Question

Which expression is equivalent to One-fourth minus three-fourths x? One-fourth (1 3 x) One-fourth (1 minus 3 x) One-fourth (negative 1 3 x) 4(1 3x).

Answer 1

Equivalent expressions are expressions having same value but might have different forms. The equivalent expression to given expression is given by: Option A: $\dfrac{1}{4} \times (1-3x)$ (one fourth of (1-3x)

What are equivalent expressions?

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

The given expression is

$\dfrac{1}{4} -\dfrac{3}{4}x$

Simplifying it more to get an equivalent expression to this expression:

$\dfrac{1}{4} -\dfrac{3}{4}x = \dfrac{1-3x}{4}$ (since denominators are same, so numerators add up, and since there was negative sign in the middle, the numerators ended up in subtraction.)

(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in $3 \times x = 3x$ )

The obtained equation can be rewritten as:

$\dfrac{1-3x}{4} = \dfrac{1}{4} \times (1-3x)$

Thus,  The equivalent expression to given expression is given by: Option A: $\dfrac{1}{4} \times (1-3x)$ (one fourth of (1-3x)

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