Question

lesson 4 reteach
add and subtract unlike fractions
to add or subtract fractions with different denominators,

• rename the fractions using the least common denominator (lcd).
• add or subtract as with like fractions.
• if necessary, simplify the sum or difference.

example
find \\(\frac{2}{3} + \frac{1}{4}\\).
method 1 use a model.
\\(\

$$\begin{array}{r}\\frac{2}{3}\\\\\\underline{+ \\ \\frac{1}{4}}\\\\\\frac{11}{12}\\end{array}$$

\\)
method 2 use the lcd.
\\(\

$$\begin{align}\\frac{2}{3} + \\frac{1}{4} &= \\frac{2}{3} \\cdot \\frac{4}{4} + \\frac{1}{4} \\cdot \\frac{3}{3}\\\\&= \\frac{8}{12} + \\frac{3}{12} \\text{ or } \\frac{11}{12}\\end{align}$$

\\)
rename using the lcd, 12.
add the fractions.
exercises
add or subtract. write in simplest form.

1. \\(\frac{1}{2} + \frac{3}{4}\\)
2. \\(\frac{3}{8} - \frac{1}{2}\\)
3. \\(\frac{7}{15} + \left(-\frac{5}{6}\

ight)\\)

1. \\(\frac{2}{5} - \frac{1}{3}\\)
2. \\(\frac{5}{9} + \left(-\frac{5}{12}\

ight)\\)

1. \\(\frac{11}{12} - \frac{3}{4}\\)
2. \\(\frac{7}{8} - \left(-\frac{1}{3}\

ight)\\)

1. \\(\frac{7}{9} - \frac{1}{2}\\)
2. \\(\frac{3}{10} + \frac{7}{12}\\)
3. \\(\frac{3}{5} + \frac{2}{3}\\)

Explanation:

Step1: Find LCD, rename fractions

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

Step2: Add numerators

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

---

Step1: Find LCD, rename fractions

$\frac{1}{2} = \frac{4}{8}$

Step2: Subtract numerators

$\frac{3}{8} - \frac{4}{8} = -\frac{1}{8}$

---

Step1: Find LCD, rename fractions

$\frac{7}{15} = \frac{14}{30}$, $-\frac{5}{6} = -\frac{25}{30}$

Step2: Add numerators

$\frac{14}{30} + (-\frac{25}{30}) = -\frac{11}{30}$

---

Step1: Find LCD, rename fractions

$\frac{2}{5} = \frac{6}{15}$, $\frac{1}{3} = \frac{5}{15}$

Step2: Subtract numerators

$\frac{6}{15} - \frac{5}{15} = \frac{1}{15}$

---

Step1: Find LCD, rename fractions

$\frac{5}{9} = \frac{20}{36}$, $-\frac{5}{12} = -\frac{15}{36}$

Step2: Add numerators

$\frac{20}{36} + (-\frac{15}{36}) = \frac{5}{36}$

---

Step1: Find LCD, rename fractions

$\frac{3}{4} = \frac{9}{12}$

Step2: Subtract numerators

$\frac{11}{12} - \frac{9}{12} = \frac{2}{12} = \frac{1}{6}$

---

Step1: Rewrite subtraction as addition

$\frac{7}{8} + \frac{1}{3}$

Step2: Find LCD, rename fractions

$\frac{7}{8} = \frac{21}{24}$, $\frac{1}{3} = \frac{8}{24}$

Step3: Add numerators

$\frac{21}{24} + \frac{8}{24} = \frac{29}{24}$

---

Step1: Find LCD, rename fractions

$\frac{7}{9} = \frac{14}{18}$, $\frac{1}{2} = \frac{9}{18}$

Step2: Subtract numerators

$\frac{14}{18} - \frac{9}{18} = \frac{5}{18}$

---

Step1: Find LCD, rename fractions

$\frac{3}{10} = \frac{18}{60}$, $\frac{7}{12} = \frac{35}{60}$

Step2: Add numerators

$\frac{18}{60} + \frac{35}{60} = \frac{53}{60}$

---

Step1: Find LCD, rename fractions

$\frac{3}{5} = \frac{9}{15}$, $\frac{2}{3} = \frac{10}{15}$

Step2: Add numerators

$\frac{9}{15} + \frac{10}{15} = \frac{19}{15}$

Answer:

1. $\frac{5}{4}$
2. $-\frac{1}{8}$
3. $-\frac{11}{30}$
4. $\frac{1}{15}$
5. $\frac{5}{36}$
6. $\frac{1}{6}$
7. $\frac{29}{24}$
8. $\frac{5}{18}$
9. $\frac{53}{60}$
10. $\frac{19}{15}$