How to simplify a fraction

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SAT Math › How to simplify a fraction

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Simplify the fraction: $\frac{18}{96}$

$\frac{3}{16}$

CORRECT

$\frac{6}{16}$

$\frac{6}{23}$

$\frac{9}{23}$

$\frac{3}{23}$

Explanation

Break up the fraction into common factors.

$18=3\times 6$

$96 = 16\times 6$

Rewrite the fraction.

$\frac{18}{96}=\frac{3\times 6}{16\times 6}$

Cancel the six.

The correct reduced fraction is $\frac{3}{16}$ .

Simplify x/2 – x/5

2x/7

3x/10

CORRECT

3x/7

7x/10

5x/3

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.

Simplify the fraction: $\frac{9}{96}$

$\frac{3}{32}$

CORRECT

$\frac{1}{16}$

$\frac{6}{19}$

$\frac{6}{23}$

$\frac{3}{23}$

Explanation

Break up the fraction into common factors.

$9=3\times 3$

$96 = 16\times 6$

Rewrite the fraction.

$\frac{9}{96}=\frac{3\times 3}{16\times 3 \times 2}$

Cancel the three on the numerator and denominator.

The fraction becomes:

$\frac{3}{16 \times 2}=\frac{3}{32}$

The correct reduced fraction is $\frac{3}{32}$ .

What is the average of $\frac{2}{3}$ and $\frac{5}{6}$ ?

$\frac{3}{4}$

CORRECT

$\frac{11}{12}$

$\frac{4}{5}$

$\frac{6}{7}$

Explanation

To average, we have to add the values and divide by two. To do this we need to find a common denomenator of 6. We then add and divide by 2, yielding 4.5/6. This reduces to 3/4.

Which of the following is equivalent to $\frac{x}{2}+\frac{x-5}{x+3}$ ?

$\frac{2x-5}{x+5}$

$\frac{x^{2}-5x+10}{2x+6}$

$\frac{x^{2}+5x-10}{2x+6}$

CORRECT

$\frac{x^{2}-5x}{2x+6}$

None of the answers are correct

Explanation

This problem is solved the same way ½ + 1/3 is solved. For example, ½ + 1/3 = 3/6 + 2/6 = 5/6. Find a common denominator then convert each fraction into an equivalent fraction using that common denominator. The final step is to add the two new fractions and simplify.

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

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

CORRECT

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

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

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

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

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

$\frac{4}{11}$

CORRECT

$\frac{2}{11}$

$\frac{1}{4}$

$\frac{8}{11}$

$\frac{3}{8}$

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.

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

The expression $(\frac{a^{2}}{b^{3}})(\frac{a^{-2}}{b^{-3}}) = ?$

$1$

CORRECT

$0$

$\frac{a^{-4}}{b^{-9}}$

$\frac{b^{9}}{a^{4}}$

$b^{-9}$

Explanation

A negative exponent in the numerator of a fraction can be rewritten with a positive exponent in the denominator. The same is true for a negative exponent in the denominator. Thus, $\frac{a^{-2}}{b^{-3}} =\frac{b^{3}}{a^{2}}$ .