Calculate the following: $$ \begin{array}{ll} ext { a. } 5 \frac{1}{3}+1 \frac{2}{4} & ext { b. } 4 \frac{3}{8}-3 \frac{4}{6}\end{array} $$

Question

Calculate the following: $$ \begin{array}{ll}	ext { a. } 5 \frac{1}{3}+1 \frac{2}{4} & 	ext { b. } 4 \frac{3}{8}-3 \frac{4}{6}\end{array} $$

UpStudy AI · Accepted Answer

**Step 1. Simplify Expression (a): $$5 \frac{1}{3}+1 \frac{2}{4}$$**

1. Convert to improper fractions:

- $$5 \frac{1}{3}=\frac{5\times3+1}{3}=\frac{15+1}{3}=\frac{16}{3}$$
   - Notice that $$1 \frac{2}{4}=1 \frac{1}{2}$$ because $$\frac{2}{4}$$ simplifies to $$\frac{1}{2}$$. Then,
     
     $$1 \frac{1}{2}=\frac{1\times2+1}{2}=\frac{2+1}{2}=\frac{3}{2}$$

2. Add the fractions:

$$
   \frac{16}{3}+\frac{3}{2}
   $$
   
   Find the least common denominator (LCD) of 3 and 2, which is 6:

$$
   \frac{16}{3}=\frac{16\times2}{3\times2}=\frac{32}{6},\quad \frac{3}{2}=\frac{3\times3}{2\times3}=\frac{9}{6}
   $$
   
3. Now add:

$$
   \frac{32}{6}+\frac{9}{6}=\frac{32+9}{6}=\frac{41}{6}
   $$

4. Convert $$\frac{41}{6}$$ to a mixed number:

$$
   41\div6=6\text{ remainder }5,\quad \text{so } \frac{41}{6}=6 \frac{5}{6}
   $$

---

**Step 2. Simplify Expression (b): $$4 \frac{3}{8}-3 \frac{4}{6}$$**

1. Convert to improper fractions:

- $$4 \frac{3}{8}=\frac{4\times8+3}{8}=\frac{32+3}{8}=\frac{35}{8}$$
   - Simplify $$3 \frac{4}{6}$$ first: $$\frac{4}{6}=\frac{2}{3}$$. Now,
     
     $$3 \frac{2}{3}=\frac{3\times3+2}{3}=\frac{9+2}{3}=\frac{11}{3}$$

2. Subtract the fractions:

$$
   \frac{35}{8}-\frac{11}{3}
   $$
   
   Find the least common denominator (LCD) of 8 and 3, which is 24:

$$
   \frac{35}{8}=\frac{35\times3}{8\times3}=\frac{105}{24},\quad \frac{11}{3}=\frac{11\times8}{3\times8}=\frac{88}{24}
   $$
   
3. Now subtract:

$$
   \frac{105}{24}-\frac{88}{24}=\frac{105-88}{24}=\frac{17}{24}
   $$

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**Final Answers**

(a) $$5 \frac{1}{3}+1 \frac{2}{4}=6 \frac{5}{6}$$  
(b) $$4 \frac{3}{8}-3 \frac{4}{6}=\frac{17}{24}$$
(a) $$5 \frac{1}{3} + 1 \frac{2}{4} = 6 \frac{5}{6}$$ (b) $$4 \frac{3}{8} - 3 \frac{4}{6} = \frac{17}{24}$$

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