8. \( 44= \) \( \qquad \) \( - \) - Ryan and Kim ordered pizza of the same size. Ryan ate \( 1 / 5 \) of his pizza and Kim ate 1/6 of her pizza. Who ate more? 10. Anna has 18 stamps. She wants to give her friend one-third of the stamps. How many stamps will she give her friend"? 11. Allen had 15 pens. He gave his brother two-third of the pens. How many pens did he give his brother? 12. Find any three equivalent fractions of \( 6 / 10 \) 13. Find any three equivalent fractions of \( 5 / 9 \). 14. Are \( 3 / 6 \) and \( 7 / 2 \) equivalent fractions? 15. Are \( 3 / 8 \) and \( 21 / 56 \) equivalent fractions? 16. Are \( 2 / 5 \) and \( 6 / 15 \) equivalent fractions? 17. Find any three equivalent fractions of \( 5 / 12 \) BLOCK-17 Points to remember - Fractions that have different denominators is called as unlike fractions. - Fractions that have same denominators is called as like fractions. 1. Convert \( 3 / 4 \) and \( 2 / 3 \) into like fractions. 2. Convert \( 5 / 3 \) and \( 6 / 4 \) into like fractions. 3. Convert \( 3 / 5 \) and \( 2 / 3 \) into like fractions. 4. Add 1/9 and 4/9. 5. Add \( 2 / 3,4 / 3 \) and \( 7 / 3 \). 6. Add \( 1 / 8,2 / 8 \) and \( 4 / 8 \). Page 2 of 3

**8.** One possible expression is \[ 44 = 50 - 6 \] (since \(50-6=44\)). **Ryan and Kim ordered pizza of the same size.** Ryan ate \(\frac{1}{5}\) of his pizza and Kim ate \(\frac{1}{6}\) of her pizza. To compare, express both fractions with a common denominator. The least common denominator of 5 and 6 is 30: \[ \frac{1}{5}=\frac{6}{30} \quad\text{and}\quad \frac{1}{6}=\frac{5}{30}. \] Since \( \frac{6}{30} > \frac{5}{30} \), Ryan ate more. **10.** Anna has 18 stamps and wants to give her friend one-third of them. To find the number of stamps she gives, calculate: \[ \frac{1}{3} \times 18 = 6. \] **11.** Allen had 15 pens and gave his brother two-thirds of them. Calculate the number of pens given by: \[ \frac{2}{3} \times 15 = 10. \] **12.** Three equivalent fractions of \(\frac{6}{10}\) can be found by multiplying the numerator and denominator by the same number. For example: \[ \frac{6}{10}=\frac{6 \times 2}{10 \times 2}=\frac{12}{20},\quad \frac{6}{10}=\frac{6 \times 3}{10 \times 3}=\frac{18}{30},\quad \frac{6}{10}=\frac{6 \times 4}{10 \times 4}=\frac{24}{40}. \] **13.** Three equivalent fractions of \(\frac{5}{9}\) include: \[ \frac{5}{9}=\frac{5 \times 2}{9 \times 2}=\frac{10}{18},\quad \frac{5}{9}=\frac{5 \times 3}{9 \times 3}=\frac{15}{27},\quad \frac{5}{9}=\frac{5 \times 4}{9 \times 4}=\frac{20}{36}. \] **14.** To check if \(\frac{3}{6}\) and \(\frac{7}{2}\) are equivalent, simplify \(\frac{3}{6}\): \[ \frac{3}{6}=\frac{1}{2}. \] Since \(\frac{7}{2} \neq \frac{1}{2}\), the fractions are not equivalent. **15.** Simplify \(\frac{21}{56}\) by dividing the numerator and denominator by 7: \[ \frac{21}{56}=\frac{21\div7}{56\div7}=\frac{3}{8}. \] Since \(\frac{3}{8}=\frac{3}{8}\), the fractions are equivalent. **16.** Check if \(\frac{2}{5}\) and \(\frac{6}{15}\) are equivalent by cross-multiplying or simplifying \(\frac{6}{15}\). Divide numerator and denominator of \(\frac{6}{15}\) by 3: \[ \frac{6 \div 3}{15 \div 3}=\frac{2}{5}. \] They are equivalent. **17.** Three equivalent fractions of \(\frac{5}{12}\) can be obtained by multiplying the numerator and denominator by the same number. For example: \[ \frac{5}{12}=\frac{5 \times 2}{12 \times 2}=\frac{10}{24},\quad \frac{5}{12}=\frac{5 \times 3}{12 \times 3}=\frac{15}{36},\quad \frac{5}{12}=\frac{5 \times 4}{12 \times 4}=\frac{20}{48}. \] --- **BLOCK-17** **1. Convert \(\frac{3}{4}\) and \(\frac{2}{3}\) into like fractions.** The least common denominator (LCD) for 4 and 3 is 12. \[ \frac{3}{4}=\frac{3 \times 3}{4 \times 3}=\frac{9}{12},\quad \frac{2}{3}=\frac{2 \times 4}{3 \times 4}=\frac{8}{12}. \] **2. Convert \(\frac{5}{3}\) and \(\frac{6}{4}\) into like fractions.** The LCD for 3 and 4 is 12. \[ \frac{5}{3}=\frac{5 \times 4}{3 \times 4}=\frac{20}{12},\quad \frac{6}{4}=\frac{6 \times 3}{4 \times 3}=\frac{18}{12}. \] **3. Convert \(\frac{3}{5}\) and \(\frac{2}{3}\) into like fractions.** The LCD for 5 and 3 is 15. \[ \frac{3}{5}=\frac{3 \times 3}{5 \times 3}=\frac{9}{15},\quad \frac{2}{3}=\frac{2 \times 5}{3 \times 5}=\frac{10}{15}. \] **4. Add \(\frac{1}{9}\) and \(\frac{4}{9}\).** Since the denominators are the same, add the numerators: \[ \frac{1}{9}+\frac{4}{9}=\frac{1+4}{9}=\frac{5}{9}. \] **5. Add \(\frac{2}{3}\), \(\frac{4}{3}\), and \(\frac{7}{3}\).** The common denominator makes this simple: \[ \frac{2}{3}+\frac{4}{3}+\frac{7}{3}=\frac{2+4+7}{3}=\frac{13}{3}. \] **6. Add \(\frac{1}{8}\), \(\frac{2}{8}\), and \(\frac{4}{8}\).** Again, add the numerators: \[ \frac{1}{8}+\frac{2}{8}+\frac{4}{8}=\frac{1+2+4}{8}=\frac{7}{8}. \]