In cross method ++ is equal ? _ +?

Mathematics

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Answer

ad + bc

Step-by-step solution

2 steps

The "cross method" can refer to two main operations involving ratios or fractions:

  1. Cross-multiplication for solving proportions

    When two ratios are set equal to each other, forming a proportion, like ab=cd\frac{a}{b} = \frac{c}{d}, the cross method involves multiplying the numerator of one ratio by the denominator of the other. This gives the equality:

    a×d=b×ca \times d = b \times c

    In this context, there isn't a direct "++" operation that is typically equated to something.

  2. Cross method for adding fractions (ratios)

    When adding two fractions (ratios) like ab+cd\frac{a}{b} + \frac{c}{d}, the "cross method" is used to find a common denominator and combine the numerators.

    ab+cd=(a×d)+(b×c)b×d\frac{a}{b} + \frac{c}{d} = \frac{(a \times d) + (b \times c)}{b \times d}

    In this case, the "++" in your question likely refers to the sum of the cross products in the numerator:

    ++=a×d+b×c\text{++} = a \times d + b \times c

    And the denominator would be b×db \times d.

    So, if you are referring to the addition of two ratios ab\frac{a}{b} and cd\frac{c}{d} using the cross method:

    ab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

    Here, the "++" would be equal to the numerator, which is the sum of the cross products.

    The final answer is ad+bcad + bc.

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