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- https://math.libretexts.org/Courses/Western_Technical_College/PrePALS_PreAlgebra/02%3A_Fractions/2.04%3A_Adding_and_Subtracting_Fractions\[ \begin{aligned} \frac{4} + \frac{1}{6} &= \frac{4 \cdot \textcolor{red}{2}}{9 \cdot \textcolor{red}{2}} + \frac{1 \cdot \textcolor{red}{3}}{6 \cdot \textcolor{red}{3}} ~ & \textcolor{red}{ \text{ E...\[ \begin{aligned} \frac{4} + \frac{1}{6} &= \frac{4 \cdot \textcolor{red}{2}}{9 \cdot \textcolor{red}{2}} + \frac{1 \cdot \textcolor{red}{3}}{6 \cdot \textcolor{red}{3}} ~ & \textcolor{red}{ \text{ Equivalent fractions with LCD = 18.}} \\ &= \frac{8}{18} + \frac{3}{18} ~ & \textcolor{red}{ \text{ Simplify numerators and denominators.}} \\ &= \frac{8+3}{18} ~ & \textcolor{red}{ \text{ Keep common denominator; add numerators.}} \\ &= \frac{11}{18} ~ & \textcolor{red}{ \text{ Simplify numerator.}…
- https://math.libretexts.org/Courses/City_University_of_New_York/College_Algebra_and_Trigonometry-_Expressions_Equations_and_Graphs/01%3A_Expressions/1.01%3A_Arithmetic/1.1.02%3A_FractionsWe see that the denominator comes from the product of the denominators and the numerator comes from the product of the numerators. To be able to add or subtract fractions, we need to go one more step:...We see that the denominator comes from the product of the denominators and the numerator comes from the product of the numerators. To be able to add or subtract fractions, we need to go one more step: Once you’ve identified the LCD, rewrite both fractions (by multiplying both numerator and denominator by the appropriate same number) to get the LCD as denominator.
- https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Arithmetic_and_Algebra_(ElHitti_Bonanome_Carley_Tradler_and_Zhou)/01%3A_Chapters/1.04%3A_FractionsWe can perform arithmetic operations with rational numbers (fractions). The two types of fractions we will encounter are called proper and improper: Proper fractions have value less than 1, for exa...We can perform arithmetic operations with rational numbers (fractions). The two types of fractions we will encounter are called proper and improper: Proper fractions have value less than 1, for example 2/5 and 1/8. Observe that for these fractions the numerator is less than the denominator. Improper fractions have value greater than or equal to 1, for example 7/6 and 3/2. For these fractions the numerator is greater than the denominator.
- https://math.libretexts.org/Courses/Western_Technical_College/PrePALS_Math_with_Business_Apps/02%3A_Fractions/2.04%3A_Adding_and_Subtracting_Fractions\[ \begin{aligned} -\frac{1}{4} - \frac{5}{6} &= - \frac{1 \cdot \textcolor{red}{3}}{4 \cdot \textcolor{red}{3}} - \frac{5 \cdot \textcolor{red}{2}}{6 \cdot \textcolor{red}{2}} ~ & \textcolor{red}{ \t...\[ \begin{aligned} -\frac{1}{4} - \frac{5}{6} &= - \frac{1 \cdot \textcolor{red}{3}}{4 \cdot \textcolor{red}{3}} - \frac{5 \cdot \textcolor{red}{2}}{6 \cdot \textcolor{red}{2}} ~ & \textcolor{red}{ \text{ Equivalent fractions with LCD =12.}} \\ &= - \frac{3}{12} - \frac{10}{12} ~ & \textcolor{red}{ \text{ Simplify numerators and denominators.}} \\ &= \frac{-3-10}{12} ~ & \textcolor{red}{ \text{ Keep LCD; subtract numerators.}} \\ &= \frac{-13}{12} ~ & \textcolor{red}{ \text{ Simplify numerator.…
- https://math.libretexts.org/Bookshelves/PreAlgebra/Prealgebra_(Arnold)/04%3A_Fractions/4.05%3A_Adding_and_Subtracting_Fractions\[ \begin{aligned} -\frac{1}{4} - \frac{5}{6} &= - \frac{1 \cdot \textcolor{red}{3}}{4 \cdot \textcolor{red}{3}} - \frac{5 \cdot \textcolor{red}{2}}{6 \cdot \textcolor{red}{2}} ~ & \textcolor{red}{ \t...\[ \begin{aligned} -\frac{1}{4} - \frac{5}{6} &= - \frac{1 \cdot \textcolor{red}{3}}{4 \cdot \textcolor{red}{3}} - \frac{5 \cdot \textcolor{red}{2}}{6 \cdot \textcolor{red}{2}} ~ & \textcolor{red}{ \text{ Equivalent fractions with LCD =12.}} \\ &= - \frac{3}{12} - \frac{10}{12} ~ & \textcolor{red}{ \text{ Simplify numerators and denominators.}} \\ &= \frac{-3-10}{12} ~ & \textcolor{red}{ \text{ Keep LCD; subtract numerators.}} \\ &= \frac{-13}{12} ~ & \textcolor{red}{ \text{ Simplify numerator.…
