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Basic Arithmetic : Operations with Fractions

Study concepts, example questions & explanations for Basic Arithmetic

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Example Questions

Example Question #41 : Operations With Fractions

Subtract.

$\frac{8}{9}-\frac{1}{81}$

Possible Answers:

$\frac{7}{72}$

$\frac{71}{81}$

$-\frac{7}{72}$

$\frac{73}{81}$

Correct answer:

$\frac{71}{81}$

Explanation:

To subtract two fractions, they need to both share the same denominator. Since 81 is a multiple of 9, we only need to change the 1st fraction.

$\frac{8}{9}\times\frac{9}{9}=\frac{72}{81}$

Now subtract the two fractions.

$\frac{72}{81}-\frac{1}{81}=\frac{71}{81}$

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Example Question #222 : Basic Arithmetic

Determine the answer:

$\frac{3}{4}-\frac{2}{5}=$

Possible Answers:

$\frac{1}{5}$

$\frac{7}{20}$

$\frac{17}{20}$

$\frac{6}{15}$

Correct answer:

$\frac{7}{20}$

Explanation:

1. Find the least common denominator:

The lowest number that both 4 and 5 both go into is 20, making 20 the least common denominator.

2. Find the equivalent fractions using the least common denominator:

$\frac{3}{4}\times \frac{5}{5}=\frac{15}{20}$

$\frac{2}{5}\times \frac{4}{4}=\frac{8}{20}$

3. Subtract:

$\frac{15}{20}-\frac{8}{20}=\frac{7}{20}$

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Example Question #42 : Operations 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.

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

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

$1\frac{5}{12}$ 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 #43 : Operations 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:

$1\frac{1}{3}$

$2\frac{3}{4}$

$2\frac{1}{3}$

$2\frac{1}{4}$

$1\frac{1}{4}$

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:

$\frac{1}{2}$

$\frac{-7}{36}$

$\frac{-5}{6}$

$\frac{17}{36}$

$\frac{3}{4}$

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 #43 : Operations With Fractions

Subtract these fractions:

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

Possible Answers:

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

$\frac{1}{9}$

$\frac{2}{9}$

$\frac{1}{6}$

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 #41 : Operations With Fractions

Subtract these fractions:

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

Possible Answers:

$\frac{3}{7}$

$\frac{12}{21}$

$\frac{10}{21}$

$\frac{11}{21}$

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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Basic Arithmetic : Operations with Fractions

Study concepts, example questions & explanations for Basic Arithmetic

All Basic Arithmetic Resources

Example Questions

Example Question #41 : Operations With Fractions

Example Question #222 : Basic Arithmetic

Example Question #42 : Operations With Fractions

Example Question #43 : Operations With Fractions

Example Question #5 : Subtraction With Fractions

Example Question #43 : Operations With Fractions

Example Question #8 : Subtraction With Fractions

Example Question #6 : Subtraction With Fractions

Example Question #7 : Subtraction With Fractions

Example Question #41 : Operations With Fractions

All Basic Arithmetic Resources

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