Adding and Subtracting Fractions
_a_ and _b_ are positive integers.
$$\displaystyle \frac{b}{a} + \frac{a}{b} = $$
Incorrect.
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A fraction is equal to 1 if the numerator and denominator are equal. Remember to get a common denominator before adding and that the numerator and denominator of your answer will not be equal.
Alternatively, you could use the bow-tie method to add the two fractions together. As an example, $$\frac{1}{6} + \frac{1}{8}$$ will work out as as follows.
Now apply it to this problem:
$$\displaystyle \frac{b}{a} + \frac{a}{b} $$.
The denominator is the product of the two denominators, or _ab_.
The numerator is the sum of the cross-products: $$b^2+a^2$$.
So the final answer is $$\frac{b^2+a^2}{ab}$$.
Incorrect.
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When you rewrite the fractions with a common denominator, the numerators must change to keep the same values they started with. This answer choice comes from not adjusting the numerators.
Incorrect.
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This answer is the result of adding the fractions straight across. Fractions must have common denominators before you can add or subtract them.
Correct!
To add two fractions, rewrite both fractions with a common denominator by multiplying the top and bottom of the fraction by the same number. In this case, the common denominator is _ab_.
$$\displaystyle \frac{b}{a}\cdot\frac{b}{b} + \frac{a}{b}\cdot\frac{a}{a} = \frac{b^2}{ab}+\frac{a^2}{ab}$$
Then add the numerators and keep the denominator the same for the answer.
$$\displaystyle \frac{b^2}{ab}+\frac{a^2}{ab} = \frac{b^2+a^2}{ab}$$
$$1$$
$$\frac{b^2+a^2}{ab}$$
$$\frac{b+a}{ab}$$
$$\frac{b+a}{a+b}$$
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