How to divide fractions

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SAT Math › How to divide fractions

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Simplify $\frac{\frac{13x}{5y}}{\frac{3x}{8y}}$

$\frac{104}{15}$

CORRECT

$\frac{39}{40}$

$\frac{18}{8}$

$\frac{16}{13}$

Fractions with variables cannot be divided

Explanation

When you dividing fractions, multiply by the reciprocal of the denominator.

$\frac{\frac{13x}{5y}}{\frac{3x}{8y}}=\frac{13x}{5y}*\frac{8y}{3x}=\frac{13*x*8*y}{5*y*3*x}=\frac{13*8}{5*3}=\frac{104}{15}$

Evaluate the expression:

$\frac{3}{9}\div \frac{4}{15}$

$1\frac{1}{4}$

CORRECT

$\frac{4}{45}$

$\frac{5}{2}$

$\frac{3}{5}$

$1\frac{2}{7}$

Explanation

When dividing fractions, you invert the second term and multiply the numbers.

$\frac{3}{9}\times\frac{15}{4}$

You can reduce the numbers that are diagonal from each other to make the numbers smaller and easier to multiply.

$\frac{3}{3}\times\frac{5}{4}=\frac{5}{4}=1\frac{1}{4}$

If $\dpi{100} \small x=\frac{2}{3}$ and $\dpi{100} \small y= \frac {3}{4}$ , then what is the value of $\dpi{100} \small \frac {x}{y}$ ?

$\dpi{100} \small \frac{8}{9}$

CORRECT

$\dpi{100} \small \frac{9}{8}$

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small 2$

$\dpi{100} \small \frac{5}{7}$

Explanation

Dividing by a number (in this case $\dpi{100} \small \frac {3}{4}$ ) is equivalent to multiplying by its reciprocal (in this case $\dpi{100} \small \frac {4}{3}$ ). Therefore:

$\dpi{100} \small \frac {2}{3}\div \frac{3}{4} = \frac{2}{3}\times \frac{4}{3} = \frac{8}{9}$

Evaluate the following:

$\left ( \frac{5}{6}\times \frac{12}{13} \right )^{2}\div \frac{3}{4}$

$\frac{400}{507}$

CORRECT

$\frac{4}{5}$

$\frac{507}{400}$

$\frac{25}{507}$

None of the available answers

Explanation

$\left ( \frac{5}{6}\times \frac{12}{13} \right )^{2}\div \frac{3}{4}$

First we will evaluate the terms in the parentheses:

$\left ( \frac{5}{6}\times \frac{2\times 6}{13} \right )^{2}\div \frac{3}{4}$

$\left ( \frac{5}{1}\times \frac{2}{13} \right )^{2}\div \frac{3}{4}$

$\left ( \frac{10}{13} \right )^{2}\div \frac{3}{4}$

Next, we will square the first fraction:

$\left ( \frac{10^{2}}{13^{2}} \right )\div \frac{3}{4}$

$\frac{100}{169}\div \frac{3}{4}$

We can evaluate the division as such:

$\frac{100}{169}\times\frac{4}{3}=\frac{400}{507}$

If p is a positive integer, and 4 is the remainder when p-8 is divided by 5, which of the following could be the value of p?

CORRECT

Explanation

Remember that if x has a remainder of 4 when divided by 5, xminus 4 must be divisible by 5. We are therefore looking for a number p such that p - 8 - 4 is divisible by 5. The only answer choice that fits this description is 17.

Simplify:

Sat_math_167_03