Compare these two pairs of fractions: 1) 7/10 vs 11/12 2) 8/10 vs 3/4

Steps to Solve

1. Problem 19: Find a Common Denominator

To compare $\frac{7}{10}$ and $\frac{11}{12}$, we need to find a common denominator. The least common multiple (LCM) of 10 and 12 is 60.

2. Problem 19: Convert Fractions to Equivalent Fractions with Common Denominator

Convert both fractions to have the denominator 60: $\frac{7}{10} = \frac{7 \times 6}{10 \times 6} = \frac{42}{60}$ $\frac{11}{12} = \frac{11 \times 5}{12 \times 5} = \frac{55}{60}$

3. Problem 19: Compare the Fractions

Since $\frac{42}{60} < \frac{55}{60}$, we have $\frac{7}{10} < \frac{11}{12}$.

4. Problem 23: Simplify if Possible

To compare $\frac{8}{10}$ and $\frac{3}{4}$, first, simplify $\frac{8}{10}$ by dividing both numerator and denominator by 2: $\frac{8}{10} = \frac{4}{5}$

5. Problem 23: Find a Common Denominator

Now, compare $\frac{4}{5}$ and $\frac{3}{4}$. The LCM of 5 and 4 is 20.

6. Problem 23: Convert Fractions to Equivalent Fractions with Common Denominator

Convert both fractions to have the denominator 20: $\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}$ $\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$

7. Problem 23: Compare the Fractions

Since $\frac{16}{20} > \frac{15}{20}$, we have $\frac{8}{10} > \frac{3}{4}$.