Students can practice their fraction skills by arranging sets of unlike fractions from smallest to largest on this printable math sheet.
Ordering fractions worksheet with 10 problems requiring students to arrange unlike fractions from least to greatest.
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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 them. Since these are "unlike" fractions (they have different bottom numbers, or denominators), the easiest way to compare them is to find a Common Denominator. This means we change all the fractions so they have the same bottom number. Once the bottom numbers are the same, we just look at the top numbers (numerators) to see which is smallest and which is 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 by numerators: $3, 10, 12, 16, 27$.
* Result: $\frac{1}{12}, \frac{5}{18}, \frac{2}{6}, \frac{4}{9}, \frac{3}{4}$
2) $\frac{4}{8}, \frac{7}{16}, \frac{5}{12}, \frac{1}{8}, \frac{3}{12}$
* Simplify first where possible: $\frac{4}{8}=\frac{1}{2}$, $\frac{3}{12}=\frac{1}{4}$. Let's stick to LCD to be safe.
* LCD for 8, 16, 12 is 48.
* Convert fractions:
* $\frac{4}{8} = \frac{24}{48}$
* $\frac{7}{16} = \frac{21}{48}$
* $\frac{5}{12} = \frac{20}{48}$
* $\frac{1}{8} = \frac{6}{48}$
* $\frac{3}{12} = \frac{12}{48}$
* Order by numerators: $6, 12, 20, 21, 24$.
* Result: $\frac{1}{8}, \frac{3}{12}, \frac{5}{12}, \frac{7}{16}, \frac{4}{8}$
3) $\frac{3}{8}, \frac{1}{4}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
* LCD for 8, 4, 10, 6 is 120.
* Convert fractions:
* $\frac{3}{8} = \frac{45}{120}$
* $\frac{1}{4} = \frac{30}{120}$
* $\frac{4}{10} = \frac{48}{120}$
* $\frac{3}{6} = \frac{60}{120}$
* $\frac{5}{8} = \frac{75}{120}$
* Order by numerators: $30, 45, 48, 60, 75$.
* Result: $\frac{1}{4}, \frac{3}{8}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
4) $\frac{2}{5}, \frac{9}{15}, \frac{8}{10}, \frac{7}{20}, \frac{1}{5}$
* LCD for 5, 15, 10, 20 is 60.
* Convert fractions:
* $\frac{2}{5} = \frac{24}{60}$
* $\frac{9}{15} = \frac{36}{60}$
* $\frac{8}{10} = \frac{48}{60}$
* $\frac{7}{20} = \frac{21}{60}$
* $\frac{1}{5} = \frac{12}{60}$
* Order by numerators: $12, 21, 24, 36, 48$.
* Result: $\frac{1}{5}, \frac{7}{20}, \frac{2}{5}, \frac{9}{15}, \frac{8}{10}$
5) $\frac{4}{9}, \frac{9}{12}, \frac{5}{6}, \frac{3}{18}, \frac{1}{3}$
* LCD for 9, 12, 6, 18, 3 is 36.
* Convert fractions:
* $\frac{4}{9} = \frac{16}{36}$
* $\frac{9}{12} = \frac{27}{36}$
* $\frac{5}{6} = \frac{30}{36}$
* $\frac{3}{18} = \frac{6}{36}$
* $\frac{1}{3} = \frac{12}{36}$
* Order by numerators: $6, 12, 16, 27, 30$.
* Result: $\frac{3}{18}, \frac{1}{3}, \frac{4}{9}, \frac{9}{12}, \frac{5}{6}$
6) $\frac{5}{8}, \frac{7}{16}, \frac{3}{4}, \frac{1}{4}, \frac{12}{24}$
* LCD for 8, 16, 4, 24 is 48.
* Convert fractions:
* $\frac{5}{8} = \frac{30}{48}$
* $\frac{7}{16} = \frac{21}{48}$
* $\frac{3}{4} = \frac{36}{48}$
* $\frac{1}{4} = \frac{12}{48}$
* $\frac{12}{24} = \frac{24}{48}$
* Order by numerators: $12, 21, 24, 30, 36$.
* Result: $\frac{1}{4}, \frac{7}{16}, \frac{12}{24}, \frac{5}{8}, \frac{3}{4}$
7) $\frac{7}{10}, \frac{2}{5}, \frac{9}{20}, \frac{5}{15}, \frac{10}{20}$
* LCD for 10, 5, 20, 15 is 60.
* Convert fractions:
* $\frac{7}{10} = \frac{42}{60}$
* $\frac{2}{5} = \frac{24}{60}$
* $\frac{9}{20} = \frac{27}{60}$
* $\frac{5}{15} = \frac{20}{60}$
* $\frac{10}{20} = \frac{30}{60}$
* Order by numerators: $20, 24, 27, 30, 42$.
* Result: $\frac{5}{15}, \frac{2}{5}, \frac{9}{20}, \frac{10}{20}, \frac{7}{10}$
8) $\frac{9}{15}, \frac{5}{12}, \frac{7}{18}, \frac{4}{9}, \frac{1}{6}$
* LCD for 15, 12, 18, 9, 6 is 180.
* Convert fractions:
* $\frac{9}{15} = \frac{108}{180}$
* $\frac{5}{12} = \frac{75}{180}$
* $\frac{7}{18} = \frac{70}{180}$
* $\frac{4}{9} = \frac{80}{180}$
* $\frac{1}{6} = \frac{30}{180}$
* Order by numerators: $30, 70, 75, 80, 108$.
* Result: $\frac{1}{6}, \frac{7}{18}, \frac{5}{12}, \frac{4}{9}, \frac{9}{15}$
9) $\frac{4}{9}, \frac{2}{6}, \frac{15}{21}, \frac{7}{12}, \frac{9}{18}$
* LCD for 9, 6, 21, 12, 18 is 252.
* Convert fractions:
* $\frac{4}{9} = \frac{112}{252}$
* $\frac{2}{6} = \frac{84}{252}$
* $\frac{15}{21} = \frac{180}{252}$
* $\frac{7}{12} = \frac{147}{252}$
* $\frac{9}{18} = \frac{126}{252}$
* Order by numerators: $84, 112, 126, 147, 180$.
* Result: $\frac{2}{6}, \frac{4}{9}, \frac{9}{18}, \frac{7}{12}, \frac{15}{21}$
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 by numerators: $6, 45, 54, 60, 70$.
* Result: $\frac{1}{25}, \frac{3}{10}, \frac{9}{25}, \frac{2}{5}, \frac{7}{15}$
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 by numerators: $3, 10, 12, 16, 27$.
* Result: $\frac{1}{12}, \frac{5}{18}, \frac{2}{6}, \frac{4}{9}, \frac{3}{4}$
2) $\frac{4}{8}, \frac{7}{16}, \frac{5}{12}, \frac{1}{8}, \frac{3}{12}$
* Simplify first where possible: $\frac{4}{8}=\frac{1}{2}$, $\frac{3}{12}=\frac{1}{4}$. Let's stick to LCD to be safe.
* LCD for 8, 16, 12 is 48.
* Convert fractions:
* $\frac{4}{8} = \frac{24}{48}$
* $\frac{7}{16} = \frac{21}{48}$
* $\frac{5}{12} = \frac{20}{48}$
* $\frac{1}{8} = \frac{6}{48}$
* $\frac{3}{12} = \frac{12}{48}$
* Order by numerators: $6, 12, 20, 21, 24$.
* Result: $\frac{1}{8}, \frac{3}{12}, \frac{5}{12}, \frac{7}{16}, \frac{4}{8}$
3) $\frac{3}{8}, \frac{1}{4}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
* LCD for 8, 4, 10, 6 is 120.
* Convert fractions:
* $\frac{3}{8} = \frac{45}{120}$
* $\frac{1}{4} = \frac{30}{120}$
* $\frac{4}{10} = \frac{48}{120}$
* $\frac{3}{6} = \frac{60}{120}$
* $\frac{5}{8} = \frac{75}{120}$
* Order by numerators: $30, 45, 48, 60, 75$.
* Result: $\frac{1}{4}, \frac{3}{8}, \frac{4}{10}, \frac{3}{6}, \frac{5}{8}$
4) $\frac{2}{5}, \frac{9}{15}, \frac{8}{10}, \frac{7}{20}, \frac{1}{5}$
* LCD for 5, 15, 10, 20 is 60.
* Convert fractions:
* $\frac{2}{5} = \frac{24}{60}$
* $\frac{9}{15} = \frac{36}{60}$
* $\frac{8}{10} = \frac{48}{60}$
* $\frac{7}{20} = \frac{21}{60}$
* $\frac{1}{5} = \frac{12}{60}$
* Order by numerators: $12, 21, 24, 36, 48$.
* Result: $\frac{1}{5}, \frac{7}{20}, \frac{2}{5}, \frac{9}{15}, \frac{8}{10}$
5) $\frac{4}{9}, \frac{9}{12}, \frac{5}{6}, \frac{3}{18}, \frac{1}{3}$
* LCD for 9, 12, 6, 18, 3 is 36.
* Convert fractions:
* $\frac{4}{9} = \frac{16}{36}$
* $\frac{9}{12} = \frac{27}{36}$
* $\frac{5}{6} = \frac{30}{36}$
* $\frac{3}{18} = \frac{6}{36}$
* $\frac{1}{3} = \frac{12}{36}$
* Order by numerators: $6, 12, 16, 27, 30$.
* Result: $\frac{3}{18}, \frac{1}{3}, \frac{4}{9}, \frac{9}{12}, \frac{5}{6}$
6) $\frac{5}{8}, \frac{7}{16}, \frac{3}{4}, \frac{1}{4}, \frac{12}{24}$
* LCD for 8, 16, 4, 24 is 48.
* Convert fractions:
* $\frac{5}{8} = \frac{30}{48}$
* $\frac{7}{16} = \frac{21}{48}$
* $\frac{3}{4} = \frac{36}{48}$
* $\frac{1}{4} = \frac{12}{48}$
* $\frac{12}{24} = \frac{24}{48}$
* Order by numerators: $12, 21, 24, 30, 36$.
* Result: $\frac{1}{4}, \frac{7}{16}, \frac{12}{24}, \frac{5}{8}, \frac{3}{4}$
7) $\frac{7}{10}, \frac{2}{5}, \frac{9}{20}, \frac{5}{15}, \frac{10}{20}$
* LCD for 10, 5, 20, 15 is 60.
* Convert fractions:
* $\frac{7}{10} = \frac{42}{60}$
* $\frac{2}{5} = \frac{24}{60}$
* $\frac{9}{20} = \frac{27}{60}$
* $\frac{5}{15} = \frac{20}{60}$
* $\frac{10}{20} = \frac{30}{60}$
* Order by numerators: $20, 24, 27, 30, 42$.
* Result: $\frac{5}{15}, \frac{2}{5}, \frac{9}{20}, \frac{10}{20}, \frac{7}{10}$
8) $\frac{9}{15}, \frac{5}{12}, \frac{7}{18}, \frac{4}{9}, \frac{1}{6}$
* LCD for 15, 12, 18, 9, 6 is 180.
* Convert fractions:
* $\frac{9}{15} = \frac{108}{180}$
* $\frac{5}{12} = \frac{75}{180}$
* $\frac{7}{18} = \frac{70}{180}$
* $\frac{4}{9} = \frac{80}{180}$
* $\frac{1}{6} = \frac{30}{180}$
* Order by numerators: $30, 70, 75, 80, 108$.
* Result: $\frac{1}{6}, \frac{7}{18}, \frac{5}{12}, \frac{4}{9}, \frac{9}{15}$
9) $\frac{4}{9}, \frac{2}{6}, \frac{15}{21}, \frac{7}{12}, \frac{9}{18}$
* LCD for 9, 6, 21, 12, 18 is 252.
* Convert fractions:
* $\frac{4}{9} = \frac{112}{252}$
* $\frac{2}{6} = \frac{84}{252}$
* $\frac{15}{21} = \frac{180}{252}$
* $\frac{7}{12} = \frac{147}{252}$
* $\frac{9}{18} = \frac{126}{252}$
* Order by numerators: $84, 112, 126, 147, 180$.
* Result: $\frac{2}{6}, \frac{4}{9}, \frac{9}{18}, \frac{7}{12}, \frac{15}{21}$
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 by numerators: $6, 45, 54, 60, 70$.
* Result: $\frac{1}{25}, \frac{3}{10}, \frac{9}{25}, \frac{2}{5}, \frac{7}{15}$
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 4th grade.
