Lesson 3: Unknown Numbers in Addition

Definition

An equation is a mathematical sentence that uses the symbol = to show that two quantities are equal. In algebra, an unknown is a missing number in an equation.

What’s next

Next, we'll explore strategies for finding unknowns in addition and subtraction equations, guided by worked examples to make the process clear.

Property

To find a missing addend, subtract the known addend from the sum. For an equation $a + x = b$, the unknown is found by $x = b - a$.

Examples

To find $x$ in $x + 22 = 50$, you calculate $x = 50 - 22$, so $x = 28$.

To find $y$ in $35 + y = 75$, you calculate $y = 75 - 35$, so $y = 40$.

Property

To find the missing first number in a subtraction problem (the minuend), add the other two numbers. For an equation $x - a = b$, the unknown is found by $x = a + b$.

Examples

To find $w$ in $w - 25 = 40$, you calculate $w = 25 + 40$, so $w = 65$.

To find $A$ in $A - 18 = 30$, you calculate $A = 18 + 30$, so $A = 48$.

Property

To find the missing number being subtracted (the subtrahend), subtract the difference from the first number (the minuend). For an equation $a - x = b$, the unknown is found by $x = a - b$.

Examples

To find $k$ in $90 - k = 42$, you calculate $k = 90 - 42$, so $k = 48$.

To find $z$ in $150 - z = 95$, you calculate $z = 150 - 95$, so $z = 55$.