SAT-51: Percentages — Part, Whole, and Base

SAT-51: Percentages — Part, Whole, and Base

Description: Percent means "per 100." Almost every percent question is one relationship: part = percent × whole. Rearranging it solves for whichever piece is missing.

The core relationship

part = (percent ÷ 100) × whole

• Find the part: multiply (e.g. 20% of 50 = 0.20 × 50 = 10).
• Find the percent: part ÷ whole, then ×100.
• Find the whole (base): part ÷ (percent/100).

(Oʻzbekcha: foiz — "yuzdan necha". Asosiy formula: qism = (foiz ÷ 100) × butun.)

Worked Example (find the part)

What is 15% of 80?

• 0.15 × 80 = 12.

Worked Example (find the percent)

18 is what percent of 24?

• 18 ÷ 24 = 0.75 → ×100 = 75%.

(Oʻzbekcha: qismni butunga boʻlib, 100 ga koʻpaytiramiz.)

Worked Example (find the whole / base)

30 is 20% of what number?

• whole = 30 ÷ 0.20 = 150.

Watch the wording: "of" marks the whole (base); "is" marks the part. (Oʻzbekcha: "ning" — butun (asos); "bu/teng" — qism.)

Practice

A shirt costs $40 and is 25% of a person's daily budget. What is the budget? Show answer budget = 40 ÷ 0.25 = $160.

Key words — Kalit soʻzlar

• Percent — foiz
• Part — qism
• Whole / Base — butun / asos
• Per 100 — yuzdan
• Of (= multiply) — "ning" (koʻpaytirish)
• Is (= equals) — "teng"
• Decimal — oʻnli kasr
• Multiply / Divide — koʻpaytirish / boʻlish
• Budget — byudjet (mablagʻ)

Summary

• Everything comes from part = (percent/100) × whole.
• Percent = part ÷ whole × 100; whole = part ÷ (percent/100).
• "Of" → the whole/base; "is" → the part.