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SSC CGL Reasoning · Mathematical Operations

Signs to Balance an Equation

The signs are missing from a row of numbers. Put each option's signs into the gaps in order and keep the one that makes both sides equal.

All Mathematical Operations notes

Why this matters

Thirty-six questions in the bank, 19 EASY and 17 MODERATE, and 30 of them come from the 2023 shifts. Four sign orders are offered and exactly one balances, so the skill is ruling the other three out fast and then checking the last one in full.

Concept 1 of 2: Filling the gaps when the = sign is fixed

When the = sign is already in its place (printed, or last in every option), the right side is one fixed number. Drop each option's signs into the gaps from left to right and see which left side reaches it.

Definition

  • The first sign of the option goes into the first gap, the second into the second, and so on.
  • Work out the left side of each option in BODMAS order.
  • Fast routes, in this order:
  • Size: a × between two large numbers overshoots a small target; a ÷ shrinks a big number. Compare with the target before you calculate.
  • Whole numbers: if a division leaves a fraction that no later × clears, and the target is whole, the option is out.
  • Last digit: when an option leaves only + and −, the last digit of the result must match the target's.
  • A shortcut only removes options. Check the survivor in full before you mark it.

Worked example

Choose the signs that replace the * signs, in order, to balance 45∗9∗4∗6=2645 * 9 * 4 * 6 = 26. (a) ÷,×,+\div, \times, + (b) +,×,−+, \times, - (c) ÷,×,−\div, \times, - (d) −,÷,+-, \div, +
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 18 Sep 2025, Shift 2 · Q7Easy

Example 1 · Mathematical Operations · Signs to Balance an Equation

Replace special characters with mathematical signs as given in options to make it meaningful equation. 16#4@2=6216 \# 4 @ 2 = 62

Filling the gaps out of order

The option's signs are read left to right into the gaps left to right. Putting the first sign of the option into any other gap tests a different equation.

Calling a fraction a dead end too early

16÷64×8=0.25×8=216 \div 64 \times 8 = 0.25 \times 8 = 2. A quotient below 1 can be multiplied back to a whole number, so finish the block before you rule an option out.
Drill 27 more on filling the gaps when the = sign is fixed

Concept 2 of 2: When the = sign is one of the signs to place

Now the = sign moves from option to option, so each option cuts the row at a different place. Work out the two sides of each option on their own and compare them.

Definition

  • Put the option's signs in. The = sign splits the row into a left side and a right side.
  • Work out each side by itself in BODMAS order. Nothing crosses the = sign.
  • Fast route: work out the shorter side of each option first. It is quick, and it tells you the number the longer side has to reach.
  • If two options put the = sign in the same place, their left sides may match; compare only their right sides.

Worked example

Choose the signs that replace the * signs, in order, to balance 24∗6∗3∗5∗7∗124 * 6 * 3 * 5 * 7 * 1. (a) ÷,×,=,+,×\div, \times, =, +, \times (b) ÷,×,+,=,×\div, \times, +, =, \times (c) ×,÷,=,+,−\times, \div, =, +, - (d) −,÷,×,=,+-, \div, \times, =, +
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 18 Jul 2023, Shift 1 · Q14Easy

Example 2 · Mathematical Operations · Signs to Balance an Equation

Choose one of the following correct combination of mathematical signs which can be filled sequentially to balance the following equation. 28 □\square 4 □\square 3 □\square 9 □\square 42 □\square 12

Carrying a sign across the = sign

Each side is worked out alone. In 12=5+7×112 = 5 + 7 \times 1 the multiplication belongs to the right side only, and a sign just before the = sign belongs to the left side.

Assuming the last number is the right side

When the = sign is among the signs to place, the right side can be several numbers long. Find where the option puts the = sign before you calculate.
Drill 7 more on when the = sign is one of the signs to place

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Watch out for (4)

Test yourself on Mathematical Operations

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Mathematical Operations chapter testDrill all 36 questions