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343 | Simplify the following expression: $a = \dfrac{7}{5k - 1} \div \dfrac{9}{10k}$ | Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{7}{5k - 1} \times \dfrac{10k}{9}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 7 \times 10k } { (5k - 1) \times 9}$ $a = \dfrac{70k}{45k - 9}$ |
343 | Simplify the following expression: $t = \dfrac{6p - 7}{6} \times \dfrac{4}{10p}$ | When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ (6p - 7) \times 4 } { 6 \times 10p}$ $t = \dfrac{24p - 28}{60p}$ Simplify: $t = \dfrac{6p - 7}{15p}$ |
343 | Simplify the following expression: $y = \dfrac{5}{8q + 10} \div \dfrac{7}{7q}$ | Dividing by an expression is the same as multiplying by its inverse. $y = \dfrac{5}{8q + 10} \times \dfrac{7q}{7}$ When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 5 \times 7q } { (8q + 10) \times 7}$ $y = \dfrac{35q}{56q + 70}$ Simplify: $y = \dfrac{5q}{8q + 10}$ |
343 | Simplify the following expression: $r = \dfrac{5p + 7}{10} \times \dfrac{2}{9p}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (5p + 7) \times 2 } { 10 \times 9p}$ $r = \dfrac{10p + 14}{90p}$ Simplify: $r = \dfrac{5p + 7}{45p}$ |
343 | Simplify the following expression: $k = \dfrac{9}{5p} \div \dfrac{4}{7p}$ | Dividing by an expression is the same as multiplying by its inverse. $k = \dfrac{9}{5p} \times \dfrac{7p}{4}$ When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 9 \times 7p } { 5p \times 4}$ $k = \dfrac{63p}{20p}$ Simplify: $k = \dfrac{63}{20}$ |
343 | Simplify the following expression: $q = \dfrac{10}{5p - 6} \times \dfrac{6p}{2}$ | When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 10 \times 6p } { (5p - 6) \times 2}$ $q = \dfrac{60p}{10p - 12}$ Simplify: $q = \dfrac{30p}{5p - 6}$ |
343 | Simplify the following expression: $r = \dfrac{2a + 10}{4} \times \dfrac{10}{9a}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (2a + 10) \times 10 } { 4 \times 9a}$ $r = \dfrac{20a + 100}{36a}$ Simplify: $r = \dfrac{5a + 25}{9a}$ |
343 | Simplify the following expression: $a = \dfrac{8}{y} \div \dfrac{3}{2y}$ | Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{8}{y} \times \dfrac{2y}{3}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 8 \times 2y } { y \times 3}$ $a = \dfrac{16y}{3y}$ Simplify: $a = \dfrac{16}{3}$ |
343 | Simplify the following expression: $a = \dfrac{6}{7n} \times \dfrac{9n}{4}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 6 \times 9n } { 7n \times 4}$ $a = \dfrac{54n}{28n}$ Simplify: $a = \dfrac{27}{14}$ |
343 | Simplify the following expression: $n = \dfrac{8}{3r - 8} \times \dfrac{9r}{6}$ | When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 8 \times 9r } { (3r - 8) \times 6}$ $n = \dfrac{72r}{18r - 48}$ Simplify: $n = \dfrac{12r}{3r - 8}$ |
343 | Simplify the following expression: $p = \dfrac{y - 7}{6} \times \dfrac{8}{4y}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (y - 7) \times 8 } { 6 \times 4y}$ $p = \dfrac{8y - 56}{24y}$ Simplify: $p = \dfrac{y - 7}{3y}$ |
343 | Simplify the following expression: $r = \dfrac{2a + 10}{4} \div \dfrac{9a}{10}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{2a + 10}{4} \times \dfrac{10}{9a}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (2a + 10) \times 10 } { 4 \times 9a}$ $r = \dfrac{20a + 100}{36a}$ Simplify: $r = \dfrac{5a + 25}{9a}$ |
343 | Simplify the following expression: $y = \dfrac{6k}{2} \div \dfrac{9k}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $y = \dfrac{6k}{2} \times \dfrac{2}{9k}$ When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 6k \times 2 } { 2 \times 9k}$ $y = \dfrac{12k}{18k}$ Simplify: $y = \dfrac{2}{3}$ |
343 | Simplify the following expression: $t = \dfrac{6}{5z - 2} \times \dfrac{2z}{2}$ | When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ 6 \times 2z } { (5z - 2) \times 2}$ $t = \dfrac{12z}{10z - 4}$ Simplify: $t = \dfrac{6z}{5z - 2}$ |
343 | Simplify the following expression: $x = \dfrac{10}{5q + 6} \times \dfrac{5q}{3}$ | When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 10 \times 5q } { (5q + 6) \times 3}$ $x = \dfrac{50q}{15q + 18}$ |
343 | Simplify the following expression: $r = \dfrac{4p}{10} \div \dfrac{3p}{7}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{4p}{10} \times \dfrac{7}{3p}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 4p \times 7 } { 10 \times 3p}$ $r = \dfrac{28p}{30p}$ Simplify: $r = \dfrac{14}{15}$ |
343 | Simplify the following expression: $q = \dfrac{3t - 3}{8} \div \dfrac{4t}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{3t - 3}{8} \times \dfrac{4}{4t}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ (3t - 3) \times 4 } { 8 \times 4t}$ $q = \dfrac{12t - 12}{32t}$ Simplify: $q = \dfrac{3t - 3}{8t}$ |
343 | Simplify the following expression: $p = \dfrac{5}{k - 8} \div \dfrac{5}{7k}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{5}{k - 8} \times \dfrac{7k}{5}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 5 \times 7k } { (k - 8) \times 5}$ $p = \dfrac{35k}{5k - 40}$ Simplify: $p = \dfrac{7k}{k - 8}$ |
343 | Simplify the following expression: $p = \dfrac{9}{2x + 9} \times \dfrac{9x}{10}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 9 \times 9x } { (2x + 9) \times 10}$ $p = \dfrac{81x}{20x + 90}$ |
343 | Simplify the following expression: $z = \dfrac{8r + 2}{7} \div \dfrac{4r}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{8r + 2}{7} \times \dfrac{2}{4r}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ (8r + 2) \times 2 } { 7 \times 4r}$ $z = \dfrac{16r + 4}{28r}$ Simplify: $z = \dfrac{4r + 1}{7r}$ |
343 | Simplify the following expression: $p = \dfrac{4}{3n - 3} \div \dfrac{10}{5n}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{4}{3n - 3} \times \dfrac{5n}{10}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 4 \times 5n } { (3n - 3) \times 10}$ $p = \dfrac{20n}{30n - 30}$ Simplify: $p = \dfrac{2n}{3n - 3}$ |
343 | Simplify the following expression: $q = \dfrac{9}{5x + 4} \times \dfrac{8x}{10}$ | When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 9 \times 8x } { (5x + 4) \times 10}$ $q = \dfrac{72x}{50x + 40}$ Simplify: $q = \dfrac{36x}{25x + 20}$ |
343 | Simplify the following expression: $p = \dfrac{q - 1}{4} \div \dfrac{9q}{7}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{q - 1}{4} \times \dfrac{7}{9q}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (q - 1) \times 7 } { 4 \times 9q}$ $p = \dfrac{7q - 7}{36q}$ |
343 | Simplify the following expression: $t = \dfrac{5r}{3} \times \dfrac{9}{2r}$ | When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ 5r \times 9 } { 3 \times 2r}$ $t = \dfrac{45r}{6r}$ Simplify: $t = \dfrac{15}{2}$ |
343 | Simplify the following expression: $z = \dfrac{4p}{7} \div \dfrac{4p}{9}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{4p}{7} \times \dfrac{9}{4p}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 4p \times 9 } { 7 \times 4p}$ $z = \dfrac{36p}{28p}$ Simplify: $z = \dfrac{9}{7}$ |
343 | Simplify the following expression: $z = \dfrac{9}{6a - 5} \times \dfrac{4a}{2}$ | When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 9 \times 4a } { (6a - 5) \times 2}$ $z = \dfrac{36a}{12a - 10}$ Simplify: $z = \dfrac{18a}{6a - 5}$ |
343 | Simplify the following expression: $n = \dfrac{9}{5p} \times \dfrac{2p}{6}$ | When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 9 \times 2p } { 5p \times 6}$ $n = \dfrac{18p}{30p}$ Simplify: $n = \dfrac{3}{5}$ |
343 | Simplify the following expression: $t = \dfrac{3a - 5}{2} \times \dfrac{10}{2a}$ | When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ (3a - 5) \times 10 } { 2 \times 2a}$ $t = \dfrac{30a - 50}{4a}$ Simplify: $t = \dfrac{15a - 25}{2a}$ |
343 | Simplify the following expression: $r = \dfrac{10}{2t - 10} \times \dfrac{8t}{4}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 10 \times 8t } { (2t - 10) \times 4}$ $r = \dfrac{80t}{8t - 40}$ Simplify: $r = \dfrac{10t}{t - 5}$ |
343 | Simplify the following expression: $r = \dfrac{q - 3}{4} \div \dfrac{7q}{10}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{q - 3}{4} \times \dfrac{10}{7q}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (q - 3) \times 10 } { 4 \times 7q}$ $r = \dfrac{10q - 30}{28q}$ Simplify: $r = \dfrac{5q - 15}{14q}$ |
343 | Simplify the following expression: $k = \dfrac{4x - 7}{3} \times \dfrac{4}{2x}$ | When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ (4x - 7) \times 4 } { 3 \times 2x}$ $k = \dfrac{16x - 28}{6x}$ Simplify: $k = \dfrac{8x - 14}{3x}$ |
343 | Simplify the following expression: $p = \dfrac{5n - 3}{3} \times \dfrac{5}{3n}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (5n - 3) \times 5 } { 3 \times 3n}$ $p = \dfrac{25n - 15}{9n}$ |
343 | Simplify the following expression: $q = \dfrac{6}{2p + 9} \times \dfrac{10p}{6}$ | When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 6 \times 10p } { (2p + 9) \times 6}$ $q = \dfrac{60p}{12p + 54}$ Simplify: $q = \dfrac{10p}{2p + 9}$ |
343 | Simplify the following expression: $y = \dfrac{4r - 3}{2} \div \dfrac{4r}{10}$ | Dividing by an expression is the same as multiplying by its inverse. $y = \dfrac{4r - 3}{2} \times \dfrac{10}{4r}$ When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ (4r - 3) \times 10 } { 2 \times 4r}$ $y = \dfrac{40r - 30}{8r}$ Simplify: $y = \dfrac{20r - 15}{4r}$ |
343 | Simplify the following expression: $a = \dfrac{6q - 7}{7} \times \dfrac{6}{2q}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ (6q - 7) \times 6 } { 7 \times 2q}$ $a = \dfrac{36q - 42}{14q}$ Simplify: $a = \dfrac{18q - 21}{7q}$ |
343 | Simplify the following expression: $r = \dfrac{7q}{8} \div \dfrac{2q}{8}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{7q}{8} \times \dfrac{8}{2q}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 7q \times 8 } { 8 \times 2q}$ $r = \dfrac{56q}{16q}$ Simplify: $r = \dfrac{7}{2}$ |
343 | Simplify the following expression: $r = \dfrac{3}{7x - 9} \times \dfrac{10x}{4}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 3 \times 10x } { (7x - 9) \times 4}$ $r = \dfrac{30x}{28x - 36}$ Simplify: $r = \dfrac{15x}{14x - 18}$ |
343 | Simplify the following expression: $q = \dfrac{6}{y} \div \dfrac{7}{3y}$ | Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{6}{y} \times \dfrac{3y}{7}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 6 \times 3y } { y \times 7}$ $q = \dfrac{18y}{7y}$ Simplify: $q = \dfrac{18}{7}$ |
343 | Simplify the following expression: $a = \dfrac{7}{2z + 3} \times \dfrac{7z}{2}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 7 \times 7z } { (2z + 3) \times 2}$ $a = \dfrac{49z}{4z + 6}$ |
343 | Simplify the following expression: $r = \dfrac{t}{5} \div \dfrac{3t}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{t}{5} \times \dfrac{2}{3t}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ t \times 2 } { 5 \times 3t}$ $r = \dfrac{2t}{15t}$ Simplify: $r = \dfrac{2}{15}$ |
343 | Simplify the following expression: $n = \dfrac{6}{5p + 7} \div \dfrac{8}{7p}$ | Dividing by an expression is the same as multiplying by its inverse. $n = \dfrac{6}{5p + 7} \times \dfrac{7p}{8}$ When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 6 \times 7p } { (5p + 7) \times 8}$ $n = \dfrac{42p}{40p + 56}$ Simplify: $n = \dfrac{21p}{20p + 28}$ |
343 | Simplify the following expression: $q = \dfrac{10}{5p - 6} \div \dfrac{2}{6p}$ | Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{10}{5p - 6} \times \dfrac{6p}{2}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 10 \times 6p } { (5p - 6) \times 2}$ $q = \dfrac{60p}{10p - 12}$ Simplify: $q = \dfrac{30p}{5p - 6}$ |
343 | Simplify the following expression: $k = \dfrac{4a - 1}{8} \times \dfrac{4}{6a}$ | When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ (4a - 1) \times 4 } { 8 \times 6a}$ $k = \dfrac{16a - 4}{48a}$ Simplify: $k = \dfrac{4a - 1}{12a}$ |
343 | Simplify the following expression: $y = \dfrac{5n + 9}{8} \times \dfrac{5}{10n}$ | When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ (5n + 9) \times 5 } { 8 \times 10n}$ $y = \dfrac{25n + 45}{80n}$ Simplify: $y = \dfrac{5n + 9}{16n}$ |
343 | Simplify the following expression: $n = \dfrac{5}{r} \div \dfrac{5}{4r}$ | Dividing by an expression is the same as multiplying by its inverse. $n = \dfrac{5}{r} \times \dfrac{4r}{5}$ When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 5 \times 4r } { r \times 5}$ $n = \dfrac{20r}{5r}$ Simplify: $n = \dfrac{4}{1}$ |
343 | Simplify the following expression: $p = \dfrac{3z - 6}{5} \div \dfrac{9z}{8}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{3z - 6}{5} \times \dfrac{8}{9z}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (3z - 6) \times 8 } { 5 \times 9z}$ $p = \dfrac{24z - 48}{45z}$ Simplify: $p = \dfrac{8z - 16}{15z}$ |
343 | Simplify the following expression: $a = \dfrac{8}{z + 5} \times \dfrac{5z}{7}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 8 \times 5z } { (z + 5) \times 7}$ $a = \dfrac{40z}{7z + 35}$ |
343 | Simplify the following expression: $r = \dfrac{2}{8y - 3} \times \dfrac{6y}{4}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 2 \times 6y } { (8y - 3) \times 4}$ $r = \dfrac{12y}{32y - 12}$ Simplify: $r = \dfrac{3y}{8y - 3}$ |
343 | Simplify the following expression: $p = \dfrac{3z + 1}{9} \times \dfrac{2}{4z}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (3z + 1) \times 2 } { 9 \times 4z}$ $p = \dfrac{6z + 2}{36z}$ Simplify: $p = \dfrac{3z + 1}{18z}$ |
343 | Simplify the following expression: $x = \dfrac{7}{4n} \times \dfrac{7n}{7}$ | When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 7 \times 7n } { 4n \times 7}$ $x = \dfrac{49n}{28n}$ Simplify: $x = \dfrac{7}{4}$ |
343 | Simplify the following expression: $a = \dfrac{3q}{8} \times \dfrac{6}{9q}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 3q \times 6 } { 8 \times 9q}$ $a = \dfrac{18q}{72q}$ Simplify: $a = \dfrac{1}{4}$ |
343 | Simplify the following expression: $a = \dfrac{6t + 1}{6} \div \dfrac{4t}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{6t + 1}{6} \times \dfrac{2}{4t}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ (6t + 1) \times 2 } { 6 \times 4t}$ $a = \dfrac{12t + 2}{24t}$ Simplify: $a = \dfrac{6t + 1}{12t}$ |
343 | Simplify the following expression: $y = \dfrac{2k}{5} \times \dfrac{4}{7k}$ | When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 2k \times 4 } { 5 \times 7k}$ $y = \dfrac{8k}{35k}$ Simplify: $y = \dfrac{8}{35}$ |
343 | Simplify the following expression: $x = \dfrac{7}{8p + 1} \times \dfrac{8p}{8}$ | When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 7 \times 8p } { (8p + 1) \times 8}$ $x = \dfrac{56p}{64p + 8}$ Simplify: $x = \dfrac{7p}{8p + 1}$ |
343 | Simplify the following expression: $q = \dfrac{2}{4a + 9} \times \dfrac{5a}{10}$ | When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 2 \times 5a } { (4a + 9) \times 10}$ $q = \dfrac{10a}{40a + 90}$ Simplify: $q = \dfrac{a}{4a + 9}$ |
343 | Simplify the following expression: $x = \dfrac{7q}{8} \times \dfrac{7}{5q}$ | When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 7q \times 7 } { 8 \times 5q}$ $x = \dfrac{49q}{40q}$ Simplify: $x = \dfrac{49}{40}$ |
343 | Simplify the following expression: $q = \dfrac{8}{3a - 6} \div \dfrac{2}{2a}$ | Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{8}{3a - 6} \times \dfrac{2a}{2}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 8 \times 2a } { (3a - 6) \times 2}$ $q = \dfrac{16a}{6a - 12}$ Simplify: $q = \dfrac{8a}{3a - 6}$ |
343 | Simplify the following expression: $p = \dfrac{3z - 6}{5} \times \dfrac{8}{9z}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (3z - 6) \times 8 } { 5 \times 9z}$ $p = \dfrac{24z - 48}{45z}$ Simplify: $p = \dfrac{8z - 16}{15z}$ |
343 | Simplify the following expression: $a = \dfrac{q}{3} \div \dfrac{7q}{7}$ | Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{q}{3} \times \dfrac{7}{7q}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ q \times 7 } { 3 \times 7q}$ $a = \dfrac{7q}{21q}$ Simplify: $a = \dfrac{1}{3}$ |
343 | Simplify the following expression: $p = \dfrac{2}{3n - 4} \div \dfrac{3}{3n}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{2}{3n - 4} \times \dfrac{3n}{3}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 2 \times 3n } { (3n - 4) \times 3}$ $p = \dfrac{6n}{9n - 12}$ Simplify: $p = \dfrac{2n}{3n - 4}$ |
343 | Simplify the following expression: $p = \dfrac{4n - 5}{6} \times \dfrac{8}{2n}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (4n - 5) \times 8 } { 6 \times 2n}$ $p = \dfrac{32n - 40}{12n}$ Simplify: $p = \dfrac{8n - 10}{3n}$ |
343 | Simplify the following expression: $x = \dfrac{4r}{8} \div \dfrac{3r}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{4r}{8} \times \dfrac{2}{3r}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 4r \times 2 } { 8 \times 3r}$ $x = \dfrac{8r}{24r}$ Simplify: $x = \dfrac{1}{3}$ |
343 | Simplify the following expression: $r = \dfrac{4a - 4}{4} \times \dfrac{4}{5a}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (4a - 4) \times 4 } { 4 \times 5a}$ $r = \dfrac{16a - 16}{20a}$ Simplify: $r = \dfrac{4a - 4}{5a}$ |
343 | Simplify the following expression: $a = \dfrac{7}{k} \times \dfrac{7k}{4}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 7 \times 7k } { k \times 4}$ $a = \dfrac{49k}{4k}$ Simplify: $a = \dfrac{49}{4}$ |
343 | Simplify the following expression: $t = \dfrac{6p - 7}{6} \div \dfrac{10p}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{6p - 7}{6} \times \dfrac{4}{10p}$ When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ (6p - 7) \times 4 } { 6 \times 10p}$ $t = \dfrac{24p - 28}{60p}$ Simplify: $t = \dfrac{6p - 7}{15p}$ |
343 | Simplify the following expression: $x = \dfrac{4}{7k} \div \dfrac{3}{3k}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{4}{7k} \times \dfrac{3k}{3}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 4 \times 3k } { 7k \times 3}$ $x = \dfrac{12k}{21k}$ Simplify: $x = \dfrac{4}{7}$ |
343 | Simplify the following expression: $q = \dfrac{6}{2t} \times \dfrac{9t}{8}$ | When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 6 \times 9t } { 2t \times 8}$ $q = \dfrac{54t}{16t}$ Simplify: $q = \dfrac{27}{8}$ |
343 | Simplify the following expression: $q = \dfrac{4y + 3}{5} \div \dfrac{3y}{5}$ | Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{4y + 3}{5} \times \dfrac{5}{3y}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ (4y + 3) \times 5 } { 5 \times 3y}$ $q = \dfrac{20y + 15}{15y}$ Simplify: $q = \dfrac{4y + 3}{3y}$ |
343 | Simplify the following expression: $t = \dfrac{4}{z - 6} \div \dfrac{4}{4z}$ | Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{4}{z - 6} \times \dfrac{4z}{4}$ When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ 4 \times 4z } { (z - 6) \times 4}$ $t = \dfrac{16z}{4z - 24}$ Simplify: $t = \dfrac{4z}{z - 6}$ |
343 | Simplify the following expression: $x = \dfrac{3n}{2} \div \dfrac{4n}{9}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{3n}{2} \times \dfrac{9}{4n}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 3n \times 9 } { 2 \times 4n}$ $x = \dfrac{27n}{8n}$ Simplify: $x = \dfrac{27}{8}$ |
343 | Simplify the following expression: $r = \dfrac{4}{4t - 5} \div \dfrac{6}{4t}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{4}{4t - 5} \times \dfrac{4t}{6}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 4 \times 4t } { (4t - 5) \times 6}$ $r = \dfrac{16t}{24t - 30}$ Simplify: $r = \dfrac{8t}{12t - 15}$ |
343 | Simplify the following expression: $t = \dfrac{2k + 2}{2} \times \dfrac{4}{4k}$ | When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ (2k + 2) \times 4 } { 2 \times 4k}$ $t = \dfrac{8k + 8}{8k}$ Simplify: $t = \dfrac{k + 1}{k}$ |
343 | Simplify the following expression: $p = \dfrac{9}{2n + 2} \times \dfrac{10n}{4}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 9 \times 10n } { (2n + 2) \times 4}$ $p = \dfrac{90n}{8n + 8}$ Simplify: $p = \dfrac{45n}{4n + 4}$ |
343 | Simplify the following expression: $y = \dfrac{8}{7k + 7} \div \dfrac{8}{2k}$ | Dividing by an expression is the same as multiplying by its inverse. $y = \dfrac{8}{7k + 7} \times \dfrac{2k}{8}$ When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 8 \times 2k } { (7k + 7) \times 8}$ $y = \dfrac{16k}{56k + 56}$ Simplify: $y = \dfrac{2k}{7k + 7}$ |
343 | Simplify the following expression: $p = \dfrac{6}{8q + 9} \div \dfrac{10}{3q}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{6}{8q + 9} \times \dfrac{3q}{10}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 6 \times 3q } { (8q + 9) \times 10}$ $p = \dfrac{18q}{80q + 90}$ Simplify: $p = \dfrac{9q}{40q + 45}$ |
343 | Simplify the following expression: $p = \dfrac{9}{2x + 9} \div \dfrac{10}{9x}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{9}{2x + 9} \times \dfrac{9x}{10}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 9 \times 9x } { (2x + 9) \times 10}$ $p = \dfrac{81x}{20x + 90}$ |
343 | Simplify the following expression: $p = \dfrac{3x + 7}{8} \div \dfrac{10x}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{3x + 7}{8} \times \dfrac{4}{10x}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (3x + 7) \times 4 } { 8 \times 10x}$ $p = \dfrac{12x + 28}{80x}$ Simplify: $p = \dfrac{3x + 7}{20x}$ |
343 | Simplify the following expression: $a = \dfrac{8z + 7}{6} \times \dfrac{6}{10z}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ (8z + 7) \times 6 } { 6 \times 10z}$ $a = \dfrac{48z + 42}{60z}$ Simplify: $a = \dfrac{8z + 7}{10z}$ |
343 | Simplify the following expression: $x = \dfrac{4}{8n + 4} \div \dfrac{10}{4n}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{4}{8n + 4} \times \dfrac{4n}{10}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 4 \times 4n } { (8n + 4) \times 10}$ $x = \dfrac{16n}{80n + 40}$ Simplify: $x = \dfrac{2n}{10n + 5}$ |
343 | Simplify the following expression: $n = \dfrac{4}{7r + 1} \times \dfrac{2r}{5}$ | When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 4 \times 2r } { (7r + 1) \times 5}$ $n = \dfrac{8r}{35r + 5}$ |
343 | Simplify the following expression: $p = \dfrac{6}{t} \times \dfrac{6t}{8}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 6 \times 6t } { t \times 8}$ $p = \dfrac{36t}{8t}$ Simplify: $p = \dfrac{9}{2}$ |
343 | Simplify the following expression: $p = \dfrac{2}{5x - 10} \times \dfrac{2x}{9}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 2 \times 2x } { (5x - 10) \times 9}$ $p = \dfrac{4x}{45x - 90}$ |
343 | Simplify the following expression: $k = \dfrac{6r + 4}{5} \div \dfrac{8r}{3}$ | Dividing by an expression is the same as multiplying by its inverse. $k = \dfrac{6r + 4}{5} \times \dfrac{3}{8r}$ When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ (6r + 4) \times 3 } { 5 \times 8r}$ $k = \dfrac{18r + 12}{40r}$ Simplify: $k = \dfrac{9r + 6}{20r}$ |
343 | Simplify the following expression: $p = \dfrac{9}{2k + 5} \times \dfrac{4k}{10}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 9 \times 4k } { (2k + 5) \times 10}$ $p = \dfrac{36k}{20k + 50}$ Simplify: $p = \dfrac{18k}{10k + 25}$ |
343 | Simplify the following expression: $x = \dfrac{4r}{8} \times \dfrac{2}{3r}$ | When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 4r \times 2 } { 8 \times 3r}$ $x = \dfrac{8r}{24r}$ Simplify: $x = \dfrac{1}{3}$ |
343 | Simplify the following expression: $z = \dfrac{4n}{8} \div \dfrac{5n}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{4n}{8} \times \dfrac{2}{5n}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 4n \times 2 } { 8 \times 5n}$ $z = \dfrac{8n}{40n}$ Simplify: $z = \dfrac{1}{5}$ |
343 | Simplify the following expression: $x = \dfrac{5}{r} \div \dfrac{5}{9r}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{5}{r} \times \dfrac{9r}{5}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 5 \times 9r } { r \times 5}$ $x = \dfrac{45r}{5r}$ Simplify: $x = \dfrac{9}{1}$ |
343 | Simplify the following expression: $r = \dfrac{3}{8t + 3} \div \dfrac{7}{3t}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{3}{8t + 3} \times \dfrac{3t}{7}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 3 \times 3t } { (8t + 3) \times 7}$ $r = \dfrac{9t}{56t + 21}$ |
343 | Simplify the following expression: $a = \dfrac{8}{y} \times \dfrac{2y}{3}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 8 \times 2y } { y \times 3}$ $a = \dfrac{16y}{3y}$ Simplify: $a = \dfrac{16}{3}$ |
343 | Simplify the following expression: $a = \dfrac{5}{z + 1} \times \dfrac{7z}{5}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 5 \times 7z } { (z + 1) \times 5}$ $a = \dfrac{35z}{5z + 5}$ Simplify: $a = \dfrac{7z}{z + 1}$ |
343 | Simplify the following expression: $p = \dfrac{n + 1}{3} \times \dfrac{3}{8n}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (n + 1) \times 3 } { 3 \times 8n}$ $p = \dfrac{3n + 3}{24n}$ Simplify: $p = \dfrac{n + 1}{8n}$ |
343 | Simplify the following expression: $r = \dfrac{3}{4y + 8} \times \dfrac{10y}{9}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 3 \times 10y } { (4y + 8) \times 9}$ $r = \dfrac{30y}{36y + 72}$ Simplify: $r = \dfrac{5y}{6y + 12}$ |
343 | Simplify the following expression: $x = \dfrac{7}{4n} \div \dfrac{7}{7n}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{7}{4n} \times \dfrac{7n}{7}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 7 \times 7n } { 4n \times 7}$ $x = \dfrac{49n}{28n}$ Simplify: $x = \dfrac{7}{4}$ |
343 | Simplify the following expression: $r = \dfrac{4a - 4}{4} \div \dfrac{5a}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{4a - 4}{4} \times \dfrac{4}{5a}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (4a - 4) \times 4 } { 4 \times 5a}$ $r = \dfrac{16a - 16}{20a}$ Simplify: $r = \dfrac{4a - 4}{5a}$ |
343 | Simplify the following expression: $p = \dfrac{2}{3n - 4} \times \dfrac{3n}{3}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 2 \times 3n } { (3n - 4) \times 3}$ $p = \dfrac{6n}{9n - 12}$ Simplify: $p = \dfrac{2n}{3n - 4}$ |
343 | Simplify the following expression: $r = \dfrac{5}{3n} \times \dfrac{8n}{7}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 5 \times 8n } { 3n \times 7}$ $r = \dfrac{40n}{21n}$ Simplify: $r = \dfrac{40}{21}$ |
343 | Simplify the following expression: $y = \dfrac{5}{6q} \times \dfrac{10q}{9}$ | When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 5 \times 10q } { 6q \times 9}$ $y = \dfrac{50q}{54q}$ Simplify: $y = \dfrac{25}{27}$ |
343 | Simplify the following expression: $n = \dfrac{6}{4y - 10} \times \dfrac{8y}{9}$ | When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 6 \times 8y } { (4y - 10) \times 9}$ $n = \dfrac{48y}{36y - 90}$ Simplify: $n = \dfrac{8y}{6y - 15}$ |
343 | Simplify the following expression: $a = \dfrac{k + 1}{5} \div \dfrac{7k}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{k + 1}{5} \times \dfrac{2}{7k}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ (k + 1) \times 2 } { 5 \times 7k}$ $a = \dfrac{2k + 2}{35k}$ |
343 | Simplify the following expression: $k = \dfrac{8}{4r + 5} \div \dfrac{5}{6r}$ | Dividing by an expression is the same as multiplying by its inverse. $k = \dfrac{8}{4r + 5} \times \dfrac{6r}{5}$ When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 8 \times 6r } { (4r + 5) \times 5}$ $k = \dfrac{48r}{20r + 25}$ |
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