Prove Sum of Unlike Fractions With Values

After the previous exercise of proving the sum of unlike fractions of the general form, we delve into a specific problem. Instead of variables, you play with real values to match your intuitive knowledge of how to solve a fraction using the LCM method to match with the real number properties active in the backend.

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 −712−518=−21−1036-\dfrac{7}{12} - \dfrac{5}{18} = \dfrac{-21 - 10}{36}

L.H.S.=−712−518L.H.S. = -\dfrac{7}{12} - \dfrac{5}{18}

=−712⋅1−518⋅1[Multiplicative Identity]= -\dfrac{7}{12} \cdot 1 - \dfrac{5}{18} \cdot 1 \quad \text{[Multiplicative Identity]}

=−712⋅33−518⋅22[Multiplicative Inverse]= -\dfrac{7}{12} \cdot \dfrac{3}{3} - \dfrac{5}{18} \cdot \dfrac{2}{2} \quad \text{[Multiplicative Inverse]}

=−7⋅312⋅3−5⋅218⋅2[Multiplying Fractions]= -\dfrac{7 \cdot 3}{12 \cdot 3} - \dfrac{5 \cdot 2}{18 \cdot 2} \quad \text{[Multiplying Fractions]}

=−2136−1036[Multiplication]= -\dfrac{21}{36} - \dfrac{10}{36} \quad \text{[Multiplication]}

=136⋅(−21)−136⋅10= \dfrac{1}{36} \cdot (-21) - \dfrac{1}{36} \cdot 10

=136⋅(−21−10)[Distributive Property]= \dfrac{1}{36} \cdot (-21 - 10) \quad \text{[Distributive Property]}

=−21−1036=R.H.S.= \dfrac{-21 - 10}{36} = R.H.S.


End of Lesson

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Task 05 - Prove Sum of Unlike Fractions
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Properties of Equality