SAT Math : How to simplify a fraction

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Simplify A Fraction

Simplify x/2 – x/5

Possible Answers:

5x/3

3x/7

7x/10

2x/7

3x/10

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.

Example Question #2 : 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 4

\dpi{100} \small 0

\dpi{100} \small 3

\dpi{100} \small 2

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.

Example Question #3 : How To Simplify A Fraction

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

Possible Answers:

 

 

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

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

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

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

 

Example Question #4 : How To Simplify A Fraction

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

Possible Answers:

160/96

224/168

4/3

16/12

96/72

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

Example Question #1 : How To Simplify A Fraction

Find the root of

Possible Answers:

Can not be determined

Correct answer:

Explanation:

The root occurs where . So we substitute 0 for .

This means that the root is at .

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}

\frac{12}{90}

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 x 2 = 12, but 45 x 2 = 90.

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

Example Question #5 : How To Simplify A Fraction

Simplify the fraction below:

Possible Answers:

Correct answer:

Explanation:

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

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,

 and the denominator becomes .

Therefore the final answer is .

Example Question #6 : How To Simplify A Fraction

Simplify:  

Possible Answers:

Correct answer:

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.

Example Question #7 : Simplifying Fractions

Simply the following fraction: 

Possible Answers:

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,

Simplifying this final fraction gives us our correct answer, .

 

Example Question #3 : How To Simplify A Fraction

Solve for .

Possible Answers:

Correct answer:

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.

Now, simplify the first fraction by calculating four squared.

From here, factor the denominator of the second fraction.

Next, factor the 16.

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

Now, distribute the eight.

Next, multiply both sides by the denominator.

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

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.

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