Other Fraction Manipulations - Basic Arithmetic

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Question

Express the following fraction as a decimal:

$\frac{18}{30}$

Answer

To easily express a fraction as a decimal, we need to convert the denominator into a power of . We can do this by dividing both the top and the bottom of the given fraction by to express it in tenths.

$\frac{18}{30}\div \frac{3}{3}= \frac{6}{10}$

$\frac{6}{10}$ , or six tenths, can be expressed as .

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Question

What is the decimal equivalent to $\frac{3}{4}$ ?

Answer

The correct answer is

$\frac{3}{4}$ is greater than half so you can eliminate and right away.

You should memorize common fractions:

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{1}{6}$

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Question

Which fraction is less than $\frac{2}{3}$ ?

Answer

The best way to answer this question is to find the smallest fraction among the answer choices.

Comparing fractions can be done easily when they are converted to decimals.

$\frac{2}{3}=2\div3=0.667$

$\frac{6}{7}=6\div7=0.857$

$\frac{8}{11}=8\div11=0.727$

$\frac{17}{23}=17\div23=0.739$

$\frac{18}{23}=18\div23=0.783$

$\frac{3}{5}=3\div5=0.60$

Of these options, only ${\frac{3}{5}}$ , or 0.60, is less than $\frac{2}{3}$ .

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Question

$\frac{2}{7}\cdot\frac{1}{4}=?$

What is the result of the above equation?

Answer

So we first multiply the numerators:

$2\cdot1=2$

We then multiply the denominators

$7\cdot4=28$

Our resulting fraction is:

$\frac{2}{28}$

We reduce by dividing by 2 from the numerator and denominator.

For the numerator:

$\frac{2}{2}=1$

For the denominator:

$\frac{28}{2}=14$

The resulting fraction is:

$\frac{1}{14}$

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Question

$\frac{3}{4}\cdot\frac{4}{6}=?$

What is the result of the above equation?

Answer

We first multiply the numerators:

$3 \cdot4=12$

Then we multiply the denominators:

$4\cdot6=24$

The resulting fraction is:

$\frac{12}{24}$

We divide the numerator and denominator by 12.

The numerator is:

$\frac{12}{12}=1$

The denominator results in:

$\frac{24}{12}=2$

Our resulting fraction is:

$\frac{1}{2}$

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Question

What is the result of the below equation?

$\frac{2}{5}\times\frac{3}{6}=?$

Answer

First, multiply the terms in the numerators:

$2\times3=6$

Then multiply the terms in the denominators:

$5\times6=30$

This results in the fraction $\frac{6}{30}$ .

Notice that both the numerator and denominator have a common factor of 6. Dividing both the numerator and denominator by 6 results in the simplest form fraction $\frac{1}{5}$ .

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Question

What is the result of the below equation?

$\frac{9}{10}\times \frac{2}{3}=?$

Answer

First, multiply the numerators of the terms:

$9\times2=18$

Then, multiply the denominators of the terms:

$10\times3=30$

The resulting fraction is $\frac{18}{30}$ . Note that the numerator and denominator both have a common factor of 6. Dividing both parts of the fraction by 6, we get the simplest form fraction $\frac{3}{5}$ .

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Question

What is the result of the below equation?

$\frac{7}{12}\times\frac{4}{5}=?$

Answer

First, multiply the numerators of each term:

$7\times4=28$

Then, multiply the denominators:

$12\times5=60$

This results in a fraction of $\frac{28}{60}$ . Since the numerator and denominator both have a common factor of 4, reduce both the numerator and denominator by dividing by 4 to get the simplest form fraction $\frac{7}{15}$ .

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