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SAT Math : Fractions

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Example Questions

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Example Question #1 : How To Find The Lowest / Least Common Denominator

What is the lowest common denominator of the fractions below?

$\frac{1}{6}, \frac{4}{21}, \frac{2}{3}$

Possible Answers:

Correct answer:

Explanation:

In order to find the lowest common denominator, you must first list the multiples of each of the denominators of the three fractions:

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45

6: 6, 12, 18, 24, 30, 36, 42, 48

21: 21, 42, 63

The lowest common denominator between these three sets of multiples is .

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Example Question #2 : Lowest Common Denominator

What is the Lowest Common Denominator of $\frac{1}{6}$ , $\frac{1}{3}$ and $\frac{1}{7}$ ?

Possible Answers:

126

Correct answer:

Explanation:

3:3,6,9,12,15,18,21,24,27,30,33,36,39,42

6:6,12,18,24,30,36,42

7:7,14,21,28,35,42

The smallest number they all have in common in .

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Example Question #1 : How To Simplify A Fraction

Simplify x/2 – x/5

Possible Answers:

7x/10

5x/3

2x/7

3x/10

3x/7

Correct answer:

3x/10

Explanation:

Simplifying this expression is similar to 1/2 – 1/5. The denominators are relatively prime (have no common factors) so the least common denominator (LCD) is 2 * 5 = 10. So the problem becomes 1/2 – 1/5 = 5/10 – 2/10 = 3/10.

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Example Question #1 : How To Simplify A Fraction

If $\dpi{100} \small \frac{p}{6}$ is an integer, which of the following is a possible value of $\dpi{100} \small p$ ?

Possible Answers:

$\dpi{100} \small 16$

$\dpi{100} \small 0$

$\dpi{100} \small 2$

$\dpi{100} \small 3$

$\dpi{100} \small 4$

Correct answer:

$\dpi{100} \small 0$

Explanation:

$\dpi{100} \small \frac{0}{6}=0$ , which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

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Example Question #3 : Simplifying Fractions

Simplify: $\frac{4x^{5}y^{3}z}{12x^{3}y^{6}z^{2}}$

Possible Answers:

$\frac{1}{3x^{2}y^{3}z}$

$\frac{3x^{2}y^{3}}{z}$

$\frac{x^{2}}{8y^{3}z}$

$\frac{x^{2}}{3y^{3}z}$

Correct answer:

$\frac{x^{2}}{3y^{3}z}$

Explanation:

$\frac{4x^{5}y^{3}z}{12x^{3}y^{6}z^{2}}=\frac{x^{2}}{3y^{3}z}$

First, let's simplify $\frac{4}{12}$ . The greatest common factor of 4 and 12 is 4. 4 divided by 4 is 1 and 12 divided by 4 is 3. Therefore $\frac{4}{12}=\frac{1}{3}$ .

To simply fractions with exponents, subtract the exponent in the numerator from the exponent in the denominator. That leaves us with $\frac{1}{3}x^{2}y^{-3}z^{-1}$ or $\frac{x^{2}}{3y^{3}z}$

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Example Question #4 : Simplifying Fractions

Which of the following is not equal to 32/24?

Possible Answers:

16/12

224/168

160/96

96/72

4/3

Correct answer:

160/96

Explanation:

24/32 = 1.33

16/12 =1.33

224/168 =1.33

4/3 = 1.33

96/72 = 1.33

160/96 = 1.67

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Example Question #1 : How To Simplify A Fraction

Find the root of

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}$

Possible Answers:

Can not be determined

$\sqrt3$

$-\sqrt3$

$\sqrt5$

$-\sqrt{5 }$

Correct answer:

$-\sqrt{5 }$

Explanation:

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}=\frac{(x-\sqrt3)(x+\sqrt5)}{x-\sqrt3}=x+\sqrt5$

The root occurs where y=0 . So we substitute 0 for .

$y=x+\sqrt{5}$

$0=x+\sqrt{5}$

This means that the root is at $x=-\sqrt5$ .

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Example Question #5 : Simplifying Fractions

Simplify the fraction below:

$\frac{5}{125}$

Possible Answers:

$\frac{1}{25}$

$\frac{1}{20}$

$\frac{1}{4}$

$\frac{2}{13}$

Correct answer:

$\frac{1}{25}$

Explanation:

The correct approach to solve this problem is to first write factors for the numerator and the denominator:

5: 1, 5

125: 1, 5, 25, 125

The highest common factor is 5. Therefore, you can divide the numerator and denominator by 5 in order to get a simplified fraction.

Thus the numerator becomes,

$\frac{5}{5}=1$ and the denominator becomes $\frac{125}{5}=25$ .

Therefore the final answer is $\frac{1}{25}$ .

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Example Question #1 : Simplifying Fractions

Simplify: $\frac{32}{88}$

Possible Answers:

$\frac{4}{11}$

$\frac{8}{11}$

$\frac{1}{4}$

$\frac{3}{8}$

$\frac{2}{11}$

Correct answer:

$\frac{4}{11}$

Explanation:

Find the common factors of the numerator and denominator. They both share factors of 2,4, and 8. For simplicity, factor out an 8 from both terms and simplify.

$\frac{32}{88}= \frac{8\times 4}{8\times 11}= \frac{4}{11}$

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Example Question #7 : Simplifying Fractions

Simply the following fraction:

$\frac{\frac{a^2}{b}}{\frac{a}{b}}$

Possible Answers:

$\frac{a^3}{b^2}$

$\frac{a^2}{b}$

$\infty$

Correct answer:

Explanation:

Remember that when you divide a fraction by a fraction, that is the same as multiplying the fraction in the numerator by the reciprocal of the fraction in the denominator.

In other words,

$\frac{\frac{a^2}{b}}{\frac{a}{b}} = \frac{a^2}{b}\cdot\frac{b}{a}=\frac{a^2b}{ab}$

Simplifying this final fraction gives us our correct answer, .

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SAT Math : Fractions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Find The Lowest / Least Common Denominator

Example Question #2 : Lowest Common Denominator

Example Question #1 : How To Simplify A Fraction

Example Question #1 : How To Simplify A Fraction

Example Question #3 : Simplifying Fractions

Example Question #4 : Simplifying Fractions

Example Question #1 : How To Simplify A Fraction

Example Question #5 : Simplifying Fractions

Example Question #1 : Simplifying Fractions

Example Question #7 : Simplifying Fractions

All SAT Math Resources

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