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Basic Arithmetic : Basic Arithmetic

Study concepts, example questions & explanations for Basic Arithmetic

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6 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Subtraction With Fractions

Please choose the best answer for the question below.

Amanda has $2\frac{3}{4}$ pounds of cake leftover from her birthday. If she eats a third of a pound of cake, how much will she have left over?

Possible Answers:

$2 \frac{1}{8}$ pounds of cake.

pounds of cake.

$1\frac{5}{12}$ pounds of cake.

$2 \frac{7}{12}$ pounds of cake.

$2\frac{5}{12}$ pounds of cake.

Correct answer:

$2\frac{5}{12}$ pounds of cake.

Explanation:

To tackle this question, first convert 2 and 3/4ths into a fraction.

$2 \cdot \frac{4}{4} = \frac{8}{4}$

$\frac{8}{4} + \frac{3}{4} =\frac{11}{4}$

Then, you can subtract 1/3 from 11/4 :

$\frac{11}{4} - \frac{1}{3} = ?$

$\frac{11\cdot3}{4 \cdot3} + \frac{1\cdot4}{3\cdot4} = ?$

33/12 - 4/12 = 29/12

Then you convert to a mixed number for your final answer.

29/12= $2\frac{5}{12}$ .

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Example Question #4 : Subtraction With Fractions

Please choose the best answer for the question below.

If you have three pies, and someone eats one quarter of each pie, how much pie do you have left? The answers will be expressed as mixed numbers.

Possible Answers:

$2\frac{1}{3}$

$2\frac{3}{4}$

$1\frac{1}{4}$

$2\frac{1}{4}$

$1\frac{1}{3}$

Correct answer:

$2\frac{1}{4}$

Explanation:

To find the answer for this problem, first figure out how much of each pie is left:

3 - 3/4 = ?

12/4 - 3/4 = 9/4

Then, because 4/4 = 1 , you know that you have whole pies left, and a quarter besides.

$\frac{9}{4}=2\frac{1}{4}$

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Example Question #5 : Subtraction With Fractions

$\frac{5}{6} -\frac{12}{36}= ?$

Possible Answers:

$\frac{17}{36}$

$\frac{-7}{36}$

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{-5}{6}$

Correct answer:

$\frac{1}{2}$

Explanation:

To subtract fractions, they must have the same number in the denominator. Begin by simplifying $\frac{12}{36}$ so that its denominator is .

To simplify, divide the numerator and denominator by 6.

$12 \div6=2$

$36\div6=6$

$\frac{12}{36}=\frac{2}{6}$

Then, subtract:

$\frac{5}{6}-\frac{2}{6}=\frac{3}{6}=\frac{1}{2}$

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Example Question #4 : Subtraction With Fractions

Subtract these fractions:

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

Possible Answers:

$\frac{1}{9}$

$\frac{5}{6}{}$

$\frac{2}{9}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{6}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 2 over 2 and the second fraction by 3 over 3.

$\frac{2}{3}*\frac{2}{2}=\frac{4}{6}$

$\frac{1}{2}*\frac{3}{3}=\frac{3}{6}$

Subtract these fractions to get the final answer.

$\frac{4}{6}-\frac{3}{6}=\frac{1}{6}$

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Example Question #8 : Subtraction With Fractions

Subtract these fractions:

$\frac{4}{5}-\frac{1}{3}$

Possible Answers:

$\frac{7}{15}$

$\frac{9}{12}$

$\frac{5}{12}$

$\frac{11}{12}$

Correct answer:

$\frac{7}{15}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 3 over 3 and the second fraction by 5 over 5.

$\frac{4}{5}*\frac{3}{3}=\frac{12}{15}$

$\frac{1}{3}*\frac{5}{5}=\frac{5}{15}$

Subtract the numerators of the fractions to get the final answer.

$\frac{12}{15}-\frac{5}{15}=\frac{7}{15}$

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Example Question #6 : Subtraction With Fractions

Subtract these fractions:

$\frac{3}{7}-\frac{1}{4}$

Possible Answers:

$\frac{9}{28}$

$\frac{11}{28}$

$\frac{3}{14}$

$\frac{5}{28}$

Correct answer:

$\frac{5}{28}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 4 over 4 and the second fraction by 7 over 7.

$\frac{3}{7}*\frac{4}{4}=\frac{12}{28}$

$\frac{1}{4}*\frac{7}{7}=\frac{7}{28}$

Subtract the numerators of these fractions to get the final answer.

$\frac{12}{28}-\frac{7}{28}=\frac{5}{28}$

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Example Question #7 : Subtraction With Fractions

Subtract these fractions:

$\frac{1}{8}-\frac{1}{9}$

Possible Answers:

$\frac{1}{36}$

$\frac{1}{17}$

$\frac{1}{24}$

$\frac{1}{72}$

Correct answer:

$\frac{1}{72}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 9 over 9 and the second fraction by 8 over 8.

$\frac{1}{8}*\frac{9}{9}=\frac{9}{72}$

$\frac{1}{9}*\frac{8}{8}=\frac{8}{72}$

Subtract the numerators of these fractions to get the final answer.

$\frac{9}{72}-\frac{8}{72}=\frac{1}{72}$

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Example Question #1724 : Mathematical Relationships And Basic Graphs

Subtract these fractions:

$\frac{6}{7}-\frac{1}{3}$

Possible Answers:

$\frac{10}{21}$

$\frac{3}{7}$

$\frac{11}{21}$

$\frac{12}{21}$

Correct answer:

$\frac{11}{21}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 3 over 3 and the second fraction by 7 over 7.

$\frac{6}{7}*\frac{3}{3}=\frac{18}{21}$

$\frac{1}{3}*\frac{7}{7}=\frac{7}{21}$

Subtract the numerators of these fractions to get the final answer.

$\frac{18}{21}-\frac{7}{21}=\frac{11}{21}$

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Example Question #1 : Manipulation Of Fractions

What is the reciprocal of $\frac{4}{7}$ ?

Possible Answers:

$-\frac{7}{4}$

$-\frac{4}{7}$

$\frac{7}{4}$

$\frac{1}{4}$

$\frac{1}{7}$

Correct answer:

$\frac{7}{4}$

Explanation:

To get the reciprocal of a fraction, you simply switch the numerator and the denominator.

In our case our numerator is and our denominator is .

So $\frac{4}{7}$ becomes $\frac{7}{4}$ .

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Example Question #2 : Manipulation Of Fractions

Compute: $\frac{x}{\left(2x)^{-2}\right }$

Possible Answers:

$\frac{4}{x}$

$\frac{1}{4x}$

$\frac{4}{x^3}$

$\frac{1}{4}$

$4x^{3}$

Correct answer:

$4x^{3}$

Explanation:

We will need to rewrite this in order to eliminate the negative exponent in the problem.

Because the denominator has a negative exponent, that is the same as having a positive exponent in the numerator. Therefore we can rewrite the problem as follows and then multiply.

$\frac{x}{\left(2x)^{-2}\right } = x\cdot (2x)^2 = x\cdot4x^2 = 4x^3$

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Basic Arithmetic : Basic Arithmetic

Study concepts, example questions & explanations for Basic Arithmetic

All Basic Arithmetic Resources

Example Questions

Example Question #3 : Subtraction With Fractions

Example Question #4 : Subtraction With Fractions

Example Question #5 : Subtraction With Fractions

Example Question #4 : Subtraction With Fractions

Example Question #8 : Subtraction With Fractions

Example Question #6 : Subtraction With Fractions

Example Question #7 : Subtraction With Fractions

Example Question #1724 : Mathematical Relationships And Basic Graphs

Example Question #1 : Manipulation Of Fractions

Example Question #2 : Manipulation Of Fractions

All Basic Arithmetic Resources

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