Rational expressions - HiSET

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Question

Add or subtract: $\dfrac {7}{12}-\dfrac {2}{3}+\dfrac {2}{7}$

Answer

Step 1: Find the Least Common Denominator of these fraction. We will list out multiples of each denominator until we find a common number for all three fractions...

$12,24,36,48,60,72,{\color{Red} 84},...$

$7,14,21,28,35,42,...,63,70,77,{\color{Red} 84}$

$3,6,9,...,72,75,78,81,{\color{Red} 84}$

The smallest common denominator is .

Step 2: Since the denominator is , we will convert all denominators to .

$\dfrac {7}{12}=\dfrac {x}{84}\rightarrow \dfrac {7\times 7}{12 \times 7}=\dfrac {x}{84}\rightarrow \dfrac {49}{84}=\dfrac {x}{84}\implies x=49$

$-\dfrac {2}{3}=\dfrac {x}{84}\rightarrow -\dfrac{2\times 28}{3\times 28}=\dfrac {x}{84}\rightarrow -\dfrac {56}{84}=\dfrac {x}{84}\implies x=-56$

$\dfrac {2}{7}=\dfrac {x}{84}\rightarrow \dfrac {2\times12}{7\times 12}=\dfrac {x}{84}\rightarrow \dfrac {24}{84}=\dfrac {x}{84}\implies x=24$

Step 3: Add up all the values of x...

Step 4: The result from step is the numerator and is the denominator. We will put these together.

Final Answer: $\dfrac {17}{84}$

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Question

Add or subtract: $\dfrac {7}{12}-\dfrac {2}{3}+\dfrac {2}{7}$

Answer

Step 1: Find the Least Common Denominator of these fraction. We will list out multiples of each denominator until we find a common number for all three fractions...

$12,24,36,48,60,72,{\color{Red} 84},...$

$7,14,21,28,35,42,...,63,70,77,{\color{Red} 84}$

$3,6,9,...,72,75,78,81,{\color{Red} 84}$

The smallest common denominator is .

Step 2: Since the denominator is , we will convert all denominators to .

$\dfrac {7}{12}=\dfrac {x}{84}\rightarrow \dfrac {7\times 7}{12 \times 7}=\dfrac {x}{84}\rightarrow \dfrac {49}{84}=\dfrac {x}{84}\implies x=49$

$-\dfrac {2}{3}=\dfrac {x}{84}\rightarrow -\dfrac{2\times 28}{3\times 28}=\dfrac {x}{84}\rightarrow -\dfrac {56}{84}=\dfrac {x}{84}\implies x=-56$

$\dfrac {2}{7}=\dfrac {x}{84}\rightarrow \dfrac {2\times12}{7\times 12}=\dfrac {x}{84}\rightarrow \dfrac {24}{84}=\dfrac {x}{84}\implies x=24$

Step 3: Add up all the values of x...

Step 4: The result from step is the numerator and is the denominator. We will put these together.

Final Answer: $\dfrac {17}{84}$

Compare your answer with the correct one above

Question

Add or subtract: $\dfrac {7}{12}-\dfrac {2}{3}+\dfrac {2}{7}$

Answer

Step 1: Find the Least Common Denominator of these fraction. We will list out multiples of each denominator until we find a common number for all three fractions...

$12,24,36,48,60,72,{\color{Red} 84},...$

$7,14,21,28,35,42,...,63,70,77,{\color{Red} 84}$

$3,6,9,...,72,75,78,81,{\color{Red} 84}$

The smallest common denominator is .

Step 2: Since the denominator is , we will convert all denominators to .

$\dfrac {7}{12}=\dfrac {x}{84}\rightarrow \dfrac {7\times 7}{12 \times 7}=\dfrac {x}{84}\rightarrow \dfrac {49}{84}=\dfrac {x}{84}\implies x=49$

$-\dfrac {2}{3}=\dfrac {x}{84}\rightarrow -\dfrac{2\times 28}{3\times 28}=\dfrac {x}{84}\rightarrow -\dfrac {56}{84}=\dfrac {x}{84}\implies x=-56$

$\dfrac {2}{7}=\dfrac {x}{84}\rightarrow \dfrac {2\times12}{7\times 12}=\dfrac {x}{84}\rightarrow \dfrac {24}{84}=\dfrac {x}{84}\implies x=24$

Step 3: Add up all the values of x...

Step 4: The result from step is the numerator and is the denominator. We will put these together.

Final Answer: $\dfrac {17}{84}$

Compare your answer with the correct one above

Question

Add or subtract: $\dfrac {7}{12}-\dfrac {2}{3}+\dfrac {2}{7}$

Answer

Step 1: Find the Least Common Denominator of these fraction. We will list out multiples of each denominator until we find a common number for all three fractions...

$12,24,36,48,60,72,{\color{Red} 84},...$

$7,14,21,28,35,42,...,63,70,77,{\color{Red} 84}$

$3,6,9,...,72,75,78,81,{\color{Red} 84}$

The smallest common denominator is .

Step 2: Since the denominator is , we will convert all denominators to .

$\dfrac {7}{12}=\dfrac {x}{84}\rightarrow \dfrac {7\times 7}{12 \times 7}=\dfrac {x}{84}\rightarrow \dfrac {49}{84}=\dfrac {x}{84}\implies x=49$

$-\dfrac {2}{3}=\dfrac {x}{84}\rightarrow -\dfrac{2\times 28}{3\times 28}=\dfrac {x}{84}\rightarrow -\dfrac {56}{84}=\dfrac {x}{84}\implies x=-56$

$\dfrac {2}{7}=\dfrac {x}{84}\rightarrow \dfrac {2\times12}{7\times 12}=\dfrac {x}{84}\rightarrow \dfrac {24}{84}=\dfrac {x}{84}\implies x=24$

Step 3: Add up all the values of x...

Step 4: The result from step is the numerator and is the denominator. We will put these together.

Final Answer: $\dfrac {17}{84}$

Compare your answer with the correct one above

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