1 find the lcd of each pair of fractions mentally.
a. $\frac{7}{8}, \frac{1}{2}$ lcd =
b. $\frac{3}{5}, \frac{2}{3}$ lcd =
c. $\frac{3}{4}, \frac{3}{10}$ lcd =
d. $\frac{3}{7}, \frac{3}{14}, \frac{1}{2}$ lcd =
e. $\frac{1}{3}, \frac{5}{6}, \frac{5}{8}$ lcd =
f. $\frac{1}{2}, \frac{2}{3}, \frac{2}{5}$ lcd =

2 add or subtract. simplify when possible.
a. $\begin{array}{r} \frac{1}{2} \\ + \frac{1}{3} \\ \hline \end{array}$
b. $\begin{array}{r} \frac{3}{4} \\ + \frac{1}{8} \\ \hline \end{array}$
c. $\begin{array}{r} \frac{5}{6} \\ - \frac{1}{4} \\ \hline \end{array}$
d. $\begin{r} 3\frac{1}{2} \\ - 1\frac{1}{5} \\ \hline \end{array}$
e. $\begin{array}{r} \frac{5}{6} \\ + \frac{5}{9} \\ \hline \end{array}$
f. $\begin{array}{r} 4\frac{7}{9} \\ + 2\frac{2}{3} \\ \hline \end{array}$
g. $\begin{array}{r} 5\frac{11}{15} \\ - 3\frac{2}{5} \\ \hline \end{array}$
h. $\begin{array}{r} 4\frac{5}{8} \\ + 1\frac{4}{7} \\ \hline \end{array}$
i. $\begin{array}{r} 7\frac{11}{12} \\ - 6\frac{1}{4} \\ \hline \end{array}$
j. $\begin{array}{r} 9\frac{3}{4} \\ + 2\frac{5}{9} \\ \hline \end{array}$

Question

1 find the lcd of each pair of fractions mentally.
a. $\frac{7}{8}, \frac{1}{2}$ lcd =
b. $\frac{3}{5}, \frac{2}{3}$ lcd =
c. $\frac{3}{4}, \frac{3}{10}$ lcd =
d. $\frac{3}{7}, \frac{3}{14}, \frac{1}{2}$ lcd =
e. $\frac{1}{3}, \frac{5}{6}, \frac{5}{8}$ lcd =
f. $\frac{1}{2}, \frac{2}{3}, \frac{2}{5}$ lcd =

2 add or subtract. simplify when possible.
a. $\begin{array}{r} \frac{1}{2} \\ + \frac{1}{3} \\ \hline \end{array}$
b. $\begin{array}{r} \frac{3}{4} \\ + \frac{1}{8} \\ \hline \end{array}$
c. $\begin{array}{r} \frac{5}{6} \\ - \frac{1}{4} \\ \hline \end{array}$
d. $\begin{r} 3\frac{1}{2} \\ - 1\frac{1}{5} \\ \hline \end{array}$
e. $\begin{array}{r} \frac{5}{6} \\ + \frac{5}{9} \\ \hline \end{array}$
f. $\begin{array}{r} 4\frac{7}{9} \\ + 2\frac{2}{3} \\ \hline \end{array}$
g. $\begin{array}{r} 5\frac{11}{15} \\ - 3\frac{2}{5} \\ \hline \end{array}$
h. $\begin{array}{r} 4\frac{5}{8} \\ + 1\frac{4}{7} \\ \hline \end{array}$
i. $\begin{array}{r} 7\frac{11}{12} \\ - 6\frac{1}{4} \\ \hline \end{array}$
j. $\begin{array}{r} 9\frac{3}{4} \\ + 2\frac{5}{9} \\ \hline \end{array}$

Accepted Answer

{ "quality": "clear", "question_count": 16, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Least Common Denominator", "Fraction Addition", "Fraction Subtraction" ], "current_concepts": [ "Least Common Denominator", "Fraction Addition", "Fraction Subtraction" ] } ## Find the LCD for each pair or group of fractions $$ \begin{aligned} &\text{a. } \frac{7}{8}, \frac{1}{2} \implies \text{LCD} = \text{lcm}(8, 2) = 8\ &\text{b. } \frac{3}{5}, \frac{2}{3} \implies \text{LCD} = \text{lcm}(5, 3) = 15\ &\text{c. } \frac{3}{4}, \frac{3}{10} \implies \text{LCD} = \text{lcm}(4, 10) = 20\ &\text{d. } \frac{3}{7}, \frac{3}{14}, \frac{1}{2} \implies \text{LCD} = \text{lcm}(7, 14, 2) = 14\ &\text{e. } \frac{1}{3}, \frac{5}{6}, \frac{5}{8} \implies \text{LCD} = \text{lcm}(3, 6, 8) = 24\ &\text{f. } \frac{1}{2}, \frac{2}{3}, \frac{2}{5} \implies \text{LCD} = \text{lcm}(2, 3, 5) = 30 \end{aligned} $$ ## Add or subtract the fractions (a to e) $$ \begin{aligned} &\text{a. } \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}\ &\text{b. } \frac{3}{4} + \frac{1}{8} = \frac{6}{8} + \frac{1}{8} = \frac{7}{8}\ &\text{c. } \frac{5}{6} - \frac{1}{4} = \frac{10}{12} - \frac{3}{12} = \frac{7}{12}\ &\text{d. } 3\frac{1}{2} - 1\frac{1}{5} = 3\frac{5}{10} - 1\frac{2}{10} = 2\frac{3}{10}\ &\text{e. } \frac{5}{6} + \frac{5}{9} = \frac{15}{18} + \frac{10}{18} = \frac{25}{18} = 1\frac{7}{18} \end{aligned} $$ ## Add or subtract the fractions (f to j) $$ \begin{aligned} &\text{f. } 4\frac{7}{9} + 2\frac{2}{3} = 4\frac{7}{9} + 2\frac{6}{9} = 6\frac{13}{9} = 7\frac{4}{9}\ &\text{g. } 5\frac{11}{15} - 3\frac{2}{5} = 5\frac{11}{15} - 3\frac{6}{15} = 2\frac{5}{15} = 2\frac{1}{3}\ &\text{h. } 4\frac{5}{8} + 1\frac{4}{7} = 4\frac{35}{56} + 1\frac{32}{56} = 5\frac{67}{56} = 6\frac{11}{56}\ &\text{i. } 7\frac{11}{12} - 6\frac{1}{4} = 7\frac{11}{12} - 6\frac{3}{12} = 1\frac{8}{12} = 1\frac{2}{3}\ &\text{j. } 9\frac{3}{4} + 2\frac{5}{9} = 9\frac{27}{36} + 2\frac{20}{36} = 11\frac{47}{36} = 12\frac{11}{36} \end{aligned} $$ | Section | Item | Answer | | :--- | :--- | :--- | | **1. Find the LCD** | a. | $8$ | | | b. | $15$ | | | c. | $20$ | | | d. | $14$ | | | e. | $24$ | | | f. | $30$ | | **2. Add or subtract** | a. | $\frac{5}{6}$ | | | b. | $\frac{7}{8}$ | | | c. | $\frac{7}{12}$ | | | d. | $2\frac{3}{10}$ | | | e. | $1\frac{7}{18}$ | | | f. | $7\frac{4}{9}$ | | | g. | $2\frac{1}{3}$ | | | h. | $6\frac{11}{56}$ | | | i. | $1\frac{2}{3}$ | | | j. | $12\frac{11}{36}$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Arithmetic", "Fraction Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Find the LCD for each pair or group of fractions

Add or subtract the fractions (a to e)

Add or subtract the fractions (f to j)

Answer:

Section	Item	Answer
	b.	\(15\)
	c.	\(20\)
	d.	\(14\)
	e.	\(24\)
	f.	\(30\)
2. Add or subtract	a.	\(\frac{5}{6}\)
	b.	\(\frac{7}{8}\)
	c.	\(\frac{7}{12}\)
	d.	\(2\frac{3}{10}\)
	e.	\(1\frac{7}{18}\)
	f.	\(7\frac{4}{9}\)
	g.	\(2\frac{1}{3}\)
	h.	\(6\frac{11}{56}\)
	i.	\(1\frac{2}{3}\)
	j.	\(12\frac{11}{36}\)