How to divide fractions - SAT Math

Card 0 of 6

Question

Simplify:

Answer

Division is the same as multiplying by the reciprocal. Thus, a/b ÷ c/d = a/b x d/c = ad/bc

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Question

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?

Answer

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.

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Question

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

Answer

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:

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

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Question

Evaluate the following:

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

Answer

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

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:

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

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Question

Evaluate the expression:

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

Answer

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.

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

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Question

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

Answer

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

$\frac{\frac{13x}{5y}}{\frac{3x}{8y}}=\frac{13x}{5y}\frac{8y}{3x}=\frac{13x8y}{5y3x}=\frac{138}{5*3}=\frac{104}{15}$

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