 + 2 + 3 + \dots + n

when

n = 40

?

BasicTry it yourself first

What is

1 + 3 + 5 + \dots + (2 n - 1)

when

n = 15

?

StandardTry it yourself first

What is

1^{2} + 2^{2} + 3^{2} + \dots + n^{2}

when

n = 12

?

StandardTry it yourself first

What is

1^{3} + 2^{3} + 3^{3} + \dots + n^{3}

when

n = 9

?

AdvancedTry it yourself first

What is

1^{2} + 2^{2} + 3^{2} + \dots + n^{2}

when

n = 25

?

AdvancedTry it yourself first

What is

1^{3} + 2^{3} + 3^{3} + \dots + n^{3}

when

n = 14

?

“Find ?” questions

Work backwards

The fill-in-the-blank questions of bank exams: undo each operation with its opposite.

Two routes: (1) work backwards — undo addition with subtraction, multiplication with division; (2) test the options — the one that gives the right left-hand value. When ? appears more than once ( $? + ? \times 4$ ), think of it as algebra.

Example 14 · Basic

If

(? + 18) \times 4 \div 3 = 48

, what is ?

Solution, step by step

1Undo $\times 4 \div 3$ : $48 \times 3 \div 4 = 36$ .
2 $? + 18 = 36$ ⟹ $? = 18$

Answer 18

BasicTry it yourself first

If (? + 18) × 4 ÷ 3 = 56, what is ?

BasicTry it yourself first

If 7 × ? − 15 = 69, what is ?

StandardTry it yourself first

If (? − 9) × 6 + 20 = 152, what is ?

StandardTry it yourself first

If ? ÷ 8 + ? ÷ 4 = 15, what is ?

StandardTry it yourself first

If 3/5 of ? + 14 = 59, what is ?

AdvancedTry it yourself first

If (? + 36) ÷ 4 − 17 = 5, what is ?

AdvancedTry it yourself first

If 5/6 of (? − 12) + 9 = 109, what is ?

4

Traps and fast tricks

Slips · saving time

How marks are lost in simplification, and how to turn a 2-minute calculation into 30 seconds.

The commonest mistakes

Six traps

The slips that cost marks.

Trap 1Forgetting left to right.

24 \div 4 \times 3 = 6 \times 3 = 18

, not

24 \div 12 = 2

. D and M have equal priority.

Trap 2Adding before multiplying.

5 + 3 \times 4 = 17

, not 32.

Trap 3Not distributing the minus before a bracket.

10 - (3 - 8) = 10 - (- 5) = 15

, not

10 - 3 - 8

.

Trap 4Reading “of” loosely. In

\frac{1}{4}

of

80 + 20

do

\frac{1}{4}

of 80 = 20 first, then +20.

Trap 5Dropping $2 ab$ in $(a + b)^{2}$ . The same slip spoils every identity question.

Trap 6Dropping the minus outside a modulus.

- ∣3 - 9∣ = - 6

, not

+ 6

.

Fast tricks

Cut options · last digit · estimate

Ways to discard wrong options without solving fully.

Last-digit check: the last digit of a product follows from the last digits of the factors. $47 \times 63$ ends in $7 \times 3 = 21$ → 1.
Digit-sum check (casting out nines): the remainder mod 9 of a product equals the product of the remainders.
Estimate: $498.7 \times 2.01 \approx 500 \times 2 = 1000$ — drop the options far from 1000.
Group the terms: $97 + 98 + 99 + 101 + 102 + 103 = 600$ (pair them around 100 and cancel the ±).
Pair identities: $\frac{a ^{2} - b ^{2}}{a - b} = a + b$ and $\frac{a ^{3} + b ^{3}}{a ^{2} - ab + b ^{2}} = a + b$ — when a fraction appears, look for an identity first.

Example 15 · Standard

Evaluate

\frac{( 8.4 ) ^{3} + ( 1.6 ) ^{3}}{( 8.4 ) ^{2} - 8.4 \times 1.6 + ( 1.6 ) ^{2}}

.

Solution, step by step

1This is $\frac{a ^{3} + b ^{3}}{a ^{2} - ab + b ^{2}}$ , which equals $a + b$ .
2 $8.4 + 1.6 = 10$

Answer 10

5

The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

BasicTry it yourself first

What is the value of 45 − 5 × 6 + 12?

BasicTry it yourself first

What is the value of (63 ÷ 9) × 4 + 8?

BasicTry it yourself first

What is the value of 100 − 36 ÷ 4 × 2?

BasicTry it yourself first

What is the value of 7 + 8 × (30 − 24) ÷ 2?

BasicTry it yourself first

What is the value of 2/3 of 120 − 15?

BasicTry it yourself first

What is the value of 9 × 12 ÷ 6 + 4?

BasicTry it yourself first

What is the value of (25 + 35) ÷ 5 − 3 × 2?

BasicTry it yourself first

What is

∣5 - 12∣ + ∣14 - 8∣

?

BasicTry it yourself first

If ? × 9 + 12 = 84, what is ?

BasicTry it yourself first

If (? − 6) × 5 = 40, what is ?

BasicTry it yourself first

What is 7.5² + 2 × 7.5 × 2.5 + 2.5²?

BasicTry it yourself first

What is

\frac{9 1 ^{2} - 9 ^{2}}{91 - 9}

?

BasicTry it yourself first

What is

(9 + 4)^{2} - (9 - 4)^{2}

?

BasicTry it yourself first

What is 44 × 25?

BasicTry it yourself first

What is 52 × 99?

BasicTry it yourself first

What is 38 × 11?

BasicTry it yourself first

What is

1 + 2 + 3 + \dots + n

when

n = 50

?

BasicTry it yourself first

What is

1 + 3 + 5 + \dots + (2 n - 1)

when

n = 20

?

BasicTry it yourself first

What is 5/6 of 480?

Level 2 — Standard

Two ideas combined

Exam-level questions.

StandardTry it yourself first

What is the value of 84 ÷ 7 × 3 − (18 + 6) ÷ 4?

StandardTry it yourself first

What is the value of {150 − (25 × 3 − 15)} ÷ 6?

StandardTry it yourself first

What is the value of 56 + [48 ÷ (3 + 5) × 7] − 20?

StandardTry it yourself first

What is the value of 3/4 of 360 − 2/5 of 150?

StandardTry it yourself first

What is the value of (3.5 × 4 + 2.4 ÷ 0.8) ÷ 0.5?

StandardTry it yourself first

What is the value of 0.6 × 25 − 4.5 ÷ 1.5 + 8?

StandardTry it yourself first

What is the value of 7/9 of 189 ÷ 21 + 13?

StandardTry it yourself first

What is the value of 100 ÷ {4 + (18 − 2 × 5) × 2} + 17?

StandardTry it yourself first

What is

∣11 - 30∣ - ∣5 - 25∣ + ∣8 - 8∣

?

StandardTry it yourself first

What is

∣7 - 31∣ + ∣29 - 14∣ - ∣4 - 20∣

?

StandardTry it yourself first

If (? + 24) ÷ 5 × 3 = 36, what is ?

StandardTry it yourself first

If ? × 4 − ? ÷ 2 = 105, what is ?

StandardTry it yourself first

If 5/8 of ? − 17 = 43, what is ?

StandardTry it yourself first

If (? − 7) × 9 ÷ 4 = 81, what is ?

StandardTry it yourself first

What is 16.5² + 2 × 16.5 × 3.5 + 3.5²?

StandardTry it yourself first

What is 0.46² + 2 × 0.46 × 0.54 + 0.54²?

StandardTry it yourself first

What is

\frac{25 3 ^{2} - 4 7 ^{2}}{253 - 47}

?

StandardTry it yourself first

What is

(17 + 6)^{2} - (17 - 6)^{2}

?

StandardTry it yourself first

If

3 x + 5 y = 17

and

x y = 4

, what is

9 x^{2} + 25 y^{2}

?

StandardTry it yourself first

If

a + b = 8

and

ab = 15

, what is

a^{3} + b^{3}

?

StandardTry it yourself first

What is 76 × 125?

StandardTry it yourself first

What is 91 × 101?

StandardTry it yourself first

What is 64 × 25?

StandardTry it yourself first

What is

1 + 2 + 3 + \dots + n

when

n = 30

?

StandardTry it yourself first

What is

1^{3} + 2^{3} + 3^{3} + \dots + n^{3}

when

n = 8

?

StandardTry it yourself first

What is

1^{2} + 2^{2} + 3^{2} + \dots + n^{2}

when

n = 15

?

StandardTry it yourself first

What is 9/14 of 2,100?

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

AdvancedTry it yourself first

What is the value of 480 ÷ {12 + [45 − (8 × 4 − 11)] × 2} × 3 − 9?

AdvancedTry it yourself first

What is the value of 5/7 of 497 − 3/8 of {64 + 8 × (21 − 13)}?

AdvancedTry it yourself first

What is the value of [(2.5 × 3.2) + 0.84 ÷ 0.07] ÷ 0.4 − 17?

AdvancedTry it yourself first

What is the value of 84 × 15 ÷ 12 − 7/9 of 135 + 36 ÷ 4 × 3?

AdvancedTry it yourself first

What is the value of {0.75 × 64 − 0.4 × 45} ÷ 0.6 + 12?

AdvancedTry it yourself first

What is the value of 3/5 of {2/3 of 450 + 150} ÷ 9 − 8?

AdvancedTry it yourself first

What is

∣19 - 52∣ - ∣33 - 17∣ + ∣6 - 48∣ - ∣25 - 25∣

?

AdvancedTry it yourself first

If (? − 9) × 12 ÷ 7 + 5 = 89, what is ?

AdvancedTry it yourself first

If 7/12 of (? + 24) − 18 = 59, what is ?

AdvancedTry it yourself first

If ? ÷ 6 + ? ÷ 4 + ? ÷ 3 = 54, what is ?

AdvancedTry it yourself first

What is 27.25² + 2 × 27.25 × 22.75 + 22.75²?

AdvancedTry it yourself first

What is

\frac{1 , 27 5 ^{2} - 72 5 ^{2}}{1 , 275 - 725}

?

AdvancedTry it yourself first

What is

(15 + 4)^{2} - (15 - 4)^{2}

?

AdvancedTry it yourself first

If

7 x + 3 y = 25

and

x y = 6

, what is

49 x^{2} + 9 y^{2}

?

AdvancedTry it yourself first

If

a + b = 13

and

ab = 36

, what is

a^{3} + b^{3}

?

AdvancedTry it yourself first

What is 168 × 125?

AdvancedTry it yourself first

What is 249 × 99?

AdvancedTry it yourself first

What is 372 × 101?

AdvancedTry it yourself first

What is

1^{2} + 2^{2} + 3^{2} + \dots + n^{2}

when

n = 40

?

AdvancedTry it yourself first

What is

1^{3} + 2^{3} + 3^{3} + \dots + n^{3}

when

n = 18

?

AdvancedTry it yourself first

What is 13/20 of 4,600?

AdvancedTry it yourself first

What is

\frac{0.8 \times 0.8 \times 0.8 + 0.2 \times 0.2 \times 0.2}{0.8 \times 0.8 - 0.8 \times 0.2 + 0.2 \times 0.2}

?

6

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.