Algebraic Fractions Worksheet with Answers

Algebraic Fractions Worksheet with Answers

Algebraic Fractions Worksheet

Name: ___________________________
Class: ___________________________
Date: ___________________________

Instructions:

Simplify each algebraic fraction and show all working.

A. Simplify the Algebraic Fractions

  1. 6x12\frac{6x}{12}126x​ = __________________
  2. 10y15\frac{10y}{15}1510y​ = __________________
  3. 8a20\frac{8a}{20}208a​ = __________________
  4. 14m21\frac{14m}{21}2114m​ = __________________
  5. 18n24\frac{18n}{24}2418n​ = __________________
  6. 12x218x\frac{12x^2}{18x}18x12x2​ = __________________
  7. 15y220y\frac{15y^2}{20y}20y15y2​ = __________________
  8. 16a224a\frac{16a^2}{24a}24a16a2​ = __________________
  9. 25m235m\frac{25m^2}{35m}35m25m2​ = __________________
  10. 21n228n\frac{21n^2}{28n}28n21n2​ = __________________

B. Cancel Common Factors and Simplify

  1. 3x9\frac{3x}{9}93x​ = __________________
  2. 4y16\frac{4y}{16}164y​ = __________________
  3. 5a25\frac{5a}{25}255a​ = __________________
  4. 6m18\frac{6m}{18}186m​ = __________________
  5. 7n21\frac{7n}{21}217n​ = __________________
  6. 9x227x\frac{9x^2}{27x}27x9x2​ = __________________
  7. 12y236y\frac{12y^2}{36y}36y12y2​ = __________________
  8. 15a245a\frac{15a^2}{45a}45a15a2​ = __________________
  9. 20m260m\frac{20m^2}{60m}60m20m2​ = __________________
  10. 24n272n\frac{24n^2}{72n}72n24n2​ = __________________

C. Multiply the Algebraic Fractions

  1. x2×34\frac{x}{2} \times \frac{3}{4}2x​×43​ = __________________
  2. a5×103\frac{a}{5} \times \frac{10}{3}5a​×310​ = __________________
  3. 2m7×145\frac{2m}{7} \times \frac{14}{5}72m​×514​ = __________________
  4. 3n8×169\frac{3n}{8} \times \frac{16}{9}83n​×916​ = __________________
  5. 5x6×1210\frac{5x}{6} \times \frac{12}{10}65x​×1012​ = __________________
  6. 4y9×188\frac{4y}{9} \times \frac{18}{8}94y​×818​ = __________________
  7. 7a12×2414\frac{7a}{12} \times \frac{24}{14}127a​×1424​ = __________________
  8. 9m10×2015\frac{9m}{10} \times \frac{20}{15}109m​×1520​ = __________________
  9. 11n6×1822\frac{11n}{6} \times \frac{18}{22}611n​×2218​ = __________________
  10. 13x8×1626\frac{13x}{8} \times \frac{16}{26}813x​×2616​ = __________________

D. Divide the Algebraic Fractions

  1. x3÷25\frac{x}{3} \div \frac{2}{5}3x​÷52​ = __________________
  2. a4÷38\frac{a}{4} \div \frac{3}{8}4a​÷83​ = __________________
  3. m7÷27\frac{m}{7} \div \frac{2}{7}7m​÷72​ = __________________
  4. n9÷43\frac{n}{9} \div \frac{4}{3}9n​÷34​ = __________________
  5. x10÷52\frac{x}{10} \div \frac{5}{2}10x​÷25​ = __________________
  6. 3a8÷65\frac{3a}{8} \div \frac{6}{5}83a​÷56​ = __________________
  7. 5m12÷109\frac{5m}{12} \div \frac{10}{9}125m​÷910​ = __________________
  8. 7n15÷145\frac{7n}{15} \div \frac{14}{5}157n​÷514​ = __________________
  9. 9x16÷188\frac{9x}{16} \div \frac{18}{8}169x​÷818​ = __________________
  10. 11y20÷225\frac{11y}{20} \div \frac{22}{5}2011y​÷522​ = __________________

E. Add the Algebraic Fractions

  1. x4+x4\frac{x}{4} + \frac{x}{4}4x​+4x​ = __________________
  2. a5+2a5\frac{a}{5} + \frac{2a}{5}5a​+52a​ = __________________
  3. m6+3m6\frac{m}{6} + \frac{3m}{6}6m​+63m​ = __________________
  4. n8+5n8\frac{n}{8} + \frac{5n}{8}8n​+85n​ = __________________
  5. x10+4x10\frac{x}{10} + \frac{4x}{10}10x​+104x​ = __________________
  6. 2a7+3a7\frac{2a}{7} + \frac{3a}{7}72a​+73a​ = __________________
  7. 4m9+2m9\frac{4m}{9} + \frac{2m}{9}94m​+92m​ = __________________
  8. 5n12+n12\frac{5n}{12} + \frac{n}{12}125n​+12n​ = __________________
  9. 3x11+4x11\frac{3x}{11} + \frac{4x}{11}113x​+114x​ = __________________
  10. 6y13+2y13\frac{6y}{13} + \frac{2y}{13}136y​+132y​ = __________________

F. Subtract the Algebraic Fractions

  1. 3x4−x4\frac{3x}{4} – \frac{x}{4}43x​−4x​ = __________________
  2. 5a6−2a6\frac{5a}{6} – \frac{2a}{6}65a​−62a​ = __________________
  3. 7m8−3m8\frac{7m}{8} – \frac{3m}{8}87m​−83m​ = __________________
  4. 9n10−4n10\frac{9n}{10} – \frac{4n}{10}109n​−104n​ = __________________
  5. 6x11−x11\frac{6x}{11} – \frac{x}{11}116x​−11x​ = __________________
  6. 8a13−3a13\frac{8a}{13} – \frac{3a}{13}138a​−133a​ = __________________
  7. 10m15−4m15\frac{10m}{15} – \frac{4m}{15}1510m​−154m​ = __________________
  8. 12n17−5n17\frac{12n}{17} – \frac{5n}{17}1712n​−175n​ = __________________
  9. 14x19−6x19\frac{14x}{19} – \frac{6x}{19}1914x​−196x​ = __________________
  10. 15y20−5y20\frac{15y}{20} – \frac{5y}{20}2015y​−205y​ = __________________

Challenge Questions ⭐

  1. x2−9x2−3x\frac{x^2-9}{x^2-3x}x2−3xx2−9​ = __________________
  2. x2−16x2−4x\frac{x^2-16}{x^2-4x}x2−4xx2−16​ = __________________
  3. a2−25a2−5a\frac{a^2-25}{a^2-5a}a2−5aa2−25​ = __________________
  4. m2−49m2−7m\frac{m^2-49}{m^2-7m}m2−7mm2−49​ = __________________
  5. n2−64n2−8n\frac{n^2-64}{n^2-8n}n2−8nn2−64​ = __________________

Teacher’s Remarks:

Score: ________ / 55 ⭐