(7) Exercise 2.10 1. Convert the following unlike fractions into like fractions. $$ \begin{array}{lll} ext { (a) } \frac{3}{4} ext { and } \frac{1}{3} & ext { (b) } \frac{3}{8} ext { and } \frac{5}{12} & ext { (c) } \frac{4}{15} ext { and } \frac{7}{5}\end{array} $$

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(7) Exercise 2.10 1. Convert the following unlike fractions into like fractions. $$ \begin{array}{lll}	ext { (a) } \frac{3}{4} 	ext { and } \frac{1}{3} & 	ext { (b) } \frac{3}{8} 	ext { and } \frac{5}{12} & 	ext { (c) } \frac{4}{15} 	ext { and } \frac{7}{5}\end{array} $$

UpStudy AI · Accepted Answer

To convert unlike fractions into like fractions, we need to find a common denominator for each pair of fractions. Here’s how to do it for each pair:

### (a) $$\frac{3}{4}$$ and $$\frac{1}{3}$$

1. **Find the least common denominator (LCD)**:
   - The denominators are 4 and 3.
   - The least common multiple (LCM) of 4 and 3 is 12.

2. **Convert each fraction**:
   - For $$\frac{3}{4}$$:
     $$
     \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
     $$
   - For $$\frac{1}{3}$$:
     $$
     \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
     $$

So, the like fractions are $$\frac{9}{12}$$ and $$\frac{4}{12}$$.

### (b) $$\frac{3}{8}$$ and $$\frac{5}{12}$$

1. **Find the least common denominator (LCD)**:
   - The denominators are 8 and 12.
   - The least common multiple (LCM) of 8 and 12 is 24.

2. **Convert each fraction**:
   - For $$\frac{3}{8}$$:
     $$
     \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
     $$
   - For $$\frac{5}{12}$$:
     $$
     \frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}
     $$

So, the like fractions are $$\frac{9}{24}$$ and $$\frac{10}{24}$$.

### (c) $$\frac{4}{15}$$ and $$\frac{7}{5}$$

1. **Find the least common denominator (LCD)**:
   - The denominators are 15 and 5.
   - The least common multiple (LCM) of 15 and 5 is 15.

2. **Convert each fraction**:
   - For $$\frac{4}{15}$$:
     $$
     \frac{4}{15} = \frac{4 \times 1}{15 \times 1} = \frac{4}{15}
     $$
   - For $$\frac{7}{5}$$:
     $$
     \frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15}
     $$

So, the like fractions are $$\frac{4}{15}$$ and $$\frac{21}{15}$$.

### Summary of Like Fractions:
- (a) $$\frac{9}{12}$$ and $$\frac{4}{12}$$
- (b) $$\frac{9}{24}$$ and $$\frac{10}{24}$$
- (c) $$\frac{4}{15}$$ and $$\frac{21}{15}$$
- (a) $$\frac{9}{12}$$ and $$\frac{4}{12}$$ - (b) $$\frac{9}{24}$$ and $$\frac{10}{24}$$ - (c) $$\frac{4}{15}$$ and $$\frac{21}{15}$$

(7) Exercise 2.10

Convert the following unlike fractions into like fractions.

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(7) Exercise 2.10 Convert the following unlike fractions into like fractions.