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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1881 : Mathematical Relationships And Basic Graphs

Divide these fractions:

$\frac{15}{75}\div \frac{3}{5}$

Possible Answers:

$\frac{1}{3}$

$1\frac{1}{3}$

$\frac{1}{5}$

$\frac{2}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

$\frac{15}{75}\div \frac{3}{5}=\frac{15}{75}* \frac{5}{3}=\frac{15*5}{75*3}=\frac{75}{225}$

Simplify the fraction to get the final answer:

$\frac{75}{225}\div \frac{75}{75}=\frac{1}{3}$

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Example Question #1882 : Mathematical Relationships And Basic Graphs

Divide these fractions:

$\frac{4}{25}\div \frac{2}{5}$

Possible Answers:

$\frac{2}{3}$

$\frac{3}{5}$

$\frac{1}{5}$

$\frac{2}{5}$

Correct answer:

$\frac{2}{5}$

Explanation:

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

$\frac{4}{25}\div \frac{2}{5}=\frac{4}{25}*\frac{5}{2}=\frac{4*5}{25*2}=\frac{20}{50}$

Simplify the fraction to get the final answer:

$\frac{20}{50}\div \frac{10}{10}=\frac{2}{5}$

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Example Question #1883 : Mathematical Relationships And Basic Graphs

Divide these fractions:

$\frac{9}{21}\div \frac{3}{7}$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{7}$

$1\frac{1}{7}$

Correct answer:

Explanation:

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

$\frac{9}{21}\div \frac{3}{7}=\frac{9}{21}*\frac{7}{3}=\frac{9*7}{21*3}=\frac{63}{63}$

Simplify the fraction to get the final answer:

$\frac{63}{63}=1$

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Example Question #1884 : Mathematical Relationships And Basic Graphs

Divide these fractions:

$\frac{5}{35}\div7$

Possible Answers:

$\frac{1}{49}$

$\frac{1}{7}$

$\frac{2}{49}$

$\frac{5}{49}$

Correct answer:

$\frac{1}{49}$

Explanation:

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

$\frac{5}{35}\div7=\frac{5}{35}*\frac{1}{7}=\frac{5*1}{35*7}=\frac{5}{245}$

Simplify the fraction to get the final answer:

$\frac{5}{245}\div \frac{5}{5}=\frac{1}{49}$

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Example Question #1885 : Mathematical Relationships And Basic Graphs

Divide these fractions:

$\frac{13}{54}\div \frac{3}{4}$

Possible Answers:

$\frac{26}{81}$

$\frac{25}{81}$

$\frac{24}{81}$

$\frac{13}{81}$

Correct answer:

$\frac{26}{81}$

Explanation:

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

$\frac{13}{54}\div \frac{3}{4}=\frac{13}{54}*\frac{4}{3}=\frac{13*4}{54*3}=\frac{52}{162}$

Simplify the fraction to get the final answer:

$\frac{52}{162}\div \frac{2}{2}=\frac{26}{81}$

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Example Question #32 : Multiplying And Dividing Fractions

Simplify the following expression:

$\frac{24x}{72y^{2}}\cdot \frac{8y^{3}}{3}$

Possible Answers:

$=\frac{8x}{9y}$

$=\frac{8y}{9}$

$=\frac{8xy}{9}$

$=\frac{x}{9y^{5}}$

$=\frac{9}{8xy}$

Correct answer:

$=\frac{8xy}{9}$

Explanation:

Cancel out terms with common factors.

$\frac{24x}{72y^{2}}\cdot \frac{8y^{3}}{3}$

$=\frac{8\cdot 3x}{9\cdot 8y^{2}}\cdot \frac{8y^{3}}{3}$

$=\frac{8xy}{9}$

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Example Question #207 : Fractions

Simplify the following fractional expression:

$\frac{343}{144}*\frac{60}{49}$

Possible Answers:

$\frac{35}{17}$

$\frac{35}{12}$

$\frac{12}{35}$

Correct answer:

$\frac{35}{12}$

Explanation:

Simplify the following fractional expression:

$\frac{343}{144}*\frac{60}{49}$

To simplify the expression, we need to simplify each fraction and then multiply.

To simplify each fraction, try to look for common factors on the tops and bottoms of each fraction.

$\frac{343}{144}*\frac{60}{49}=\frac{{\color{Green} 49}*7}{12*{\color{Red} 12}}*\frac{5*{\color{Red} 12}}{{\color{Green} 49}}=\frac{35}{12}$

Note how the common-colored numbers can cancel out to simplify the entire expression into:

$\frac{35}{12}$

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Example Question #4549 : Algebra Ii

Divide: $5\div \frac{9}{5}$

Possible Answers:

$\frac{1}{9}$

$\frac{9}{25}$

$-\frac{9}{4}$

$\frac{25}{9}$

Correct answer:

$\frac{25}{9}$

Explanation:

To divide this, we will need to convert the sign to multiplication and take the reciprocal of the second term in the expression.

$5\div \frac{9}{5} = 5\times \frac{5}{9}$

Multiply the first term with the numerator of the fraction.

$5\times \frac{5}{9} = \frac{25}{9}$

The fraction cannot be reduced.

The answer is: $\frac{25}{9}$

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Example Question #211 : Fractions

Multiply: $\frac{2}{7}\times \frac{14}{30}$

Possible Answers:

$\frac{79}{105}$

$\frac{4}{105}$

$\frac{2}{15}$

$\frac{11}{15}$

$\frac{7}{15}$

Correct answer:

$\frac{2}{15}$

Explanation:

Instead of multiplying the numerator with numerator and denominator with denominator, find the common factors of the terms in the fractions.

Write out the common factors in the fractions.

$\frac{2}{7}\times \frac{14}{30} = \frac{2}{7}\times \frac{7\times 2}{2\times 15}$

Cancel out the common terms in the numerator and denominator.

The answer is $\frac{2}{15}$ .

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Example Question #1886 : Mathematical Relationships And Basic Graphs

A recipe for a cake calls for two-thirds a cup of flower per cake. If you have 12 cups of flour, how many cakes can you make?

Possible Answers:

Can not be determined

Correct answer:

Explanation:

The key here is to recognize that you are dividing twelve by two-thirds because that will give you the total number of cakes that twelve cups of flour.

So:

$\frac{\frac{12}{1}}{\frac{2}{3}}$

When you divide fractions, it is equivalent to multiplying by the reciprocal of one of the divisor.

Which looks like this:

$\frac{12}{1}*\frac{3}{2}=18$

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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1881 : Mathematical Relationships And Basic Graphs

Example Question #1882 : Mathematical Relationships And Basic Graphs

Example Question #1883 : Mathematical Relationships And Basic Graphs

Example Question #1884 : Mathematical Relationships And Basic Graphs

Example Question #1885 : Mathematical Relationships And Basic Graphs

Example Question #32 : Multiplying And Dividing Fractions

Example Question #207 : Fractions

Example Question #4549 : Algebra Ii

Example Question #211 : Fractions

Example Question #1886 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

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