SAT-91: Translating English into Math (Key Terms Dictionary)

SAT-91: Translating English into Math (Key Terms Dictionary)

Description: Word problems are just equations hidden inside sentences. Once you know which English words become which math symbols, you can translate almost any sentence into an equation you can solve. This lesson is your dictionary.

The key terms dictionary

• "is", "was", "equals", "will be" → =
• "sum", "more than", "increased by", "total" → +
• "difference", "less than", "decreased by", "fewer" → −
• "product", "of", "times", "twice", "triple" → ×
• "quotient", "per", "ratio", "divided by" → ÷
• "a number", "what", "some value" → a variable (x)

(Oʻzbekcha: "is" = teng, "of" = koʻpaytirish, "per" = boʻlish — soʻzlarni belgilarga aylantiramiz.)

The two famous order traps

"Less than" and "more than" flip the order: "5 less than x" is x − 5, not 5 − x. And "the quotient of a and b" is a ÷ b, in that order. Read carefully. (Oʻzbekcha: "less than" tartibni teskari qiladi: "x dan 5 kam" = x − 5.)

Worked Example 1 — a basic sentence

"Three more than twice a number is 11." Translate and solve.

• Twice a number = 2x; three more = 2x + 3; "is 11" = = 11.
• 2x + 3 = 11 → 2x = 8 → x = 4.

Worked Example 2 — the "less than" trap

"Seven less than a number equals 12." Translate and solve.

• "Seven less than a number" = x − 7 (not 7 − x); "equals 12" = = 12.
• x − 7 = 12 → x = 19.

(Oʻzbekcha: "seven less than" = x − 7, tartibga eʼtibor bering.)

Worked Example 3 — "of" means multiply

"Half of a number, increased by 4, is 9." Translate and solve.

• Half of a number = x/2; increased by 4 = + 4; is 9 = = 9.
• x/2 + 4 = 9 → x/2 = 5 → x = 10.

Worked Example 4 — two quantities

"A pen costs 3 dollars more than a pencil. Together they cost 9 dollars." Find the pencil's price.

• Let pencil = p. Pen = p + 3. Together: p + (p + 3) = 9.
• 2p + 3 = 9 → 2p = 6 → p = 3 (pencil $3, pen $6).

Strategy: translate the sentence piece by piece, left to right, replacing each phrase with its symbol. (Oʻzbekcha: gapni qism-qismga boʻlib, har birini belgiga aylantiring.)

The two phrases that flip order — in detail

It's worth slowing down on the order-flippers because they cause more errors than any other translation. "5 less than x" means you start with x and take 5 away: x − 5. "5 fewer than x" works the same way. The same logic applies to subtraction words generally — the thing being subtracted comes after the phrase. Compare "the difference of x and 5" (x − 5) with "5 less than x" (also x − 5) — both land in the same order, but the wording feels reversed, which is exactly the trap. (Oʻzbekcha: "less than" va "fewer than" tartibni teskari qiladi — ayiriladigan son keyin keladi.)

Naming the unknown clearly

Always write "let x = …" in words before translating, so you don't lose track of what the variable stands for. In a problem about ages, "let x = Ben's age in years" is far safer than a bare x, especially when the question later asks for a different quantity (like Anna's age). Clear labels turn multi-step word problems into routine algebra. (Oʻzbekcha: tarjimadan oldin "x = ..." deb soʻz bilan yozing — oʻzgaruvchi nimani bildirishini unutmaysiz.)

Practice 1

"Five more than three times a number is 20." Find the number.

Practice 2

"Four less than half of a number is 6." Find the number.

Key words — Kalit soʻzlar

• Translate — tarjima qilish (oʻgirish)
• Sum — yigʻindi
• Difference — ayirma
• Product — koʻpaytma
• Quotient — boʻlinma
• Less than / More than — kam / koʻp
• Of (= multiply) — "ning" (koʻpaytirish)
• Per — har biriga (boʻlish)
• Variable — oʻzgaruvchi

Summary

• "Is" → =, "of" → ×, "per" → ÷, "more/less than" → +/−.
• "Less than" flips the order: "5 less than x" = x − 5.
• Translate left to right, phrase by phrase, then solve the equation.