Viral Maths — Ch10: Decimal

📌 What This Chapter Covers

Decimals ek number type hain jinme whole number aur fractional part ek decimal point se separate hote hain.
Chapter 4 operations mein bata hai: Addition, Subtraction, Multiplication, Division — har ek ke apne named types hain.
Core idea sabme common hai: decimal ko "ignore" karke pehle poore number pe operation karo, phir decimal ko sahi jagah wapas rakho.

⚡ QUICK RECALL

Yeh chapter Ch09 (Percentage) ki fraction table use karta hai (.25=1/4, .5=1/2, .75=3/4, .125=1/8) — Multiplication section mein directly connect hota hai.

🗂️ Chapter Index

Tab	Section	Types
2	Decimal Addition	Decimal+Whole, Decimal+Decimal
3	Decimal Subtraction	Decimal−Single Digit, Whole−2-digit Decimal
4	Decimal Multiplication	Decimal×Whole, Decimal(.25/.5/.75/.125)×Number
5	Decimal Division	Decimal÷Whole, Decimal÷Decimal
6	Master Table	All sections summarized

Type 1 — Decimal Number + Whole (Non-decimal) Number

Example: 2.4 + 9

Step 1: Add whole parts: 2+9 = 11 Step 2: Add back the decimal part: 11+0.4 = 11.4

Type 2 — Decimal Number + Decimal Number

Example: 87.5 + 12.7

Step 1: Break the numbers: 87+0.5 and 12+0.7 Step 2: Add whole parts: 87+12 = 99 Step 3: Add decimal parts: 0.5+0.7 = 1.2 Step 4: Combine: 99+1.2 = 100.2

⚠ EXAM TRAP

Decimal parts ka sum ≥1 ho sakta hai (jaise 0.5+0.7=1.2) — is extra "1" ko whole-part total mein carry karna mat bhoolo jab final answer likho.

⚡ QUICK RECALL

Whole parts alag add karo, decimal parts alag add karo, phir dono ko combine karo — yeh Ch02 Addition ke "2-digit+2-digit base method" jaisa hi hai.

Type 1 — Decimal Number − Single-digit Whole Number

Example: 58.4 − 7

Step 1: Subtract whole parts: 58−7 = 51 Step 2: Add back the decimal part: 51+0.4 = 51.4

Type 2 — Whole Number − Two-digit Decimal Number

Example: 167 − 3.6

Step 1: Round 3.6 up to 4 (extra = 0.4) Step 2: Subtract the rounded value: 167−4 = 163 Step 3: Add back the extra: 163+0.4 = 163.4

Example: 453 − 7.3

Step 1: Round 7.3 up to 8 (extra = 0.7) Step 2: Subtract: 453−8 = 445 Step 3: Add back extra: 445+0.7 = 445.7

⚡ QUICK RECALL

Yeh Ch03 Subtraction ke Tidding-Tidding Approach jaisa hi concept hai — round up karo, subtract karo, phir extra add-back karo.

Type 1 — Decimal Number × Whole Number

Example: 80.9 × 4

Step 1: Multiply ignoring the decimal: 809×4 = 3236 Step 2: Count decimal places in original (here 1) Step 3: Place decimal 1 place from right: 323.6

Type 2 — Decimal Ending in .25/.5/.75/.125 × Number

Know: .25=1/4, .5=1/2, .75=3/4, .125=1/8

Example: 80.25 × 4

Step 1: Multiply whole part: 80×4 = 320 Step 2: Multiply decimal part: 0.25×4 = 1/4×4 = 1 Step 3: Add both: 320+1 = 321

⚠ EXAM TRAP

Yeh trick sirf .25, .5, .75, .125 endings ke liye specifically fast hai — kyunki inke fraction-forms simple hain. Random decimals (jaise .37) ke liye Type 1 use karo.

⚡ QUICK RECALL

Directly Ch09 Percentage ki fraction table se jud raha hai — .25=25%=1/4, .75=75%=3/4.

Type 1 — Decimal Number ÷ Whole (Non-decimal) Number

Example: 80.24 ÷ 4

Step 1: Divide ignoring decimal: 8024÷4 = 2006 Step 2: Count decimal places in original (here 2) Step 3: Place decimal 2 places from right: 20.06

Type 2 — Decimal Number ÷ Decimal Number (Kargil Approach)

Example: 62.5 ÷ 0.25

Step 1: Ignore decimals, divide: 625÷25 = 25 Step 2: Numerator decimal place = 1, Denominator decimal place = 2 Step 3: Subtract: 1−2 = −1 (negative result) Step 4: Negative result of magnitude 1 → add 1 zero to answer Ans: 250

Example: 0.625 ÷ 2.5

Step 1: Ignore decimals: 625÷25 = 25 Step 2: Numerator place=3, Denominator place=1 Step 3: Subtract: 3−1 = +2 (positive result) Step 4: Positive result of 2 → place decimal 2 digits from right Ans: 0.25

Example: 62.5 ÷ 2.5 (equal places)

Step 1: Ignore decimals: 625÷25 = 25 Step 2: Both places = 1, difference = 0 Step 3: Just cancel out the decimal Ans: 25

⚠ EXAM TRAP

Direction of subtraction matters: (numerator places − denominator places). NEGATIVE result → ADD that many zeros to the answer (makes it bigger). POSITIVE result → PLACE decimal that many digits from the right (makes it smaller). ZERO → no decimal adjustment needed.

⚡ QUICK RECALL

Yeh Ch05 Division ka Kargil Approach hi hai, ab formally decimal-place-counting ke साथ explain kiya gaya hai.

📋 Master Table — All Decimal Operations

Operation	Type	Core Rule
Addition	Decimal + Whole	Add whole parts, add back decimal
Addition	Decimal + Decimal	Add whole parts separately, add decimal parts separately, combine
Subtraction	Decimal − Single Digit	Subtract whole parts, add back decimal
Subtraction	Whole − 2-digit Decimal	Round up, subtract, add back the extra
Multiplication	Decimal × Whole	Multiply ignoring decimal, place decimal back by counting places
Multiplication	.25/.5/.75/.125 × Number	Multiply whole and fraction parts separately using known fractions, add
Division	Decimal ÷ Whole	Divide ignoring decimal, place decimal back by counting places
Division	Decimal ÷ Decimal (Kargil)	Divide ignoring decimals, then adjust by (numerator places − denominator places)