Ordering Fractions Worksheet - Arrange Unlike Fractions in Increasing Order
A worksheet titled "Ordering Fractions" with ten problems asking students to order sets of unlike fractions in increasing order. The worksheet includes spaces for answers and is from 15Worksheets.com.
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Step-by-step solution for: Ordering Fractions Worksheets - 15 Worksheets Library
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Show Answer Key & Explanations
Step-by-step solution for: Ordering Fractions Worksheets - 15 Worksheets Library
To order fractions from least to greatest (increasing order), we need to compare their values. Since these are "unlike" fractions (they have different denominators), the best way to compare them is to find a Common Denominator. This allows us to rewrite each fraction so they all have the same bottom number, making it easy to see which top number (numerator) is smallest or largest.
Here is the step-by-step solution for each problem:
1) $\frac{3}{4}, \frac{2}{6}, \frac{1}{12}, \frac{5}{18}, \frac{4}{9}$
* Find the Least Common Denominator (LCD) for 4, 6, 12, 18, 9. The LCD is 36.
* Convert fractions:
* $\frac{3}{4} = \frac{27}{36}$
* $\frac{2}{6} = \frac{12}{36}$
* $\frac{1}{12} = \frac{3}{36}$
* $\frac{5}{18} = \frac{10}{36}$
* $\frac{4}{9} = \frac{16}{36}$
* Order numerators: $3, 10, 12, 16, 27$
* Answer: $\frac{1}{12}, \frac{5}{18}, \frac{2}{6}, \frac{4}{9}, \frac{3}{4}$
2) $\frac{4}{8}, \frac{7}{16}, \frac{5}{12}, \frac{1}{8}, \frac{3}{12}$
* Simplify first where possible: $\frac{4}{8}=\frac{1}{2}$, $\frac{3}{12}=\frac{1}{4}$.
* New set: $\frac{1}{2}, \frac{7}{16}, \frac{5}{12}, \frac{1}{8}, \frac{1}{4}$.
* LCD for 2, 16, 12, 8, 4 is 48.
* Convert fractions:
* $\frac{1}{2} = \frac{24}{48}$
* $\frac{7}{16} = \frac{21}{48}$
* $\frac{5}{12} = \frac{20}{48}$
* $\frac{1}{8} = \frac{6}{48}$
* $\frac{1}{4} = \frac{12}{48}$
* Order numerators: $6, 12, 20, 21, 24$
* Answer: $\frac{1}{8}, \frac{3}{12}, \frac{5}{12}, \frac{7}{16}, \frac{4}{8}$
3) $\frac{3}{8}, \frac{1}{4}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
* Simplify: $\frac{4}{10}=\frac{2}{5}$, $\frac{3}{6}=\frac{1}{2}$.
* Set: $\frac{3}{8}, \frac{1}{4}, \frac{2}{5}, \frac{1}{2}, \frac{5}{8}$.
* LCD for 8, 4, 5, 2 is 40.
* Convert fractions:
* $\frac{3}{8} = \frac{15}{40}$
* $\frac{1}{4} = \frac{10}{40}$
* $\frac{2}{5} = \frac{16}{40}$
* $\frac{1}{2} = \frac{20}{40}$
* $\frac{5}{8} = \frac{25}{40}$
* Order numerators: $10, 15, 16, 20, 25$
* Answer: $\frac{1}{4}, \frac{3}{8}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
4) $\frac{2}{5}, \frac{9}{15}, \frac{8}{10}, \frac{7}{20}, \frac{1}{5}$
* Simplify: $\frac{9}{15}=\frac{3}{5}$, $\frac{8}{10}=\frac{4}{5}$.
* Set: $\frac{2}{5}, \frac{3}{5}, \frac{4}{5}, \frac{7}{20}, \frac{1}{5}$.
* Notice most have denominator 5. Let's use LCD 20.
* Convert fractions:
* $\frac{2}{5} = \frac{8}{20}$
* $\frac{3}{5} = \frac{12}{20}$
* $\frac{4}{5} = \frac{16}{20}$
* $\frac{7}{20} = \frac{7}{20}$
* $\frac{1}{5} = \frac{4}{20}$
* Order numerators: $4, 7, 8, 12, 16$
* Answer: $\frac{1}{5}, \frac{7}{20}, \frac{2}{5}, \frac{9}{15}, \frac{8}{10}$
5) $\frac{4}{9}, \frac{9}{12}, \frac{5}{6}, \frac{3}{18}, \frac{1}{3}$
* Simplify: $\frac{9}{12}=\frac{3}{4}$, $\frac{3}{18}=\frac{1}{6}$.
* Set: $\frac{4}{9}, \frac{3}{4}, \frac{5}{6}, \frac{1}{6}, \frac{1}{3}$.
* LCD for 9, 4, 6, 3 is 36.
* Convert fractions:
* $\frac{4}{9} = \frac{16}{36}$
* $\frac{3}{4} = \frac{27}{36}$
* $\frac{5}{6} = \frac{30}{36}$
* $\frac{1}{6} = \frac{6}{36}$
* $\frac{1}{3} = \frac{12}{36}$
* Order numerators: $6, 12, 16, 27, 30$
* Answer: $\frac{3}{18}, \frac{1}{3}, \frac{4}{9}, \frac{9}{12}, \frac{5}{6}$
6) $\frac{5}{8}, \frac{7}{16}, \frac{3}{4}, \frac{1}{4}, \frac{12}{24}$
* Simplify: $\frac{12}{24}=\frac{1}{2}$.
* Set: $\frac{5}{8}, \frac{7}{16}, \frac{3}{4}, \frac{1}{4}, \frac{1}{2}$.
* LCD for 8, 16, 4, 2 is 16.
* Convert fractions:
* $\frac{5}{8} = \frac{10}{16}$
* $\frac{7}{16} = \frac{7}{16}$
* $\frac{3}{4} = \frac{12}{16}$
* $\frac{1}{4} = \frac{4}{16}$
* $\frac{1}{2} = \frac{8}{16}$
* Order numerators: $4, 7, 8, 10, 12$
* Answer: $\frac{1}{4}, \frac{7}{16}, \frac{12}{24}, \frac{5}{8}, \frac{3}{4}$
7) $\frac{7}{10}, \frac{2}{5}, \frac{9}{20}, \frac{5}{15}, \frac{10}{20}$
* Simplify: $\frac{5}{15}=\frac{1}{3}$, $\frac{10}{20}=\frac{1}{2}$.
* Set: $\frac{7}{10}, \frac{2}{5}, \frac{9}{20}, \frac{1}{3}, \frac{1}{2}$.
* LCD for 10, 5, 20, 3, 2 is 60.
* Convert fractions:
* $\frac{7}{10} = \frac{42}{60}$
* $\frac{2}{5} = \frac{24}{60}$
* $\frac{9}{20} = \frac{27}{60}$
* $\frac{1}{3} = \frac{20}{60}$
* $\frac{1}{2} = \frac{30}{60}$
* Order numerators: $20, 24, 27, 30, 42$
* Answer: $\frac{5}{15}, \frac{2}{5}, \frac{9}{20}, \frac{10}{20}, \frac{7}{10}$
8) $\frac{9}{15}, \frac{5}{12}, \frac{7}{18}, \frac{4}{9}, \frac{1}{6}$
* Simplify: $\frac{9}{15}=\frac{3}{5}$.
* Set: $\frac{3}{5}, \frac{5}{12}, \frac{7}{18}, \frac{4}{9}, \frac{1}{6}$.
* LCD for 5, 12, 18, 9, 6 is 180.
* Convert fractions:
* $\frac{3}{5} = \frac{108}{180}$
* $\frac{5}{12} = \frac{75}{180}$
* $\frac{7}{18} = \frac{70}{180}$
* $\frac{4}{9} = \frac{80}{180}$
* $\frac{1}{6} = \frac{30}{180}$
* Order numerators: $30, 70, 75, 80, 108$
* Answer: $\frac{1}{6}, \frac{7}{18}, \frac{5}{12}, \frac{4}{9}, \frac{9}{15}$
9) $\frac{4}{9}, \frac{2}{6}, \frac{15}{21}, \frac{7}{12}, \frac{9}{18}$
* Simplify: $\frac{2}{6}=\frac{1}{3}$, $\frac{15}{21}=\frac{5}{7}$, $\frac{9}{18}=\frac{1}{2}$.
* Set: $\frac{4}{9}, \frac{1}{3}, \frac{5}{7}, \frac{7}{12}, \frac{1}{2}$.
* LCD for 9, 3, 7, 12, 2 is 252.
* Convert fractions:
* $\frac{4}{9} = \frac{112}{252}$
* $\frac{1}{3} = \frac{84}{252}$
* $\frac{5}{7} = \frac{180}{252}$
* $\frac{7}{12} = \frac{147}{252}$
* $\frac{1}{2} = \frac{126}{252}$
* Order numerators: $84, 112, 126, 147, 180$
* Answer: $\frac{2}{6}, \frac{4}{9}, \frac{9}{18}, \frac{7}{12}, \frac{15}{21}$
10) $\frac{1}{25}, \frac{7}{15}, \frac{9}{25}, \frac{3}{10}, \frac{2}{5}$
* LCD for 25, 15, 10, 5 is 150.
* Convert fractions:
* $\frac{1}{25} = \frac{6}{150}$
* $\frac{7}{15} = \frac{70}{150}$
* $\frac{9}{25} = \frac{54}{150}$
* $\frac{3}{10} = \frac{45}{150}$
* $\frac{2}{5} = \frac{60}{150}$
* Order numerators: $6, 45, 54, 60, 70$
* Answer: $\frac{1}{25}, \frac{3}{10}, \frac{9}{25}, \frac{2}{5}, \frac{7}{15}$
Final Answer:
1) $\frac{1}{12}, \frac{5}{18}, \frac{2}{6}, \frac{4}{9}, \frac{3}{4}$
2) $\frac{1}{8}, \frac{3}{12}, \frac{5}{12}, \frac{7}{16}, \frac{4}{8}$
3) $\frac{1}{4}, \frac{3}{8}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
4) $\frac{1}{5}, \frac{7}{20}, \frac{2}{5}, \frac{9}{15}, \frac{8}{10}$
5) $\frac{3}{18}, \frac{1}{3}, \frac{4}{9}, \frac{9}{12}, \frac{5}{6}$
6) $\frac{1}{4}, \frac{7}{16}, \frac{12}{24}, \frac{5}{8}, \frac{3}{4}$
7) $\frac{5}{15}, \frac{2}{5}, \frac{9}{20}, \frac{10}{20}, \frac{7}{10}$
8) $\frac{1}{6}, \frac{7}{18}, \frac{5}{12}, \frac{4}{9}, \frac{9}{15}$
9) $\frac{2}{6}, \frac{4}{9}, \frac{9}{18}, \frac{7}{12}, \frac{15}{21}$
10) $\frac{1}{25}, \frac{3}{10}, \frac{9}{25}, \frac{2}{5}, \frac{7}{15}$
Here is the step-by-step solution for each problem:
1) $\frac{3}{4}, \frac{2}{6}, \frac{1}{12}, \frac{5}{18}, \frac{4}{9}$
* Find the Least Common Denominator (LCD) for 4, 6, 12, 18, 9. The LCD is 36.
* Convert fractions:
* $\frac{3}{4} = \frac{27}{36}$
* $\frac{2}{6} = \frac{12}{36}$
* $\frac{1}{12} = \frac{3}{36}$
* $\frac{5}{18} = \frac{10}{36}$
* $\frac{4}{9} = \frac{16}{36}$
* Order numerators: $3, 10, 12, 16, 27$
* Answer: $\frac{1}{12}, \frac{5}{18}, \frac{2}{6}, \frac{4}{9}, \frac{3}{4}$
2) $\frac{4}{8}, \frac{7}{16}, \frac{5}{12}, \frac{1}{8}, \frac{3}{12}$
* Simplify first where possible: $\frac{4}{8}=\frac{1}{2}$, $\frac{3}{12}=\frac{1}{4}$.
* New set: $\frac{1}{2}, \frac{7}{16}, \frac{5}{12}, \frac{1}{8}, \frac{1}{4}$.
* LCD for 2, 16, 12, 8, 4 is 48.
* Convert fractions:
* $\frac{1}{2} = \frac{24}{48}$
* $\frac{7}{16} = \frac{21}{48}$
* $\frac{5}{12} = \frac{20}{48}$
* $\frac{1}{8} = \frac{6}{48}$
* $\frac{1}{4} = \frac{12}{48}$
* Order numerators: $6, 12, 20, 21, 24$
* Answer: $\frac{1}{8}, \frac{3}{12}, \frac{5}{12}, \frac{7}{16}, \frac{4}{8}$
3) $\frac{3}{8}, \frac{1}{4}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
* Simplify: $\frac{4}{10}=\frac{2}{5}$, $\frac{3}{6}=\frac{1}{2}$.
* Set: $\frac{3}{8}, \frac{1}{4}, \frac{2}{5}, \frac{1}{2}, \frac{5}{8}$.
* LCD for 8, 4, 5, 2 is 40.
* Convert fractions:
* $\frac{3}{8} = \frac{15}{40}$
* $\frac{1}{4} = \frac{10}{40}$
* $\frac{2}{5} = \frac{16}{40}$
* $\frac{1}{2} = \frac{20}{40}$
* $\frac{5}{8} = \frac{25}{40}$
* Order numerators: $10, 15, 16, 20, 25$
* Answer: $\frac{1}{4}, \frac{3}{8}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
4) $\frac{2}{5}, \frac{9}{15}, \frac{8}{10}, \frac{7}{20}, \frac{1}{5}$
* Simplify: $\frac{9}{15}=\frac{3}{5}$, $\frac{8}{10}=\frac{4}{5}$.
* Set: $\frac{2}{5}, \frac{3}{5}, \frac{4}{5}, \frac{7}{20}, \frac{1}{5}$.
* Notice most have denominator 5. Let's use LCD 20.
* Convert fractions:
* $\frac{2}{5} = \frac{8}{20}$
* $\frac{3}{5} = \frac{12}{20}$
* $\frac{4}{5} = \frac{16}{20}$
* $\frac{7}{20} = \frac{7}{20}$
* $\frac{1}{5} = \frac{4}{20}$
* Order numerators: $4, 7, 8, 12, 16$
* Answer: $\frac{1}{5}, \frac{7}{20}, \frac{2}{5}, \frac{9}{15}, \frac{8}{10}$
5) $\frac{4}{9}, \frac{9}{12}, \frac{5}{6}, \frac{3}{18}, \frac{1}{3}$
* Simplify: $\frac{9}{12}=\frac{3}{4}$, $\frac{3}{18}=\frac{1}{6}$.
* Set: $\frac{4}{9}, \frac{3}{4}, \frac{5}{6}, \frac{1}{6}, \frac{1}{3}$.
* LCD for 9, 4, 6, 3 is 36.
* Convert fractions:
* $\frac{4}{9} = \frac{16}{36}$
* $\frac{3}{4} = \frac{27}{36}$
* $\frac{5}{6} = \frac{30}{36}$
* $\frac{1}{6} = \frac{6}{36}$
* $\frac{1}{3} = \frac{12}{36}$
* Order numerators: $6, 12, 16, 27, 30$
* Answer: $\frac{3}{18}, \frac{1}{3}, \frac{4}{9}, \frac{9}{12}, \frac{5}{6}$
6) $\frac{5}{8}, \frac{7}{16}, \frac{3}{4}, \frac{1}{4}, \frac{12}{24}$
* Simplify: $\frac{12}{24}=\frac{1}{2}$.
* Set: $\frac{5}{8}, \frac{7}{16}, \frac{3}{4}, \frac{1}{4}, \frac{1}{2}$.
* LCD for 8, 16, 4, 2 is 16.
* Convert fractions:
* $\frac{5}{8} = \frac{10}{16}$
* $\frac{7}{16} = \frac{7}{16}$
* $\frac{3}{4} = \frac{12}{16}$
* $\frac{1}{4} = \frac{4}{16}$
* $\frac{1}{2} = \frac{8}{16}$
* Order numerators: $4, 7, 8, 10, 12$
* Answer: $\frac{1}{4}, \frac{7}{16}, \frac{12}{24}, \frac{5}{8}, \frac{3}{4}$
7) $\frac{7}{10}, \frac{2}{5}, \frac{9}{20}, \frac{5}{15}, \frac{10}{20}$
* Simplify: $\frac{5}{15}=\frac{1}{3}$, $\frac{10}{20}=\frac{1}{2}$.
* Set: $\frac{7}{10}, \frac{2}{5}, \frac{9}{20}, \frac{1}{3}, \frac{1}{2}$.
* LCD for 10, 5, 20, 3, 2 is 60.
* Convert fractions:
* $\frac{7}{10} = \frac{42}{60}$
* $\frac{2}{5} = \frac{24}{60}$
* $\frac{9}{20} = \frac{27}{60}$
* $\frac{1}{3} = \frac{20}{60}$
* $\frac{1}{2} = \frac{30}{60}$
* Order numerators: $20, 24, 27, 30, 42$
* Answer: $\frac{5}{15}, \frac{2}{5}, \frac{9}{20}, \frac{10}{20}, \frac{7}{10}$
8) $\frac{9}{15}, \frac{5}{12}, \frac{7}{18}, \frac{4}{9}, \frac{1}{6}$
* Simplify: $\frac{9}{15}=\frac{3}{5}$.
* Set: $\frac{3}{5}, \frac{5}{12}, \frac{7}{18}, \frac{4}{9}, \frac{1}{6}$.
* LCD for 5, 12, 18, 9, 6 is 180.
* Convert fractions:
* $\frac{3}{5} = \frac{108}{180}$
* $\frac{5}{12} = \frac{75}{180}$
* $\frac{7}{18} = \frac{70}{180}$
* $\frac{4}{9} = \frac{80}{180}$
* $\frac{1}{6} = \frac{30}{180}$
* Order numerators: $30, 70, 75, 80, 108$
* Answer: $\frac{1}{6}, \frac{7}{18}, \frac{5}{12}, \frac{4}{9}, \frac{9}{15}$
9) $\frac{4}{9}, \frac{2}{6}, \frac{15}{21}, \frac{7}{12}, \frac{9}{18}$
* Simplify: $\frac{2}{6}=\frac{1}{3}$, $\frac{15}{21}=\frac{5}{7}$, $\frac{9}{18}=\frac{1}{2}$.
* Set: $\frac{4}{9}, \frac{1}{3}, \frac{5}{7}, \frac{7}{12}, \frac{1}{2}$.
* LCD for 9, 3, 7, 12, 2 is 252.
* Convert fractions:
* $\frac{4}{9} = \frac{112}{252}$
* $\frac{1}{3} = \frac{84}{252}$
* $\frac{5}{7} = \frac{180}{252}$
* $\frac{7}{12} = \frac{147}{252}$
* $\frac{1}{2} = \frac{126}{252}$
* Order numerators: $84, 112, 126, 147, 180$
* Answer: $\frac{2}{6}, \frac{4}{9}, \frac{9}{18}, \frac{7}{12}, \frac{15}{21}$
10) $\frac{1}{25}, \frac{7}{15}, \frac{9}{25}, \frac{3}{10}, \frac{2}{5}$
* LCD for 25, 15, 10, 5 is 150.
* Convert fractions:
* $\frac{1}{25} = \frac{6}{150}$
* $\frac{7}{15} = \frac{70}{150}$
* $\frac{9}{25} = \frac{54}{150}$
* $\frac{3}{10} = \frac{45}{150}$
* $\frac{2}{5} = \frac{60}{150}$
* Order numerators: $6, 45, 54, 60, 70$
* Answer: $\frac{1}{25}, \frac{3}{10}, \frac{9}{25}, \frac{2}{5}, \frac{7}{15}$
Final Answer:
1) $\frac{1}{12}, \frac{5}{18}, \frac{2}{6}, \frac{4}{9}, \frac{3}{4}$
2) $\frac{1}{8}, \frac{3}{12}, \frac{5}{12}, \frac{7}{16}, \frac{4}{8}$
3) $\frac{1}{4}, \frac{3}{8}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
4) $\frac{1}{5}, \frac{7}{20}, \frac{2}{5}, \frac{9}{15}, \frac{8}{10}$
5) $\frac{3}{18}, \frac{1}{3}, \frac{4}{9}, \frac{9}{12}, \frac{5}{6}$
6) $\frac{1}{4}, \frac{7}{16}, \frac{12}{24}, \frac{5}{8}, \frac{3}{4}$
7) $\frac{5}{15}, \frac{2}{5}, \frac{9}{20}, \frac{10}{20}, \frac{7}{10}$
8) $\frac{1}{6}, \frac{7}{18}, \frac{5}{12}, \frac{4}{9}, \frac{9}{15}$
9) $\frac{2}{6}, \frac{4}{9}, \frac{9}{18}, \frac{7}{12}, \frac{15}{21}$
10) $\frac{1}{25}, \frac{3}{10}, \frac{9}{25}, \frac{2}{5}, \frac{7}{15}$
Parent Tip: Review the logic above to help your child master the concept of ordering fractions worksheet.
