Prerequisite 3 of 4The skill behind every word problem

From Words to Equations വാക്കുകളിൽ നിന്ന് സമവാക്യങ്ങളിലേക്ക്

Most questions in this chapter are stories: beads in a box, prices of pens, ages, wires bent into shapes. The algebra is easy once the story is written as equations. This page is a small dictionary and a set of habits for doing that translation without mistakes.

📖 What you already know (pages 1–2 of this guide)

"5 more than x" = x + 5, "3 times x" = 3x, "twice the sum" = 2(x + y).
To solve one equation, do the same to both sides.

1. The dictionary

📖 Click a word: English ↔ Malayalam ↔ algebra

2. Choosing the letters

Start every solution by saying in words what each letter means: "let the umbrella cost x rupees and the bag y rupees". Then each sentence of the question becomes one equation. If a question gives two facts about two unknowns, use two letters and write two equations.

🎬 Animation: a story becomes two equations

3. "More than" and "times" as bar models

🎚️ The larger is k times the smaller, or d more than it

smaller number times k more by d

4. Perimeter, squares and equilateral triangles

A rectangle with length l and breadth b has perimeter (ചുറ്റളവ്) 2(l + b). Half the perimeter is just l + b – very handy: "perimeter 40" means l + b = 20. A square has 4 equal sides, an equilateral triangle 3 equal sides, so a wire bent into a square of side s uses 4s, into a triangle of side t uses 3t.

📐 Rectangle: perimeter and half-perimeter

length l breadth b

5. Fractions: numerator and denominator

In x/y, x is the numerator (അംശം) and y the denominator (ഛേദം). "Add 1 to the numerator" gives (x + 1)/y; "add 1 to the denominator" gives x/(y + 1). "Simplifying gives ½" means the new fraction equals ½.

🔢 Change the top or the bottom

x y

⚠️ Translation traps

"4 less than x" is x − 4, not 4 − x.
"10 more black than white" means black = white + 10 (or black − white = 10).
"Perimeter 40" means 2(l + b) = 40, i.e. l + b = 20 – not l + b = 40.

🌍 Real life

Writing a situation in symbols is what programmers, scientists and accountants call "modelling". A phone plan "₹99 plus ₹10 per GB" becomes 99 + 10g; a recipe "twice as much flour as sugar" becomes f = 2s. Once written, the computer – or you – can solve it.

6. Check yourself

🧭 Summary

Say what each letter means before writing anything.
തുക sum (+), വ്യത്യാസം difference (−), മടങ്ങ് times (×), കൂടുതൽ more, കുറവ് less, പകുതി half.
Two facts about two unknowns ⇒ two equations.
Perimeter of a rectangle 2(l + b); half of it is l + b. Square side s uses 4s; equilateral triangle side t uses 3t.
(x + 1)/y and x/(y + 1): add to the top or to the bottom.

Next: Digits, interest, ages and speeds ▶