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Basic Arithmetic : Basic Arithmetic

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Example Questions

Example Question #6 : Division With Fractions

Divide and simplify:

$\frac{2}{11}\div \frac{9}{22}$ .

Possible Answers:

$\frac{4}{9}$

$\frac{2}{11}$

$\frac{11}{}9$

$\frac{18}{222}$

$\frac{1}{9}$

Correct answer:

$\frac{4}{9}$

Explanation:

Multiplying fractions is a two-step process. First, you must flip the second fraction (make it its reciprocal) and then set up the equation as a multiplication problem:

$\frac{2}{11}\cdot \frac{22}{}9$ .

Then, cross-reduce: 11 goes into both 11 and 22, so you can take that out so it looks like:

$\frac{2}{1}\cdot \frac{2}{9}$ .

Then, multiply straight across so that you get $\frac{4}{}9$ .

You can't simplify any further, so that's your answer!

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Example Question #21 : Fractions

Divide these fractions:

$\frac{15}{30}\div15$

Possible Answers:

$\frac{1}{30}$

$\frac{1}{10}$

$\frac{1}{15}$

$\frac{2}{15}$

Correct answer:

$\frac{1}{30}$

Explanation:

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

$\frac{15}{30}\div15=\frac{15}{30}*\frac{1}{15}=\frac{15*1}{30*15}$

Simplify the fraction to get the final answer:

$\frac{15*1}{30*15}=\frac{1}{30}$

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Example Question #22 : Fractions

Divide these fractions:

$\frac{8}{56}\div \frac{1}{8}$

Possible Answers:

$\frac{1}{7}$

$1\frac{1}{7}$

$1\frac{6}{7}$

$1\frac{2}{7}$

Correct answer:

$1\frac{1}{7}$

Explanation:

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

$\frac{8}{56}\div \frac{1}{8}=\frac{8}{56}*{8}=\frac{8*8}{56}=\frac{64}{56}$

Simplify the fraction to get the final answer:

$\frac{64}{56}\div \frac{8}{8}=\frac{8}{7}=1\frac{1}{7}$

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Example Question #23 : Fractions

Divide these fractions:

$\frac{36}{16}\div \frac{3}{2}$

Possible Answers:

$1\frac{1}{2}$

$\frac{1}{2}$

$\frac{1}{3}$

$1\frac{1}{3}$

Correct answer:

$1\frac{1}{2}$

Explanation:

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

$\frac{36}{16}\div \frac{3}{2}=\frac{36}{16}* \frac{2}{3}=\frac{36*2}{16*3}=\frac{72}{48}$

Simplify the fraction to get the final answer:

$\frac{72}{48}\div \frac{12}{12}=\frac{6}{4}\div \frac{2}{2}=\frac{3}{2}=1\frac{1}{2}$

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Example Question #24 : Fractions

Divide these fractions:

$\frac{12}{54}\div6$

Possible Answers:

$1\frac{1}{27}$

$\frac{2}{27}$

$\frac{1}{28}$

$\frac{1}{27}$

Correct answer:

$\frac{1}{27}$

Explanation:

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

$\frac{12}{54}\div6=\frac{12}{54}*\frac{1}{6}=\frac{12*1}{54*6}=\frac{12}{324}$

Simplify the fraction to get the final answer:

$\frac{12}{324}\div \frac{12}{12}=\frac{1}{27}$

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Example Question #25 : Fractions

Solve the following expression:

$\frac{1}{2}+\frac{1}{6}$

Possible Answers:

$\frac{2}{5}$

$\frac{1}{3}$

$\frac{1}{5}$

$\frac{2}{3}$

$\frac{1}{4}$

Correct answer:

$\frac{2}{3}$

Explanation:

The correct answer is $\frac{2}{3}$ .

In order to start solving this problem, we need to get each term to have a common denominator.

The common denominator between 2 and 6 is 6. We can rewrite the expression and solve using the following method:

$\frac{1}{2}+\frac{1}{6} = \frac{3}{6}+\frac{1}{6} = \frac{4}{6} = \frac{2}{3}$

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Example Question #26 : Fractions

Determine the answer as a mixed number:

$\frac{3}{4} + \frac{5}{6} =$

Possible Answers:

$1\frac{7}{12}$

$\frac{19}{12}$

$\frac{11}{12}$

$1\frac{3}{4}$

Correct answer:

$1\frac{7}{12}$

Explanation:

1. Find the least common denominator:

The lowest number that both 4 and 6 can go into is 12 meaning that it is the least common denominator.

2. Use the new least common denominator to create two equivalent fractions with a denominator of 12.

$(\frac{3}{4})(\frac{3}{3})=\frac{9}{12}$

$(\frac{5}{6})(\frac{2}{2})=\frac{10}{12}$

3. Add the two fractions together.

$\frac{9}{12}+\frac{10}{12}=\frac{19}{12}$

4. Convert the fraction to a mixed number:

$\frac{19}{12}=1 \frac{7}{12}$

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Example Question #27 : Fractions

Evaluate:

$-\frac{6}{5}+\frac{5}{6}$

Possible Answers:

$-\frac{1}{30}$

$-\frac{61}{30}$

$-\frac{11}{30}$

Correct answer:

$-\frac{11}{30}$

Explanation:

In fractions, to add or subtract the numerator, the denominators must be equal.

Find the least common denominator, multiply the top and bottom with what was multiplied on the denominator, and simplify.

$-\frac{6}{5}+\frac{5}{6} = -\frac{6\cdot6}{5\cdot6}+\frac{5\cdot5}{6\cdot5}=-\frac{36}{30}+\frac{25}{30}$

= $-\frac{11}{30}$

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Example Question #211 : Basic Arithmetic

Please read the following question thoroughly, and then choose the answer which is most correct.

If Billy has 2/3 of a gallon of water, and Bobby has 1/8 of a gallon of water, how much water do they have between the two of them?

Possible Answers:

They have 17/24 of a gallon of water.

They have 14/15 of a gallon of water.

They have 19/24 of a gallon of water.

They have 3/4 of a gallon of water.

They have 17/28 of a gallon of water.

Correct answer:

They have 19/24 of a gallon of water.

Explanation:

To complete this question, you need to find the least common denominator in order to add the fractions. Cross multiply the fractions so that they are in the same terms, and then add. To do this, simply multiply each fraction by the denominator of the other, over itself (so that the fraction equals 1). Follow the steps below:

$\frac{2}{3}+ \frac{1}{8} = ?$

$\frac{2}{3} \cdot \frac{8}{8} = \frac{16}{24}$

$\frac{1}{8}\cdot \frac{3}{3} = \frac{3}{24}$

$\frac{16}{24} + \frac{3}{24} = \frac{19}{24}$

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Example Question #212 : Basic Arithmetic

What is the sum of $\small \small \frac{4}{9}$ and $\small \frac{2}{5}$ ?

Possible Answers:

$\small \frac{3}{7}$

$\small \small \frac{38}{45}$

$\small \frac{2}{45}$

$\small \frac{6}{14}$

$\small \frac{46}{45}$

Correct answer:

$\small \small \frac{38}{45}$

Explanation:

When adding two fractions, the denominators must be the same. When the denominators are the same, we merely add the numerators together to see what the sum is. The trickiest part is transforming the two fractions into fractions with the same denominator.

When we transform a fraction, we are multiplying it by $\small 1$ . For example, $\small \frac{2}{3}$ is the same fraction as $\small \frac{4}{6}$ because $\small \frac{2}{3}\times\frac{2}{2}=\frac{2\times 2}{3\times 2}=\frac{4}{6}$ . Because $\small \frac{2}{2}=1$ , we are not changing the value of the fraction, we are merely expressing the same value in a different form. This is essential when adding fractions with different denominators.

To rewrite these fractions with the same denominator, we need to find the Least Common Denominator (LCD). In this case, the least common denominator is $\small 9\times5=45$ , as $\small 45$ contains both $\small 9$ and $\small 5$ as factors. Our next step is to rewrite our two fractions as fractions with denominators of $\small 45$ .

To transform our first fraction, $\small \frac{4}{9}$ , into a fraction with $\small 45$ as its denominator, we need to multiply the fraction by $\small \frac{5}{5}$ .

To transform our second fraction, $\small \frac{2}{5}$ , into a fraction with as its denominator, we need to multiply the fraction by $\small \frac{9}{9}$ . Therefore, our answer becomes:

$\small \frac{4}{9}+\frac{2}{5}=\frac{4}{9}\times\frac{5}{5}+\frac{2}{5}\times\frac{9}{9}$

$\small \frac{4\times5}{9\times5}+\frac{2\times9}{5\times9}=\frac{20}{45}+\frac{18}{45}$

$\small \frac{20+18}{45}=\frac{38}{45}$

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Basic Arithmetic : Basic Arithmetic

Study concepts, example questions & explanations for Basic Arithmetic

All Basic Arithmetic Resources

Example Questions

Example Question #6 : Division With Fractions

Example Question #21 : Fractions

Example Question #22 : Fractions

Example Question #23 : Fractions

Example Question #24 : Fractions

Example Question #25 : Fractions

Example Question #26 : Fractions

Example Question #27 : Fractions

Example Question #211 : Basic Arithmetic

Example Question #212 : Basic Arithmetic

All Basic Arithmetic Resources

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