Prove Sum of Unlike Fractions

After the previous exercise of proving the sum of like fractions, we delve into a deeper problem. Unlike fractions are those fractions that do not have the same denominator. At this point, you should be able to solve these fractions intuitively. But which real number properties are being used?

In this proof, you will use the Identity, Inverse, Commutative, and Distributive Property to justify the steps we intuitively use to add fractions together.

Press start to start the proof. Choose the correct option from the given options. Click on the ? at the end of a statement to see the explanation for that step. Get all steps correct to pass the stage.

Prove That $\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}$

$L.H.S. = \dfrac{a}{b} + \dfrac{c}{d}$

$= \dfrac{a}{b} \cdot 1 + \dfrac{c}{d} \cdot 1 \quad \text{[Multiplicative Identity]}$

$= \dfrac{a}{b} \cdot \dfrac{d}{d} + \dfrac{c}{d} \cdot \dfrac{b}{b} \quad \text{[Multiplicative Inverse]}$

$= \dfrac{ad}{bd} + \dfrac{cb}{db}$

$= \dfrac{ad}{bd} + \dfrac{bc}{bd} \quad \text{[Commutative Property]}$

$= \dfrac{1}{bd} \cdot ad + \dfrac{1}{bd} \cdot bc$

$= \dfrac{1}{bd} \cdot \left(ad+bc\right) \quad \text{[Distributive Property]}$

$= \dfrac{ad+bc}{bd} = R.H.S.$

End of Lesson

Prove Sum of Unlike Fractions

In this proof, you will use the Identity, Inverse, Commutative, and Distributive Property to justify the steps we intuitively use to add fractions together.

Prove That $\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}$

$L.H.S. = \dfrac{a}{b} + \dfrac{c}{d}$

$= \dfrac{a}{b} \cdot 1 + \dfrac{c}{d} \cdot 1 \quad \text{[Multiplicative Identity]}$

$= \dfrac{a}{b} \cdot \dfrac{d}{d} + \dfrac{c}{d} \cdot \dfrac{b}{b} \quad \text{[Multiplicative Inverse]}$

$= \dfrac{ad}{bd} + \dfrac{cb}{db}$

$= \dfrac{ad}{bd} + \dfrac{bc}{bd} \quad \text{[Commutative Property]}$

$= \dfrac{1}{bd} \cdot ad + \dfrac{1}{bd} \cdot bc$

$= \dfrac{1}{bd} \cdot \left(ad+bc\right) \quad \text{[Distributive Property]}$

$= \dfrac{ad+bc}{bd} = R.H.S.$

Prove Sum of Unlike Fractions

Prove That ab+cd=ad+bcbd\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}ba​+dc​=bdad+bc​

Prove Sum of Unlike Fractions

Prove That ab+cd=ad+bcbd\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}ba​+dc​=bdad+bc​

Prove That $\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}$

Prove That $\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}$