Complex Operations - GED Math

Card 0 of 1125

Question

Simplify:

$\small \sqrt{72}=$

Answer

$\small \sqrt{72}=\sqrt{36}\times \sqrt2=6\times \sqrt2=6\sqrt2$

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Question

Simplify:

$\sqrt{147}$

Answer

$\sqrt{147}=\sqrt{49}\times \sqrt3=7\times \sqrt3=7\sqrt3$

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Question

Solve the proportion: $\frac{4}{3} =\frac{8x}{5}$

Answer

Cross multiply the terms.

Divide by 24 on both sides.

$\frac{20}{24} =\frac{ 24x}{24}$

Reduce the fractions.

The answer is: $\frac{5}{6}$

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Question

Which number has 5.25 as its reciprocal?

Do not use a calculator.

Answer

The number that has 5.25 as its reciprocal is, in return, the reciprocal of 5.25.

Convert 5.25 to a fraction:

$5.25 = \frac{525 }{100} = \frac{525 \div 25 }{100\div 25 } = \frac{21}{4}$

Switch the numerator and the denominator to obtain the reciprocal - this number is $\frac{4}{21}$ .

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Question

What is 30% of 750?

Answer

To find a percentage of a whole number, we will multiply the percentage by the whole number. So, we get

$30% \cdot 750$

$\frac{30}{100} \cdot 750$

$\frac{30}{100} \cdot \frac{750}{1}$

To make things easier, we will simply by cancelling out the zeros. So, we get

$\frac{3}{10} \cdot \frac{750}{1}$

$\frac{3}{1} \cdot \frac{75}{1}$

$\frac{3 \cdot 75}{1 \cdot 1}$

$\frac{225}{1}$

Therefore, 30% of 750 is 225.

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Question

What is 90% of 750?

Answer

To find a percentage of a whole number, we will multiply the percentage by the whole number.

So, we get

$90% \cdot 750$

$\frac{90}{100} \cdot 750$

$\frac{90}{100} \cdot \frac{750}{1}$

To simplify, we can cancel. The zeros will cancel each other out. We get

$\frac{9}{10} \cdot \frac{750}{1}$

$\frac{9}{1} \cdot \frac{75}{1}$

$\frac{9 \cdot 75}{1 \cdot 1}$

$\frac{675}{1}$

Therefore, 90% of 750 is 675.

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Question

Solve the proportion: $\frac{2x}{5} = \frac{7}{3}$

Answer

Cross multiply the terms.

Divide by six on both sides.

$\frac{6x }{6}=\frac{ 35}{6}$

The answer is: $\frac{ 35}{6}$

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Question

Rewrite 0.24 as a fraction in simplest form.

Answer

The last nonzero digit of 0.24 - namely, the "4" - is in the hundredths place, so the fractional representation is

$\frac{24}{100}$

Reduce this to simplest form by dividing both halves by their greatest common factor, which is 4:

$\frac{24}{100} = \frac{24 \div 4}{100\div 4} = \frac{6}{25}$

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Question

Rewrite $\frac{7}{5}$ as a decimal expression.

Answer

Divide 7 by 5, adding a decimal point and zeroes to the former as needed. The division looks like this:

The quotient, 1.4, is the decimal equivalent of $\frac{7}{5}$ .

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Question

Express as a decimal: $\frac{11}{12}$

Answer

Divide 11 by 12:

The "6" repeats forever, so

$\frac{11}{12} = 0.91\overline{6}$ .

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Question

Express as a fraction:

$0.4\overline{7}$

Answer

Let $x=0.4\overline{7} = 0.4777...$

Then

$10x = 10 \times 0.4777... = 4.7777...$

and

$100x = 100 \times 0.4777... = 47.777...$

We can subtract:

$\underline{10x = ; ; 4.777...}$

$x = \frac{43}{90}$

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Question

Express as a decimal: $\frac{15}{16}$

Answer

Divide 15 by 16:

$\frac{15}{16} = 0.975$

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Question

Express as a fraction: $0.\overline{42}$

Answer

Let $x = 0.\overline{42} = 0.424242...$

Then $100x = 100 \times 0.424242... = 42.424242...$

Subtract:

$\underline{x = 0.424242...}$

$x = \frac{42}{99} = \frac{42 \div 3}{99 \div 3} = \frac{14}{33}$

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Question

Express as a decimal: $\frac{16}{15}$

Answer

Divide 16 by 15:

The "6" repeats forever, so

$\frac{16}{15} = 1.0\overline{6}$ .

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Question

Express as a decimal: $\frac{12}{11}$

Answer

Divide 12 by 11:

The "09" repeasts forever, so

$\frac{12}{11} = 1.\overline{09}$ .

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Question

Which of the following numbers has $\frac{8}{29}$ as its reciprocal?

Do not use a calculator.

Answer

The number that has $\frac{8}{29}$ as its reciprocal is, in return, the reciprocal of $\frac{8}{29}$ . This number is the result of switching the numerator and denominator - $\frac{29}{8}$ . Since we are looking for the decimal equivalent, we divide 29 by 8:

$29 \div 8 = 3.625$ , the correct choice.

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Question

What is the decimal represented by the fraction $\frac{7}{50}$ ?

Answer

Set up a proportion such that this fraction is some number over 100.

$\frac{7}{50} = \frac{x}{100}$

Cross multiply.

Divide by 50 on both sides.

$\frac{700}{50} = \frac{50x}{50}$

$\frac{14}{100} = 0.14$

The answer is:

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Question

Which of the following represents the equivalent of ?

Answer

You can convert to the fraction:

$\frac{35}{100}$

After you do this, you then need to simplify. You can divide out of numerator and denominator the value , giving you:

$\frac{35\div5}{100\div5}=\frac{7}{20}$

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Question

Which of the following is equivalent to ?

Answer

You can begin by converting into the fraction:

$\frac{3024}{10000}$

Now, you can begin canceling from the numerator and the denominator. You are looking for factors of . The denominator is only made up of and factors (because it is a power of ). The denominator is really merely: $10\cdot10\cdot10\cdot10$ . This means that it has a total of four s. That is the same as $2\cdot2\cdot2\cdot2=16$ . Does the numerator have this many twos? You can try to figure that out by dividing it by . It does! This gets you the value . Therefore, you will have:

$\frac{189}{5\cdot5\cdot5\cdot5}$ , or $\frac{189}{625}$

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Question

Convert the following decimal to a fraction:

Answer

Convert the following decimal to a fraction:

To convert this to a fraction, let's begin by changing the decimal to a percent and putting it over 100.

$0.68\rightarrow 68 % \rightarrow \frac{68}{100}$

Now, we just need to simplify our fraction. We can do so by dividing out two two's from the top and bottom.

$\frac{68}{100}=\frac{34}{50}=\frac{17}{25}$

So, our answer is:

$\frac{17}{25}$

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