One step multiplication and division

An SAT Math micro-topic under Isolating quantities (Problem solving and data analysis). Free to read — no account needed.

A one-step multiplication or division equation is undone by the opposite operation on both sides.
Multiplication is undone by division, and division by multiplication.
As always, do the same step to both sides.
If the variable is multiplied by a number, divide both sides by that number.
From ax=bax = b, dividing by aa gives x=bax = \frac{b}{a}.
So 5y=355y = 35 becomes y=7y = 7.
If the variable is divided by a number, multiply both sides by it.
From x+2y3=4\frac{x + 2y}{3} = 4, multiplying by 33 gives x+2y=12x + 2y = 12.
A fraction coefficient like 12x=10\frac{1}{2}x = 10 clears the same way: multiply by 22 to get x=20x = 20.
In an equation, a negative number just carries its sign through.
From −4x=16-4x = 16, dividing both sides by −4-4 gives x=−4x = -4.
There is no inequality sign to flip here, because this is an equation.

Worked examples

Solve 3x=153x = 15.
Divide both sides by 33: 3x3=153\frac{3x}{3} = \frac{15}{3}.
So x=5x = 5.
Given a+b5=3\frac{a + b}{5} = 3, find a+ba + b.
Multiply both sides by 55: a+b=3×5a + b = 3 \times 5.
So a+b=15a + b = 15.
Solve 14x=8\frac{1}{4}x = 8.
Multiply both sides by 44: x=8×4x = 8 \times 4.
So x=32x = 32.

Is this one of the topics costing you points?

Take the free 10-question diagnostic for a predicted SAT score and a breakdown of which domains are costing you points.

Predict your SAT score →

More in Isolating quantities