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Finding the Unknown - Find the Unknowns

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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An equation is a mathematical statement where two expressions are set equal to each other using the equality sign (==).

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The 'Unknown' is a variable, usually represented by letters like x,y,zx, y, z, or nn, whose value we need to find.

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The value of the variable that makes the equation true is called the 'solution' or the 'root' of the equation.

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Balancing Method: You can add, subtract, multiply, or divide the same number on both sides of the equation without changing the equality.

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Transposition Method: Moving a term from one side of the equation to the other side changes its sign. For example, +a+a becomes −a-a, and ×a\times a becomes ÷a\div a.

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In vertical arithmetic, unknowns are often represented by letters or blanks in a column-wise calculation (e.g., finding digits in a sum or difference).

📐Formulae

x+a=b  ⟹  x=b−ax + a = b \implies x = b - a

x−a=b  ⟹  x=b+ax - a = b \implies x = b + a

ax=b  ⟹  x=baax = b \implies x = \frac{b}{a}

xa=b  ⟹  x=b×a\frac{x}{a} = b \implies x = b \times a

ax+b=c  ⟹  ax=c−b  ⟹  x=c−baax + b = c \implies ax = c - b \implies x = \frac{c - b}{a}

💡Examples

Problem 1:

Solve for xx: 3x+7=223x + 7 = 22

Solution:

x=5x = 5

Explanation:

Step 1: Transpose +7+7 to the right side, it becomes −7-7. 3x=22−73x = 22 - 7 3x=153x = 15 Step 2: Transpose 33 (multiplication) to the right side, it becomes division. x=153x = \frac{15}{3} x=5x = 5

Problem 2:

Find the value of yy in: y4−3=2\frac{y}{4} - 3 = 2

Solution:

y=20y = 20

Explanation:

Step 1: Add 33 to both sides. y4=2+3\frac{y}{4} = 2 + 3 y4=5\frac{y}{4} = 5 Step 2: Multiply both sides by 44. y=5×4y = 5 \times 4 y=20y = 20

Problem 3:

Find the missing number xx in the following subtraction: 85−x32\begin{array}{r} 85 \\ -x \\ \hline 32 \end{array}

Solution:

x=53x = 53

Explanation:

To find the subtrahend (xx), we subtract the difference from the minuend: x=85−32x = 85 - 32 x=53x = 53 Verification: 85−5332\begin{array}{r} 85 \\ -53 \\ \hline 32 \end{array}

Problem 4:

A number increased by 1515 gives 4040. Find the number.

Solution:

2525

Explanation:

Let the unknown number be nn. According to the problem: n+15=40n + 15 = 40 Transposing 1515 to the RHS: n=40−15n = 40 - 15 n=25n = 25

Find the Unknowns Class 7 Notes & Examples | CBSE Maths