topic_name
stringclasses 721
values | problem
stringlengths 4
1.36k
⌀ | hints/solutions
stringlengths 5
3.3k
|
|---|---|---|
343 | Simplify the following expression: $a = \dfrac{6q - 7}{7} \div \dfrac{2q}{6}$ | Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{6q - 7}{7} \times \dfrac{6}{2q}$ 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: $r = \dfrac{7z - 2}{5} \times \dfrac{6}{5z}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (7z - 2) \times 6 } { 5 \times 5z}$ $r = \dfrac{42z - 12}{25z}$ |
343 | Simplify the following expression: $r = \dfrac{4}{4t - 5} \times \dfrac{4t}{6}$ | 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: $y = \dfrac{6k}{2} \times \dfrac{2}{9k}$ | 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: $y = \dfrac{8k}{8} \times \dfrac{7}{7k}$ | When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 8k \times 7 } { 8 \times 7k}$ $y = \dfrac{56k}{56k}$ Simplify: $y = \dfrac{1}{1}$ |
343 | Simplify the following expression: $q = \dfrac{8}{3a - 6} \times \dfrac{2a}{2}$ | 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: $p = \dfrac{8}{4t - 2} \times \dfrac{7t}{9}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 8 \times 7t } { (4t - 2) \times 9}$ $p = \dfrac{56t}{36t - 18}$ Simplify: $p = \dfrac{28t}{18t - 9}$ |
343 | Simplify the following expression: $z = \dfrac{10}{8k - 2} \div \dfrac{2}{7k}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{10}{8k - 2} \times \dfrac{7k}{2}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 10 \times 7k } { (8k - 2) \times 2}$ $z = \dfrac{70k}{16k - 4}$ Simplify: $z = \dfrac{35k}{8k - 2}$ |
343 | Simplify the following expression: $p = \dfrac{y - 5}{4} \times \dfrac{6}{6y}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (y - 5) \times 6 } { 4 \times 6y}$ $p = \dfrac{6y - 30}{24y}$ Simplify: $p = \dfrac{y - 5}{4y}$ |
343 | Simplify the following expression: $p = \dfrac{3x + 7}{8} \times \dfrac{4}{10x}$ | 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: $a = \dfrac{7}{2z + 3} \div \dfrac{2}{7z}$ | Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{7}{2z + 3} \times \dfrac{7z}{2}$ 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: $r = \dfrac{3}{8t + 3} \times \dfrac{3t}{7}$ | 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: $n = \dfrac{10}{3x + 5} \times \dfrac{5x}{6}$ | When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 10 \times 5x } { (3x + 5) \times 6}$ $n = \dfrac{50x}{18x + 30}$ Simplify: $n = \dfrac{25x}{9x + 15}$ |
343 | Simplify the following expression: $k = \dfrac{3}{4p - 6} \times \dfrac{3p}{7}$ | When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 3 \times 3p } { (4p - 6) \times 7}$ $k = \dfrac{9p}{28p - 42}$ |
343 | Simplify the following expression: $k = \dfrac{8}{a + 5} \times \dfrac{10a}{6}$ | When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 8 \times 10a } { (a + 5) \times 6}$ $k = \dfrac{80a}{6a + 30}$ Simplify: $k = \dfrac{40a}{3a + 15}$ |
343 | Simplify the following expression: $t = \dfrac{3}{3a - 1} \times \dfrac{9a}{2}$ | When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ 3 \times 9a } { (3a - 1) \times 2}$ $t = \dfrac{27a}{6a - 2}$ |
343 | Simplify the following expression: $k = \dfrac{5}{2x - 1} \times \dfrac{5x}{6}$ | When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 5 \times 5x } { (2x - 1) \times 6}$ $k = \dfrac{25x}{12x - 6}$ |
343 | Simplify the following expression: $z = \dfrac{2r + 3}{4} \div \dfrac{10r}{9}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{2r + 3}{4} \times \dfrac{9}{10r}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ (2r + 3) \times 9 } { 4 \times 10r}$ $z = \dfrac{18r + 27}{40r}$ |
343 | Simplify the following expression: $r = \dfrac{3}{7x - 9} \div \dfrac{4}{10x}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{3}{7x - 9} \times \dfrac{10x}{4}$ 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: $t = \dfrac{6q - 4}{8} \div \dfrac{4q}{8}$ | Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{6q - 4}{8} \times \dfrac{8}{4q}$ When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ (6q - 4) \times 8 } { 8 \times 4q}$ $t = \dfrac{48q - 32}{32q}$ Simplify: $t = \dfrac{3q - 2}{2q}$ |
343 | Simplify the following expression: $x = \dfrac{10}{8k - 5} \times \dfrac{7k}{3}$ | When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 10 \times 7k } { (8k - 5) \times 3}$ $x = \dfrac{70k}{24k - 15}$ |
343 | Simplify the following expression: $a = \dfrac{q}{3} \times \dfrac{7}{7q}$ | 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: $k = \dfrac{5x - 9}{9} \div \dfrac{6x}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $k = \dfrac{5x - 9}{9} \times \dfrac{2}{6x}$ When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ (5x - 9) \times 2 } { 9 \times 6x}$ $k = \dfrac{10x - 18}{54x}$ Simplify: $k = \dfrac{5x - 9}{27x}$ |
343 | Simplify the following expression: $p = \dfrac{5n + 10}{8} \div \dfrac{7n}{5}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{5n + 10}{8} \times \dfrac{5}{7n}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (5n + 10) \times 5 } { 8 \times 7n}$ $p = \dfrac{25n + 50}{56n}$ |
343 | Simplify the following expression: $z = \dfrac{4n}{8} \times \dfrac{2}{5n}$ | 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: $r = \dfrac{10}{2t - 10} \div \dfrac{4}{8t}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{10}{2t - 10} \times \dfrac{8t}{4}$ 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: $y = \dfrac{2k}{5} \div \dfrac{7k}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $y = \dfrac{2k}{5} \times \dfrac{4}{7k}$ 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: $t = \dfrac{2k + 2}{2} \div \dfrac{4k}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{2k + 2}{2} \times \dfrac{4}{4k}$ 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: $t = \dfrac{3a - 5}{2} \div \dfrac{2a}{10}$ | Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{3a - 5}{2} \times \dfrac{10}{2a}$ 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: $r = \dfrac{7q}{8} \times \dfrac{8}{2q}$ | 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: $k = \dfrac{8}{a + 5} \div \dfrac{6}{10a}$ | Dividing by an expression is the same as multiplying by its inverse. $k = \dfrac{8}{a + 5} \times \dfrac{10a}{6}$ When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 8 \times 10a } { (a + 5) \times 6}$ $k = \dfrac{80a}{6a + 30}$ Simplify: $k = \dfrac{40a}{3a + 15}$ |
343 | Simplify the following expression: $q = \dfrac{8}{p + 1} \times \dfrac{5p}{10}$ | When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 8 \times 5p } { (p + 1) \times 10}$ $q = \dfrac{40p}{10p + 10}$ Simplify: $q = \dfrac{4p}{p + 1}$ |
343 | Simplify the following expression: $p = \dfrac{8}{4t - 2} \div \dfrac{9}{7t}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{8}{4t - 2} \times \dfrac{7t}{9}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 8 \times 7t } { (4t - 2) \times 9}$ $p = \dfrac{56t}{36t - 18}$ Simplify: $p = \dfrac{28t}{18t - 9}$ |
343 | Simplify the following expression: $a = \dfrac{7}{z - 10} \times \dfrac{3z}{3}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 7 \times 3z } { (z - 10) \times 3}$ $a = \dfrac{21z}{3z - 30}$ Simplify: $a = \dfrac{7z}{z - 10}$ |
343 | Simplify the following expression: $z = \dfrac{6}{5k + 5} \div \dfrac{6}{3k}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{6}{5k + 5} \times \dfrac{3k}{6}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 6 \times 3k } { (5k + 5) \times 6}$ $z = \dfrac{18k}{30k + 30}$ Simplify: $z = \dfrac{3k}{5k + 5}$ |
343 | Simplify the following expression: $p = \dfrac{9}{2k + 5} \div \dfrac{10}{4k}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{9}{2k + 5} \times \dfrac{4k}{10}$ 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: $p = \dfrac{4n - 5}{6} \div \dfrac{2n}{8}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{4n - 5}{6} \times \dfrac{8}{2n}$ 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: $y = \dfrac{2n + 6}{9} \times \dfrac{10}{7n}$ | When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ (2n + 6) \times 10 } { 9 \times 7n}$ $y = \dfrac{20n + 60}{63n}$ |
343 | Simplify the following expression: $q = \dfrac{6}{2t} \div \dfrac{8}{9t}$ | Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{6}{2t} \times \dfrac{9t}{8}$ 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: $n = \dfrac{5}{q + 7} \div \dfrac{2}{3q}$ | Dividing by an expression is the same as multiplying by its inverse. $n = \dfrac{5}{q + 7} \times \dfrac{3q}{2}$ When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 5 \times 3q } { (q + 7) \times 2}$ $n = \dfrac{15q}{2q + 14}$ |
343 | Simplify the following expression: $y = \dfrac{3}{8r + 3} \times \dfrac{6r}{5}$ | When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 3 \times 6r } { (8r + 3) \times 5}$ $y = \dfrac{18r}{40r + 15}$ |
343 | Simplify the following expression: $q = \dfrac{8}{6y - 2} \times \dfrac{5y}{2}$ | When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 8 \times 5y } { (6y - 2) \times 2}$ $q = \dfrac{40y}{12y - 4}$ Simplify: $q = \dfrac{10y}{3y - 1}$ |
343 | Simplify the following expression: $q = \dfrac{t + 9}{2} \times \dfrac{2}{2t}$ | When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ (t + 9) \times 2 } { 2 \times 2t}$ $q = \dfrac{2t + 18}{4t}$ Simplify: $q = \dfrac{t + 9}{2t}$ |
343 | Simplify the following expression: $z = \dfrac{7a}{9} \div \dfrac{2a}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{7a}{9} \times \dfrac{4}{2a}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 7a \times 4 } { 9 \times 2a}$ $z = \dfrac{28a}{18a}$ Simplify: $z = \dfrac{14}{9}$ |
343 | Simplify the following expression: $x = \dfrac{10}{z + 6} \div \dfrac{8}{6z}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{10}{z + 6} \times \dfrac{6z}{8}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 10 \times 6z } { (z + 6) \times 8}$ $x = \dfrac{60z}{8z + 48}$ Simplify: $x = \dfrac{15z}{2z + 12}$ |
343 | Simplify the following expression: $p = \dfrac{3z + 1}{9} \div \dfrac{4z}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{3z + 1}{9} \times \dfrac{2}{4z}$ 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: $z = \dfrac{2r + 3}{4} \times \dfrac{9}{10r}$ | When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ (2r + 3) \times 9 } { 4 \times 10r}$ $z = \dfrac{18r + 27}{40r}$ |
343 | Simplify the following expression: $n = \dfrac{6}{8q} \div \dfrac{9}{2q}$ | Dividing by an expression is the same as multiplying by its inverse. $n = \dfrac{6}{8q} \times \dfrac{2q}{9}$ When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 6 \times 2q } { 8q \times 9}$ $n = \dfrac{12q}{72q}$ Simplify: $n = \dfrac{1}{6}$ |
343 | Simplify the following expression: $t = \dfrac{8}{8y + 1} \times \dfrac{5y}{8}$ | When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ 8 \times 5y } { (8y + 1) \times 8}$ $t = \dfrac{40y}{64y + 8}$ Simplify: $t = \dfrac{5y}{8y + 1}$ |
343 | Simplify the following expression: $p = \dfrac{3}{n + 1} \div \dfrac{10}{9n}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{3}{n + 1} \times \dfrac{9n}{10}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 3 \times 9n } { (n + 1) \times 10}$ $p = \dfrac{27n}{10n + 10}$ |
343 | Simplify the following expression: $y = \dfrac{3a + 9}{7} \div \dfrac{9a}{3}$ | Dividing by an expression is the same as multiplying by its inverse. $y = \dfrac{3a + 9}{7} \times \dfrac{3}{9a}$ When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ (3a + 9) \times 3 } { 7 \times 9a}$ $y = \dfrac{9a + 27}{63a}$ Simplify: $y = \dfrac{a + 3}{7a}$ |
343 | Simplify the following expression: $x = \dfrac{4}{5t - 1} \div \dfrac{4}{4t}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{4}{5t - 1} \times \dfrac{4t}{4}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 4 \times 4t } { (5t - 1) \times 4}$ $x = \dfrac{16t}{20t - 4}$ Simplify: $x = \dfrac{4t}{5t - 1}$ |
343 | Simplify the following expression: $t = \dfrac{q}{7} \div \dfrac{5q}{8}$ | Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{q}{7} \times \dfrac{8}{5q}$ When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ q \times 8 } { 7 \times 5q}$ $t = \dfrac{8q}{35q}$ Simplify: $t = \dfrac{8}{35}$ |
343 | Simplify the following expression: $q = \dfrac{9}{5x + 4} \div \dfrac{10}{8x}$ | Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{9}{5x + 4} \times \dfrac{8x}{10}$ 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: $x = \dfrac{6p - 9}{6} \times \dfrac{10}{5p}$ | When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ (6p - 9) \times 10 } { 6 \times 5p}$ $x = \dfrac{60p - 90}{30p}$ Simplify: $x = \dfrac{2p - 3}{p}$ |
343 | Simplify the following expression: $z = \dfrac{2t}{4} \times \dfrac{6}{10t}$ | When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 2t \times 6 } { 4 \times 10t}$ $z = \dfrac{12t}{40t}$ Simplify: $z = \dfrac{3}{10}$ |
343 | Simplify the following expression: $q = \dfrac{4k + 1}{6} \times \dfrac{4}{2k}$ | When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ (4k + 1) \times 4 } { 6 \times 2k}$ $q = \dfrac{16k + 4}{12k}$ Simplify: $q = \dfrac{4k + 1}{3k}$ |
343 | Simplify the following expression: $k = \dfrac{5}{2t - 5} \times \dfrac{4t}{2}$ | When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 5 \times 4t } { (2t - 5) \times 2}$ $k = \dfrac{20t}{4t - 10}$ Simplify: $k = \dfrac{10t}{2t - 5}$ |
343 | Simplify the following expression: $x = \dfrac{n + 1}{10} \times \dfrac{6}{10n}$ | When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ (n + 1) \times 6 } { 10 \times 10n}$ $x = \dfrac{6n + 6}{100n}$ Simplify: $x = \dfrac{3n + 3}{50n}$ |
343 | Simplify the following expression: $k = \dfrac{2}{7x + 4} \div \dfrac{4}{4x}$ | Dividing by an expression is the same as multiplying by its inverse. $k = \dfrac{2}{7x + 4} \times \dfrac{4x}{4}$ When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 2 \times 4x } { (7x + 4) \times 4}$ $k = \dfrac{8x}{28x + 16}$ Simplify: $k = \dfrac{2x}{7x + 4}$ |
343 | Simplify the following expression: $y = \dfrac{2}{2p - 9} \times \dfrac{8p}{6}$ | When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 2 \times 8p } { (2p - 9) \times 6}$ $y = \dfrac{16p}{12p - 54}$ Simplify: $y = \dfrac{8p}{6p - 27}$ |
343 | Simplify the following expression: $r = \dfrac{3y + 8}{2} \div \dfrac{4y}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{3y + 8}{2} \times \dfrac{2}{4y}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (3y + 8) \times 2 } { 2 \times 4y}$ $r = \dfrac{6y + 16}{8y}$ Simplify: $r = \dfrac{3y + 8}{4y}$ |
343 | Simplify the following expression: $x = \dfrac{3}{8q - 7} \times \dfrac{8q}{4}$ | When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 3 \times 8q } { (8q - 7) \times 4}$ $x = \dfrac{24q}{32q - 28}$ Simplify: $x = \dfrac{6q}{8q - 7}$ |
343 | Simplify the following expression: $p = \dfrac{7}{4k - 7} \times \dfrac{2k}{3}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 7 \times 2k } { (4k - 7) \times 3}$ $p = \dfrac{14k}{12k - 21}$ |
343 | Simplify the following expression: $z = \dfrac{4}{4n + 8} \div \dfrac{3}{4n}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{4}{4n + 8} \times \dfrac{4n}{3}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 4 \times 4n } { (4n + 8) \times 3}$ $z = \dfrac{16n}{12n + 24}$ Simplify: $z = \dfrac{4n}{3n + 6}$ |
343 | Simplify the following expression: $z = \dfrac{6}{6a - 10} \div \dfrac{8}{5a}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{6}{6a - 10} \times \dfrac{5a}{8}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 6 \times 5a } { (6a - 10) \times 8}$ $z = \dfrac{30a}{48a - 80}$ Simplify: $z = \dfrac{15a}{24a - 40}$ |
343 | Simplify the following expression: $q = \dfrac{9}{5t} \div \dfrac{5}{10t}$ | Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{9}{5t} \times \dfrac{10t}{5}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 9 \times 10t } { 5t \times 5}$ $q = \dfrac{90t}{25t}$ Simplify: $q = \dfrac{18}{5}$ |
343 | Simplify the following expression: $t = \dfrac{5r}{3} \div \dfrac{2r}{9}$ | Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{5r}{3} \times \dfrac{9}{2r}$ 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: $z = \dfrac{8a + 9}{5} \div \dfrac{2a}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{8a + 9}{5} \times \dfrac{4}{2a}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ (8a + 9) \times 4 } { 5 \times 2a}$ $z = \dfrac{32a + 36}{10a}$ Simplify: $z = \dfrac{16a + 18}{5a}$ |
343 | Simplify the following expression: $t = \dfrac{z + 7}{6} \div \dfrac{3z}{2}$ | Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{z + 7}{6} \times \dfrac{2}{3z}$ When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ (z + 7) \times 2 } { 6 \times 3z}$ $t = \dfrac{2z + 14}{18z}$ Simplify: $t = \dfrac{z + 7}{9z}$ |
343 | Simplify the following expression: $z = \dfrac{6x + 9}{8} \times \dfrac{10}{8x}$ | When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ (6x + 9) \times 10 } { 8 \times 8x}$ $z = \dfrac{60x + 90}{64x}$ Simplify: $z = \dfrac{30x + 45}{32x}$ |
343 | Simplify the following expression: $x = \dfrac{7q}{8} \div \dfrac{5q}{7}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{7q}{8} \times \dfrac{7}{5q}$ 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: $z = \dfrac{t - 9}{6} \times \dfrac{8}{8t}$ | When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ (t - 9) \times 8 } { 6 \times 8t}$ $z = \dfrac{8t - 72}{48t}$ Simplify: $z = \dfrac{t - 9}{6t}$ |
343 | Simplify the following expression: $t = \dfrac{3n}{2} \times \dfrac{2}{6n}$ | When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ 3n \times 2 } { 2 \times 6n}$ $t = \dfrac{6n}{12n}$ Simplify: $t = \dfrac{1}{2}$ |
343 | Simplify the following expression: $x = \dfrac{9}{4n} \div \dfrac{5}{9n}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{9}{4n} \times \dfrac{9n}{5}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 9 \times 9n } { 4n \times 5}$ $x = \dfrac{81n}{20n}$ Simplify: $x = \dfrac{81}{20}$ |
343 | Simplify the following expression: $t = \dfrac{5}{4x - 4} \div \dfrac{6}{2x}$ | Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{5}{4x - 4} \times \dfrac{2x}{6}$ When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ 5 \times 2x } { (4x - 4) \times 6}$ $t = \dfrac{10x}{24x - 24}$ Simplify: $t = \dfrac{5x}{12x - 12}$ |
343 | Simplify the following expression: $a = \dfrac{5}{4r} \times \dfrac{10r}{2}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 5 \times 10r } { 4r \times 2}$ $a = \dfrac{50r}{8r}$ Simplify: $a = \dfrac{25}{4}$ |
343 | Simplify the following expression: $p = \dfrac{4a - 10}{7} \div \dfrac{9a}{10}$ | Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{4a - 10}{7} \times \dfrac{10}{9a}$ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (4a - 10) \times 10 } { 7 \times 9a}$ $p = \dfrac{40a - 100}{63a}$ |
343 | Simplify the following expression: $r = \dfrac{10}{3x - 8} \div \dfrac{10}{2x}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{10}{3x - 8} \times \dfrac{2x}{10}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 10 \times 2x } { (3x - 8) \times 10}$ $r = \dfrac{20x}{30x - 80}$ Simplify: $r = \dfrac{2x}{3x - 8}$ |
343 | Simplify the following expression: $a = \dfrac{z - 9}{8} \div \dfrac{5z}{7}$ | Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{z - 9}{8} \times \dfrac{7}{5z}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ (z - 9) \times 7 } { 8 \times 5z}$ $a = \dfrac{7z - 63}{40z}$ |
343 | Simplify the following expression: $z = \dfrac{r}{10} \times \dfrac{7}{8r}$ | When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ r \times 7 } { 10 \times 8r}$ $z = \dfrac{7r}{80r}$ Simplify: $z = \dfrac{7}{80}$ |
343 | Simplify the following expression: $p = \dfrac{4a - 10}{7} \times \dfrac{10}{9a}$ | When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ (4a - 10) \times 10 } { 7 \times 9a}$ $p = \dfrac{40a - 100}{63a}$ |
343 | Simplify the following expression: $x = \dfrac{3}{6z + 5} \div \dfrac{4}{4z}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{3}{6z + 5} \times \dfrac{4z}{4}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 3 \times 4z } { (6z + 5) \times 4}$ $x = \dfrac{12z}{24z + 20}$ Simplify: $x = \dfrac{3z}{6z + 5}$ |
343 | Simplify the following expression: $a = \dfrac{2n + 3}{6} \times \dfrac{6}{2n}$ | When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ (2n + 3) \times 6 } { 6 \times 2n}$ $a = \dfrac{12n + 18}{12n}$ Simplify: $a = \dfrac{2n + 3}{2n}$ |
343 | Simplify the following expression: $r = \dfrac{6k - 3}{2} \times \dfrac{3}{5k}$ | When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (6k - 3) \times 3 } { 2 \times 5k}$ $r = \dfrac{18k - 9}{10k}$ |
343 | Simplify the following expression: $n = \dfrac{5}{r} \times \dfrac{4r}{5}$ | 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: $r = \dfrac{10}{6q + 8} \div \dfrac{8}{4q}$ | Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{10}{6q + 8} \times \dfrac{4q}{8}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 10 \times 4q } { (6q + 8) \times 8}$ $r = \dfrac{40q}{48q + 64}$ Simplify: $r = \dfrac{5q}{6q + 8}$ |
343 | Simplify the following expression: $n = \dfrac{9}{4t} \div \dfrac{2}{9t}$ | Dividing by an expression is the same as multiplying by its inverse. $n = \dfrac{9}{4t} \times \dfrac{9t}{2}$ When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 9 \times 9t } { 4t \times 2}$ $n = \dfrac{81t}{8t}$ Simplify: $n = \dfrac{81}{8}$ |
343 | Simplify the following expression: $x = \dfrac{6p - 9}{6} \div \dfrac{5p}{10}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{6p - 9}{6} \times \dfrac{10}{5p}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ (6p - 9) \times 10 } { 6 \times 5p}$ $x = \dfrac{60p - 90}{30p}$ Simplify: $x = \dfrac{2p - 3}{p}$ |
343 | Simplify the following expression: $q = \dfrac{4y + 3}{5} \times \dfrac{5}{3y}$ | 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: $n = \dfrac{4r + 7}{8} \times \dfrac{9}{6r}$ | When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ (4r + 7) \times 9 } { 8 \times 6r}$ $n = \dfrac{36r + 63}{48r}$ Simplify: $n = \dfrac{12r + 21}{16r}$ |
343 | Simplify the following expression: $q = \dfrac{4k + 1}{6} \div \dfrac{2k}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{4k + 1}{6} \times \dfrac{4}{2k}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ (4k + 1) \times 4 } { 6 \times 2k}$ $q = \dfrac{16k + 4}{12k}$ Simplify: $q = \dfrac{4k + 1}{3k}$ |
343 | Simplify the following expression: $z = \dfrac{5}{y} \div \dfrac{2}{8y}$ | Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{5}{y} \times \dfrac{8y}{2}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 5 \times 8y } { y \times 2}$ $z = \dfrac{40y}{2y}$ Simplify: $z = \dfrac{20}{1}$ |
343 | Simplify the following expression: $y = \dfrac{2p - 10}{9} \times \dfrac{2}{3p}$ | When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ (2p - 10) \times 2 } { 9 \times 3p}$ $y = \dfrac{4p - 20}{27p}$ |
343 | Simplify the following expression: $k = \dfrac{4x - 7}{3} \div \dfrac{2x}{4}$ | Dividing by an expression is the same as multiplying by its inverse. $k = \dfrac{4x - 7}{3} \times \dfrac{4}{2x}$ 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: $z = \dfrac{7a}{9} \times \dfrac{4}{2a}$ | When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 7a \times 4 } { 9 \times 2a}$ $z = \dfrac{28a}{18a}$ Simplify: $z = \dfrac{14}{9}$ |
343 | Simplify the following expression: $y = \dfrac{3}{8r + 3} \div \dfrac{5}{6r}$ | Dividing by an expression is the same as multiplying by its inverse. $y = \dfrac{3}{8r + 3} \times \dfrac{6r}{5}$ When multiplying fractions, we multiply the numerators and the denominators. $y = \dfrac{ 3 \times 6r } { (8r + 3) \times 5}$ $y = \dfrac{18r}{40r + 15}$ |
343 | Simplify the following expression: $k = \dfrac{2}{4n - 4} \times \dfrac{2n}{7}$ | When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 2 \times 2n } { (4n - 4) \times 7}$ $k = \dfrac{4n}{28n - 28}$ Simplify: $k = \dfrac{n}{7n - 7}$ |
343 | Simplify the following expression: $z = \dfrac{6}{6a - 10} \times \dfrac{5a}{8}$ | When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 6 \times 5a } { (6a - 10) \times 8}$ $z = \dfrac{30a}{48a - 80}$ Simplify: $z = \dfrac{15a}{24a - 40}$ |
343 | Simplify the following expression: $x = \dfrac{10}{5q + 6} \div \dfrac{3}{5q}$ | Dividing by an expression is the same as multiplying by its inverse. $x = \dfrac{10}{5q + 6} \times \dfrac{5q}{3}$ When multiplying fractions, we multiply the numerators and the denominators. $x = \dfrac{ 10 \times 5q } { (5q + 6) \times 3}$ $x = \dfrac{50q}{15q + 18}$ |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.