How can I express A and B as fractions from c = A b/a + Bd?

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In summary, to express A and B as fractions in terms of c, we use the formula c = A b/a + Bd. A and B represent the numerators of the fractions and their values determine the overall value of c. If we have the value of c, b, a, and d, we can solve for A and B separately. This expression can also be used to simplify a complex fraction by substituting the values of the numerator and denominator and using the coefficient of the variable and the remaining constant. Additionally, we can use this expression to express A and B as decimals by dividing A and B by a and then multiplying them by c.
  • #1
Monster92
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I did the first section of the question. I rearranged a = 4b / (6c -5d) to be c = (A b/a) + Bd

but then it says express A and B as fractions in their simplest form. Is the question worded wrong? I've never seen anything like this before?
 
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  • #2
Can you rearrange

[tex]a=\frac{4b}{6c-5d}[/tex]

into something like

[tex]c=...[/tex]
 

FAQ: How can I express A and B as fractions from c = A b/a + Bd?

How do I express A and B as fractions in terms of c?

To express A and B as fractions in terms of c, we can use the formula c = A b/a + Bd. This means that A will be the numerator of the first fraction and B will be the numerator of the second fraction. The denominator for both fractions will be a, and the coefficient of B will be d.

What is the role of A and B in the expression c = A b/a + Bd?

A and B represent the two fractions that we are trying to find in terms of c. They are the numerators of the fractions and their values will determine the overall value of c. A is multiplied by b and divided by a, while B is simply multiplied by d. Together, they make up the total value of c.

Can I solve for A and B if I have the value of c?

Yes, you can solve for A and B if you have the value of c, as long as you also have the values of b, a, and d. Simply plug in the values into the expression c = A b/a + Bd and solve for A and B separately.

How can I use this expression to simplify a complex fraction?

If you have a complex fraction, you can use the expression c = A b/a + Bd to simplify it. Simply substitute the values of the numerator and denominator of the complex fraction for A and a, respectively. Then, use the coefficient of the variable in the denominator as d, and the remaining constant as b. This will give you the simplified form of the complex fraction in terms of c.

Can I use this expression to express A and B as decimals instead of fractions?

Yes, you can use this expression to express A and B as decimals instead of fractions. Simply divide A by a and B by a, and then multiply them by the value of c. This will give you the decimal values of A and B in terms of c.

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