Adding and Subtracting Fractions - Algebra 2

Card 1 of 568

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

Solve: $\frac{3}{5}-\frac{2}{7} -\frac{1}{2}$

Tap to reveal answer

Answer

Identify the least common denominator.

Convert the fractions.

$\frac{3}{5}-\frac{2}{7} -\frac{1}{2} =\frac{3(7)(2)}{5(7)(2)}-\frac{2(5)(2)}{7(5)(2)} -\frac{1(5)(7)}{2(5)(7)}$

Simplify the terms.

$\frac{42}{70}-\frac{20}{70}-\frac{35}{70} = -\frac{13}{70}$

The answer is: $-\frac{13}{70}$

← Didn't Know|Knew It →

Question

Add the following fractions: $\frac{1}{5x}+\frac{3}{7}+\frac{10}{x^2}$

Tap to reveal answer

Answer

Determine the least common denominator.

The first two denominators do not have an . After all denominators have an term, the coefficients of the three denominators are:

The least common denominator would be:

Convert all fractions.

$\frac{1}{5x}+\frac{3}{7}+\frac{10}{x^2}=\frac{1(7x)}{5x(7x)}+\frac{3(5x^2)}{7(5x^2)}+\frac{10(35)}{x^2 (35)}$

Simplify the fractions.

The answer is: $\frac{15x^2+7x+350}{35x^2}$

← Didn't Know|Knew It →

Question

Add the fractions: $\frac{4}{9}+\frac{1}{3}+\frac{5}{6}$

Tap to reveal answer

Answer

To add the fractions we need the least common denominator. Write the multiples for each denominator.

Convert the fractions with a denominator of 18, since this is the least common denominator.

$\frac{4}{9}+\frac{1}{3}+\frac{5}{6}=\frac{4(2)}{9(2)}+\frac{1(6)}{3(6)}+\frac{5(3)}{6(3)}$

Simplify the fractions.

$\frac{8}{18}+\frac{6}{18}+\frac{15}{18} = \frac{29}{18}$

The answer is: $\frac{29}{18}$

← Didn't Know|Knew It →

Question

Subtract: $\frac{3}{27}-\frac{9}{30}-\frac{12}{60}$

Tap to reveal answer

Answer

In order to subtract the fractions, we should reduce all the fractions first.

$\frac{3}{27}-\frac{9}{30}-\frac{12}{60} = \frac{1}{9}-\frac{3}{10}-\frac{1}{5}$

Convert the reduced fractions to a common denominator. By visualization, the common denominator is 90, since this value is divisible by all three numbers.

$\frac{1(10)}{9(10)}-\frac{3(9)}{10(9)}-\frac{1(18)}{5(18)}$

Simplify the top and bottom.

$\frac{10}{90}-\frac{27}{90}-\frac{18}{90} = -\frac{35}{90}$

Reduce this fraction.

$-\frac{35}{90} = -\frac{7\times 5}{18\times 5} = -\frac{7}{18}$

The answer is: $-\frac{7}{18}$

← Didn't Know|Knew It →

Question

$\frac{4}{11}+\frac{7}{13}=$

Tap to reveal answer

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 11 and 13 is 143. Multiply the first fraction by 13 divided by 13 and the second by 11 divided by 11 . Then add or subtract the resulting fractions.

← Didn't Know|Knew It →

Question

$\frac{3}{7}-\frac{5}{13}=$

Tap to reveal answer

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 7 and 13 is 91. Multiply the first fraction by 13 divided by 13 and the second by 7 divided by 7 . Then add or subtract the resulting fractions.

← Didn't Know|Knew It →

Question

$\frac{4}{9}-\frac{2}{7}=$

Tap to reveal answer

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 9 and 7 is 63. Multiply the first fraction by 7 divided by 7 and the second by 9 divided by 9 . Then add or subtract the resulting fractions.

← Didn't Know|Knew It →

Question

Add the fractions: $\frac{8}{11}+\frac{1}{66}$

Tap to reveal answer

Answer

Change the first fraction so that both fractions have the same denominator.

Multiply the first fraction by $\frac{6}{6}$ in order to change the fraction.

$\frac{8}{11}(\frac{6}{6})+\frac{1}{66} = \frac{48}{66}+\frac{1}{66} = \frac{49}{66}$

The answer is: $\frac{49}{66}$

← Didn't Know|Knew It →

Question

Add the fractions: $\frac{2}{3}+\frac{8}{9}+2\frac{1}{6}$

Tap to reveal answer

Answer

Change the mixed fraction to an improper fraction.

$1\frac{1}{6} = \frac{6(2)+1}{6} = \frac{13}{6}$

Rewrite the expression.

$\frac{2}{3}+\frac{8}{9}+\frac{13}{6}$

Convert all of the terms to common denominator. A common denominator is 18 since this value is divisible by all denominators given.

$\frac{2(6)}{3(6)}+\frac{8(2)}{9(2)}+\frac{13(3)}{6(3)}$

Simplify all the terms.

$\frac{12}{18}+\frac{16}{18}+\frac{39}{18} = \frac{67}{18}$

The answer is: $\frac{67}{18}$

← Didn't Know|Knew It →

Question

Compute the fractions: $\frac{7}{2}-\frac{3}{8}+\frac{3}{4}$

Tap to reveal answer

Answer

Convert the fractions to a common denominator.

The least common denominator is eight.

$\frac{7(4)}{2(4)}-\frac{3}{8}+\frac{3(2)}{4(2)} = \frac{28}{8}-\frac{3}{8}+\frac{6}{8}$

Find the sum now that the denominators are equal.

The answer is: $\frac{31}{8}$

← Didn't Know|Knew It →

Question

Add the fractions: $\frac{7}{4}+\frac{9}{8}+\frac{1}{12}$

Tap to reveal answer

Answer

Determine the least common denominator. Write out the multiples of each denominator.

Convert all fractions to a common denominator of 24.

$\frac{7}{4}+\frac{9}{8}+\frac{1}{12} = \frac{7(6)}{4(6)}+\frac{9(3)}{8(3)}+\frac{1(2)}{12(2)}$

Simplify the fractions.

$\frac{42}{24}+\frac{27}{24}+\frac{2}{24} = \frac{71}{24}$

The answer is: $\frac{71}{24}$

← Didn't Know|Knew It →

Question

Add the fractions: $\frac{7}{9}-\frac{1}{81}$

Tap to reveal answer

Answer

Change the first fraction so that both denominators are common. This will allow us to change the numerator.

$\frac{7}{9}-\frac{1}{81} = \frac{7(9)}{9(9)}-\frac{1}{81}$

Simplify the fractions.

$\frac{63}{81}-\frac{1}{81} = \frac{62}{81}$

The answer is: $\frac{62}{81}$

← Didn't Know|Knew It →

Question

Subtract the fractions: $\frac{4}{81}-\frac{2}{3}-\frac{11}{9}$

Tap to reveal answer

Answer

Convert the fractions so that all fractions have the least common denominator.

The least common denominator is 81 since this number is the least number that can be divided by all three denominators.

$\frac{4}{81}-\frac{2}{3}-\frac{11}{9} = \frac{4}{81}-\frac{2(27)}{3(27)}-\frac{11(9)}{9(9)}$

Rewrite the fractions.

$\frac{4}{81}-\frac{54}{81}-\frac{99}{81} =-\frac{149}{81}$

The answer is: $-\frac{149}{81}$

← Didn't Know|Knew It →

Question

Add the fractions: $\frac{7}{11}+\frac{2}{22}+\frac{9}{33}$

Tap to reveal answer

Answer

We can start by reducing the fractions to break down the denominator.

$\frac{7}{11}+\frac{2}{22}+\frac{9}{33}=\frac{7}{11}+\frac{2}{2\times 11}+\frac{3\times 3}{3\times 11}$

Cancel out the common terms.

$\frac{7}{11}+\frac{1}{ 11}+\frac{3}{ 11} = \frac{11}{11} = 1$

The answer is:

← Didn't Know|Knew It →

Question

Add the fractions: $\frac{3}{7}+\frac{11}{28}+\frac{1}{14}$

Tap to reveal answer

Answer

Convert all fractions to a common denominator.

The LCD is 28 since this number is the least possible number divisible by all three denominators.

$\frac{3}{7}+\frac{11}{28}+\frac{1}{14} = \frac{3(4)}{7(4)}+\frac{11}{28}+\frac{1(2)}{14(2)}$

$\frac{12}{28}+\frac{11}{28}+\frac{2}{28} = \frac{25}{28}$

The answer is: $\frac{25}{28}$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 8 and 7 is 56. Multiply the first fraction by 7 divided by 7 and the second by 8 divided by 8 . Then add or subtract the resulting fractions.

← Didn't Know|Knew It →

Question

$\frac{1}{6}+\frac{4}{5}=$

Tap to reveal answer

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 6 and 5 is 30. Multiply the first fraction by 5 divided by 5 and the second by 6 divided by 6 . Then add or subtract the resulting fractions.

← Didn't Know|Knew It →

Question

Add the fractions:

$\frac{3}{5}+\frac{1}{10}$

Tap to reveal answer

Answer

When adding fractions, the first thing we need to do is get a common denominator.

$\frac{3}{5}\cdot \frac{2}{2}=\frac{6}{10}$

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

$\frac{6}{10}+\frac{1}{10}=\frac{7}{10}$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

Convert each fraction to incorporate a common denominator. The least common denominator of 3 and 8 is 24. Multiply the first fraction by 8 divided by 8 and the second by 3 divided by 3 . Then add or subtract the resulting fractions.

← Didn't Know|Knew It →

Question

Add the following fractions: $\frac{2}{a}+\frac{2}{a^3b}$

Tap to reveal answer

Answer

To be able to add the fractions, we will need to determine the least common denominator.

The least common denominator is since this is the minimal term that is both divisible by and itself.

Convert only the first fraction with the denominator of .

$\frac{2}{a}+\frac{2}{a^3b}= \frac{2(a^2b)}{a(a^2b)}+\frac{2}{a^3b} = \frac{2a^2b+2}{a^3b}$

The answer is: $\frac{2a^2b+2}{a^3b}$

← Didn't Know|Knew It →

0

Knew It