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SAT Math : SAT Mathematics

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Example Questions

Example Question #875 : Algebra

Solve for :

$\frac{3x}{8}+12=\frac{1}{3}-2x$

Possible Answers:

$-\frac{280}{57}$

$-\frac{81}{13}$

$\frac{100}{21}$

$\frac{43}{2}$

$-\frac{5}{7}$

Correct answer:

$-\frac{280}{57}$

Explanation:

Begin by isolating the variables:

$\frac{3x}{8}+2x=\frac{1}{3}-12$

Now, the common denominator of the variable terms is . The common denominator of the constant values is . Thus, you can rewrite your equation:

$\frac{3x}{8}+\frac{16x}{8}=\frac{1}{3}-\frac{36}{3}$

Simplify:

$\frac{19x}{8}=-\frac{35}{3}$

Cross-multiply:

19x * 3 = -35*8

Simplify:

57x = -280

Finally, solve for :

$x = -\frac{280}{57}$

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Example Question #38 : Algebraic Fractions

Solve: $\frac{8}{3} + \frac{x}{2}=4$

Possible Answers:

$\frac{4}{3}$

$\frac{6}{5}$

$\frac{8}{3}$

$\frac{3}{16}$

Correct answer:

$\frac{8}{3}$

Explanation:

In order to solve $\frac{8}{3} + \frac{x}{2}=4$ , identify the least common denominator, or LCD. Multiply the uncommon denominators, and the LCD is 6.

Rewrite the equation.

$\frac{16}{6} + \frac{3x}{6}=\frac{24}{6}$

Multiply by six on both sides of the equation to cancel the denominators.

16+3x=24

3x=8

$x=\frac{8}{3}$

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Example Question #876 : Algebra

Evaluate: $\frac{x}{3}+\frac{11}{6}=6$

Possible Answers:

$\frac{11}{25}$

$\frac{25}{2}$

$\frac{51}{6}$

$\frac{6}{11}$

$\frac{2}{9}$

Correct answer:

$\frac{25}{2}$

Explanation:

Find the least common denominator, or LCD of $\frac{x}{3}+\frac{11}{6}=6$ is six.

Rewrite the equation with the correct denominator.

$\frac{2x}{6}+\frac{11}{6}=\frac{36}{6}$

Multiply by six on both sides of the equation and solve for .

2x+11=36

2x=25

$x=\frac{25}{2}$

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Example Question #36 : Algebraic Fractions

Solve the following: $\frac{1}{3}-\frac{2}{9}$

Possible Answers:

$\frac{1}{9}$

$-\frac{5}{9}$

$\frac{7}{27}$

$-\frac{1}{3}$

$-\frac{1}{9}$

Correct answer:

$\frac{1}{9}$

Explanation:

In order to subtract the fractions, the denominator must be the same. The common denominator is 9. Rewrite the fractions.

$\frac{1}{3}-\frac{2}{9}=\frac{3}{9}-\frac{2}{9}= \frac{1}{9}$

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Example Question #41 : Algebraic Fractions

Evaluate: $\frac{6}{11}-\frac{3}{8}$

Possible Answers:

$\frac{15}{11}$

$\frac{3}{88}$

$\frac{15}{44}$

$\frac{6}{88}$

$\frac{15}{88}$

Correct answer:

$\frac{15}{88}$

Explanation:

Find the common denominator by multiplying both denominators together.

$11\times 8=88$

Multiply the top with what was multiplied on the bottom to get the denominator. Simplify the fraction.

$\frac{6}{11}-\frac{3}{8}= \frac{6 \times 8}{11 \times 8}-\frac{3 \times 11}{8\times 11}=\frac{48}{88}-\frac{33}{88}=\frac{15}{88}$

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Example Question #42 : Algebraic Fractions

Evaluate: $\frac{a}{6}-\frac{b}{5}$

Possible Answers:

$\frac{a-b}{11}$

$\frac{5a+6b}{30}$

$\frac{5a-6b}{30}$

$\frac{5a-b}{6}$

$\frac{6b-5a}{30}$

Correct answer:

$\frac{5a-6b}{30}$

Explanation:

Multiply the denominators together to obtain the least common denominator, or LCD. Then multiply the numerators with what was multiplied on the denominator to get the LCD.

$\frac{a}{6}-\frac{b}{5}=\frac{a\times 5}{6\times 5}- \frac{b \times 6}{5\times 6}=\frac{5a}{30}-\frac{6b}{30}= \frac{5a-6b}{30}$

The answer is: $\frac{5a-6b}{30}$

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Example Question #21 : How To Evaluate A Fraction

Simplify: $\frac{x}{9}+\frac{10}{x}$

Possible Answers:

$\frac{x^2+10}{9x}$

$\frac{x^2+90}{9x}$

$\frac{x+90}{9}$

$\frac{10}{9}$

Correct answer:

$\frac{x^2+90}{9x}$

Explanation:

Find the common denominator and simplify.

$\frac{x}{9}+\frac{10}{x}= \frac{x\times x}{9x}+\frac{10\times 9}{9x}=\frac{x^2}{9x}+\frac{90}{9x}= \frac{x^2+90}{9x}$

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Example Question #2653 : Sat Mathematics

Solve: $\frac{3}{7}+ \frac{2}{3}$

Possible Answers:

$\frac{5}{21}$

$\frac{11}{21}$

$\frac{14}{21}$

$\frac{1}{4}$

$\frac{23}{21}$

Correct answer:

$\frac{23}{21}$

Explanation:

In order to evaluate this fraction, we will need to find the least common denominator. Multiply both denominators together.

$7\times 3=21$

Convert both fractions with the similar common denominator. Multiply the numerator with what was multiplied to get the denominator.

$\frac{3}{7}+ \frac{2}{3} = \frac{9}{21}+\frac{14}{21}$

Add the numerators on the right side. The denominators will stay the same.

$\frac{9}{21}+\frac{14}{21} = \frac{23}{21}$

The answer is: $\frac{23}{21}$

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Example Question #41 : Algebraic Fractions

In a sample of 114 students, $18\%$ of them liked baseball. If there are 1,200 students in the entire school, how many students are likely to like baseball?

Possible Answers:

240

220

210

114

216

Correct answer:

216

Explanation:

To answer this question, we need to convert $18\%$ to a decimal. $18\%=0.18$ . Now we multiply 1,200 by 0.18 . $1200\cdot 0.18=216$ .

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Example Question #1 : How To Evaluate A Fraction

Mary walked to school at an average speed of 2 miles per hour and jogged back along the same route at an average speed of 6 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?

Possible Answers:

Correct answer:

Explanation:

Since Mary traveled 3 times as quickly coming from school as she did going to school (6 miles per hour compared to 2 miles per hour), we know that Mary spent only a third of the time coming from school as she did going. If x represents the number of hours it took to get to school, then x/3 represents the number of hours it took her to return.

Knowing that the total trip took 1 hour, we have:

x + x/3 = 1

3x/3 + 1x/3 = 1

4x/3 = 1

x = 3/4

So we know it took Mary 3/4 of an hour to travel to school (and the remaining 1/4 of an hour to get back).

Remembering that distance = rate * time, the distance Mary traveled on her way to school was (2 miles per hour) * (3/4 of an hour) = 3/2 miles. Furthermore, since she took the same route coming back, she must have traveled 3/2 of a mile to return as well.

Therefore, the the total number of miles in Mary's round trip is 3/2 miles + 3/2 miles = 6/2 miles = 3 miles.

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #875 : Algebra

Example Question #38 : Algebraic Fractions

Example Question #876 : Algebra

Example Question #36 : Algebraic Fractions

Example Question #41 : Algebraic Fractions

Example Question #42 : Algebraic Fractions

Example Question #21 : How To Evaluate A Fraction

Example Question #2653 : Sat Mathematics

Example Question #41 : Algebraic Fractions

Example Question #1 : How To Evaluate A Fraction

All SAT Math Resources

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