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SAT Math : How to simplify a fraction

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Example Questions

Example Question #151 : Arithmetic

Simplify x/2 – x/5

Possible Answers:

3x/10

5x/3

3x/7

7x/10

2x/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:

$\dpi{100} \small 2$

$\dpi{100} \small 16$

$\dpi{100} \small 4$

$\dpi{100} \small 0$

$\dpi{100} \small 3$

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 #151 : Arithmetic

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

Possible Answers:

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

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

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

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

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 #1 : How To Simplify A Fraction

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

Possible Answers:

160/96

224/168

16/12

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 : Simplifying Fractions

Find the root of

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

Possible Answers:

$-\sqrt3$

$-\sqrt{5 }$

$\sqrt3$

Can not be determined

$\sqrt5$

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:

$\frac{2}{13}$

$\frac{1}{20}$

$\frac{1}{25}$

$\frac{1}{4}$

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 #2 : How To Simplify A Fraction

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

Possible Answers:

$\frac{3}{8}$

$\frac{4}{11}$

$\frac{1}{4}$

$\frac{2}{11}$

$\frac{8}{11}$

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 #2 : How To Simplify A Fraction

Simply the following fraction:

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

Possible Answers:

$\infty$

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

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

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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Example Question #2 : Simplifying Fractions

Solve for .

$\frac{\frac{x-2}{4^2}}{\frac{x^2-4}{2}}=1$

Possible Answers:

$x=-\frac{15}{8}$

$x=\frac{8}{15}$

x=-2

$x=\frac{15}{8}$

$x=-\frac{8}{15}$

Correct answer:

$x=-\frac{15}{8}$

Explanation:

To solve for , simplify the fraction. In order to do this, recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, rewrite the equation as follows.

$\frac{\frac{x-2}{4^2}}{\frac{x^2-4}{2}}=1\Rightarrow \frac{x-2}{4^2}\times \frac{2}{x^2-4}=1$

Now, simplify the first fraction by calculating four squared.

$\frac{x-2}{16}\times \frac{2}{x^2-4}=1$

From here, factor the denominator of the second fraction.

$\frac{x-2}{16}\times \frac{2}{(x-2)(x+2)}=1$

Next, factor the 16.

$\frac{x-2}{2(8)}\times \frac{2}{(x-2)(x+2)}=1$

From here, cancel out like terms that are in both the numerator and denominator. In this particular case that includes (x-2) and 2.

$\frac{1}{8(x+2)}=1$

Now, distribute the eight.

$\frac{1}{8x+16}=1$

Next, multiply both sides by the denominator.

$(8x+16)\times \frac{1}{8x+16}=1\times (8x+16)$

The (8x+16) cancels out and leaves the following equation.

1=8x+16

Now to solve for perform opposite operations to move all numerical values to one side of the equation leaving by itself on the other side of the equation.

$\\1=8x+16 \\-15=8x \\\\\frac{-15}{8}=x$

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Example Question #2 : How To Simplify A Fraction

Which of the following fractions is not equivalent to $\frac{6}{45}$ ?

Possible Answers:

$\frac{4}{30}$

$\frac{12}{89}$

$\frac{2}{15}$

$\frac{3}{22.5}$

Correct answer:

$\frac{12}{89}$

Explanation:

Let us simplify $\frac{6}{45}$ :

$\frac{6}{45}=\frac{3\times 2}{3\times 15}=\frac{2}{15}$

We can get alternate forms of the same fraction by multiplying the denominator and the numerator by the same number:

$\frac{2\times 2}{15\times 2}=\frac{4}{30}$

$\frac{2\times 1.5}{15\times 1.5}=\frac{3}{22.5}$

Now let's look at $\frac{12}{89}$ :

$6 \times 2 = 12$ , but $45 \times 2 = 90$ .

Therefore, $\frac{12}{89}$ is the correct answer, as it is not equivalent to $\frac{6}{45}$ .

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SAT Math : How to simplify a fraction

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #151 : Arithmetic

Example Question #1 : How To Simplify A Fraction

Example Question #151 : Arithmetic

Example Question #1 : How To Simplify A Fraction

Example Question #1 : Simplifying Fractions

Example Question #5 : Simplifying Fractions

Example Question #2 : How To Simplify A Fraction

Example Question #2 : How To Simplify A Fraction

Example Question #2 : Simplifying Fractions

Example Question #2 : How To Simplify A Fraction

All SAT Math Resources

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