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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 #6 : Addition With Fractions

Solve:

$\frac{3}{2}+\frac{7}{9}=$

Possible Answers:

$\frac{10}{11}$

$\frac{41}{18}$

$\frac{10}{9}$

Correct answer:

$\frac{41}{18}$

Explanation:

The least common multiple of 2 and 9 is 18.

$\frac{3}{2}=\frac{27}{18}$

$\frac{7}{9}=\frac{14}{18}$

$\frac{27}{18}+\frac{14}{18}=\frac{27+14}{18}=\frac{41}{18}$

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Example Question #1 : Adding And Subtracting Fractions

Simplify $\frac{2}{3}+\frac{1}{4}+\frac{5}{6}$

Possible Answers:

$\frac{8}{13}$

$1\frac{3}{4}$

$1\frac{1}{3}$

$1\frac{1}{6}$

$\frac{11}{12}$

Correct answer:

$1\frac{3}{4}$

Explanation:

Find the least common denominator (LCD) and convert each fraction to the LCD and then add. Simplify as necessary.

$\frac{2}{3}+\frac{1}{4}+\frac{5}{6}=\frac{8}{12}+\frac{3}{12}+\frac{10}{12}=\frac{21}{12}$

The result is an improper fraction because the numerator is larger than the denominator and can be simplified and converted to a mix numeral.

$\frac{21}{12}=\frac{7}{4}=1\frac{3}{4}$

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Example Question #4 : Adding And Subtracting Fractions

Simplify the following fraction:

$\frac{12}{39}$

Possible Answers:

$\frac{4}{39}$

$\frac{5}{6}$

$\frac{4}{13}$

$\frac{13}{2}$

$\frac{8}{13}$

Correct answer:

$\frac{4}{13}$

Explanation:

Determine the factors of both the numerator and the denominator:

$12 = 2 \times 2 \times 3$

$39 = 3 \times 13$

We notice that 3 is a factor of both 12 and 39 so we can simplify by dividing both 12 and 39 by 3.

$\frac{12}{3}=4$

$\frac{39}{3}=13$

The result is therefore,

$\frac{4}{13}$

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Example Question #1 : Adding And Subtracting Fractions

Find the simplified result:

$\frac{5}{6} + \frac{7}{8}$

Possible Answers:

$\frac{40}{48}$

$\frac{12}{14}$

$\frac{41}{24}$

$\frac{82}{48}$

$\frac{42}{48}$

Correct answer:

$\frac{41}{24}$

Explanation:

Start by making both fractions into the same denominator. One option is $6 \times 8 = 48$

Then adjust the numerators by multiplying each fraction's numerator by the other fraction's denominator:

$\frac{5}{6}\cdot \frac{8}{8}+ \frac{7}{8}\cdot \frac{6}{6}$

$=\frac{40}{48}+\frac{42}{48}$

Then add the adjusted numerators:

$=\frac{82}{48}$

Then we simplify by dividing both numerator and denominator by 2:

$=\frac{2 \cdot 41}{2 \cdot 24}=\frac{41}{24}$

which gives us the final result.

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Example Question #14 : Adding And Subtracting Fractions

Add these fractions:

$\frac{3}{5}+\frac{2}{7}$

Possible Answers:

$\frac{29}{35}$

$\frac{34}{35}$

$\frac{31}{35}$

$\frac{21}{35}$

Correct answer:

$\frac{31}{35}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 7 over 7 and the second fraction by 5 over 5.

$\frac{3}{5}*\frac{7}{7}=\frac{21}{35}$

$\frac{2}{7}*\frac{5}{5}=\frac{10}{35}$

Add these fractions together, to get the final answer.

$\frac{21}{35}+\frac{10}{35}=\frac{31}{35}$

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Example Question #31 : Operations With Fractions

Add these fractions:

$\frac{1}{7}+\frac{5}{6}$

Possible Answers:

$\frac{39}{42}$

$\frac{43}{42}$

$\frac{20}{21}$

$\frac{41}{42}$

Correct answer:

$\frac{41}{42}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 6 over 6 and the second fraction by 7 over 7.

$\frac{1}{7}*\frac{6}{6}=\frac{6}{42}$

$\frac{5}{6}*\frac{7}{7}=\frac{35}{42}$

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

$\frac{6}{42}+\frac{35}{42}=\frac{41}{42}$

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Example Question #32 : Fractions

Add these fractions:

$\frac{3}{7}+\frac{2}{5}$

Possible Answers:

$\frac{30}{35}$

$\frac{28}{35}$

$\frac{31}{35}$

$\frac{29}{35}$

Correct answer:

$\frac{29}{35}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 5 over 5 and the second fraction by 7 over 7.

$\frac{3}{7}*\frac{5}{5}=\frac{15}{35}$

$\frac{2}{5}*\frac{7}{7}=\frac{14}{35}$

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

$\frac{15}{35}+\frac{14}{35}=\frac{29}{35}$

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Example Question #221 : Basic Arithmetic

$\frac{4}{5}-\frac{3}{7}=?$

Possible Answers:

$\frac{28}{35}$

$\frac{13}{35}$

$\frac{15}{34}$

$-\frac{1}{2}$

Correct answer:

$\frac{13}{35}$

Explanation:

To subtract fractions, they need to share the same denominator. To find the same denominator, you will need to find the least common multiple of the two given denominators.

The least common denominator of 5 and 7 is 35. Remember, the number you multiply the denominator by to get the least common denominator you must also multiply by the numerator.

$\frac{4}{5}\cdot \frac{7}{7}- \frac{3}{7}\cdot \frac{5}{5}$

So the original equation becomes,

$\frac{28}{35}-\frac{15}{35}$

Now, subtract the numerators.

$\frac{28}{35}-\frac{15}{35}=\frac{13}{35}$

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Example Question #222 : Basic Arithmetic

Subtract.

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

Possible Answers:

$-\frac{7}{72}$

$\frac{7}{72}$

$\frac{73}{81}$

$\frac{71}{81}$

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 #3 : Subtraction With Fractions

Determine the answer:

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

Possible Answers:

$\frac{7}{20}$

$\frac{17}{20}$

$\frac{1}{5}$

$\frac{6}{15}$

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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Basic Arithmetic : Basic Arithmetic

Study concepts, example questions & explanations for Basic Arithmetic

All Basic Arithmetic Resources

Example Questions

Example Question #6 : Addition With Fractions

Example Question #1 : Adding And Subtracting Fractions

Example Question #4 : Adding And Subtracting Fractions

Example Question #1 : Adding And Subtracting Fractions

Example Question #14 : Adding And Subtracting Fractions

Example Question #31 : Operations With Fractions

Example Question #32 : Fractions

Example Question #221 : Basic Arithmetic

Example Question #222 : Basic Arithmetic

Example Question #3 : Subtraction With Fractions

All Basic Arithmetic Resources

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