Mathematical Relationships and Basic Graphs - Algebra 2

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Question

Multiply these fractions:

$\frac{4}{9}*\frac{2}{3}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{4}{9}\frac{2}{3}=\frac{42}{3*9}=\frac{8}{27}$

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Question

Multiply the fractions:

$\frac{3}{7}\cdot \frac{14}{23}$

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Answer

When multiplying fractions, multiply the numbers on the top together and the numbers on the bottom together. Then simplify accordingly.

$\frac{3}{7}\cdot \frac{14}{23}=\frac{42}{161}\div \frac{7}{7}=\frac{6}{23}$

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Question

Multiply the fractions:

$\frac{3}{4}\cdot \frac{2}{7}$

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Answer

When multiplying fractions, multiply the numbers on the top together and the numbers on the bottom together. Then simplify accordingly.

$\frac{3}{4}\cdot \frac{2}{7}=\frac{6}{28}\div \frac{2}{2}=\frac{3}{14}$

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Question

Multiply the fractions:

$\frac{7}{8}\cdot\frac{1}{2}$

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Answer

When multiplying fractions, multiply the numbers on the top together and the numbers on the bottom together. Then simplify accordingly.

$\frac{7}{8}\cdot \frac{1}{2}=\frac{7}{16}$

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Question

Multiply the fractions:

$\frac{1}{6}\cdot \frac{1}{6}$

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Answer

When multiplying fractions, multiply the numbers on the top together and the numbers on the bottom together. Then simplify accordingly.

$\frac{1}{6}\cdot \frac{1}{6}=\frac{1}{36}$

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Question

Simplify $x^5y^2x^{-4}$

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Answer

First, combine exponents of like variables. This gives us

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Question

Multiply the fractions:

$\frac{3}{5}\cdot \frac{5}{7}$

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Answer

When multiplying fractions, multiply the numbers on the top together and the numbers on the bottom together. Then simplify accordingly.

$\frac{3}{5}\cdot \frac{5}{7}=\frac{15}{35}\div \frac{5}{5}=\frac{3}{7}$

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Question

Simplify $z^3y^2x^6y^{-3}$

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Answer

First, combine exponents of like variables. This gives us $z^3y^{-1}x^6$ which simplifies to $\frac{z^3x^6}{y}$

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Question

Expand:

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Answer

To expand the exponent, we multiply the base by whatever the exponent is.

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Question

Evaluate: $\frac{3}{x^0+y^0}$

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Answer

Although we have two variables, we do know that a number raised to a zero power is one. Therefore:

$\frac{3}{x^0+y^0}=\frac{3}{1+1}=\frac{3}{2}$

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Question

Simplify.

$3^{-14}3^{23}3^{-15}$

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Answer

When multiplying exponents with the same base, you just have to add the exponents.

$3^{-14}3^{23}3^{-15}=3^{-14+23-15}=3^{-6}$

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Question

Simplify.

$\frac{a^{45}}{a^{30}}$

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Answer

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{45}}{a^{30}}=a^{45-30}=a^{15}$

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Question

Simplify.

$\frac{a^7}{a^{18}}$

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Answer

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{7}}{a^{18}}=a^{7-18}=a^{-11}$

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Question

Simplify: $12^{19}\div12^7$

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Answer

When dividing exponents with the same base, we subtract the exponents and keep the base the same.

$12^{19}\div12^7=12^{19-7}=12^{12}$

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Question

Simplify:

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Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$23^7*23^8=23^{7+8}=23^{15}$

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Question

Simplify: $2^4*2^{-12}$

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Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$2^4*2^{-12}=2^{4+(-12)}=2^{-8}$

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Question

Where would fall on the number line? $(i^{2}= -1 )$

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Answer

Imaginary numbers do not fall on the number line-- they are by definition not real numbers.

** If the question asked where $4i^{2}$ falls on the number line, the answer would be to the left of 0, because $4i^{2}=-4$ .

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Question

Divide the fractions:

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

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{1}{2}\div \frac{1}{3}=\frac{1}{2}\cdot \frac{3}{1}=\frac{3}{2}=1\frac{1}{2}$

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Question

Divide the fractions:

$\frac{7}{9}\div \frac{5}{6}$

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Answer

When dividing fractions, first we flip the second fraction in the problem. Then we multiply the numbers on the top together and the numbers on the bottom together. Finally simplify accordingly.

$\frac{7}{9}\div \frac{5}{6}=\frac{7}{9}\cdot \frac{6}{5}=\frac{42}{45}\div \frac{3}{3}=\frac{14}{15}$

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Question

Simplify: $(-3)^7*(-3)^{-2}$

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Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$(-3)^7*(-3)^{-2}=(-3)^{7+(-2)}=(-3)^{5}$

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