Question

grade 6 fraction worksheet
find the product
1 ( 6\frac{8}{9} \times 12\frac{1}{6} = ) 2. ( 4\frac{3}{6} \times 11\frac{7}{12} = ) 3. ( 3\frac{3}{8} \times 1\frac{1}{9} = )

1. ( \frac{7}{9} \times 6\frac{2}{5} = ) 5. ( \frac{4}{5} \times 6\frac{3}{4} = ) 6. ( \frac{4}{10} \times 4\frac{1}{3} = )
2. ( \frac{4}{8} \times \frac{43}{7} = ) 8. ( \frac{4}{12} \times \frac{19}{3} = ) 9. ( \frac{2}{5} \times \frac{19}{4} = )
3. ( \frac{1}{4} \times 9 = ) 11. ( \frac{8}{11} \times 6 = ) 12. ( \frac{8}{9} \times 11 = )
4. ( 7\frac{8}{11} \times 6 = ) 14. ( 2\frac{1}{2} \times 8 = ) 15. ( 7\frac{3}{6} \times 5 = )
5. ( 6 \times 2 = ) 17. ( 15 \times 2 = ) 18. ( 9 \times 14 = )

Answer:

Let's solve these fraction multiplication problems one by one. We'll start with problem 1:

Problem 1: $6\frac{8}{9} \times 12\frac{1}{6}$

Step 1: Convert mixed numbers to improper fractions

$6\frac{8}{9} = \frac{6 \times 9 + 8}{9} = \frac{54 + 8}{9} = \frac{62}{9}$
$12\frac{1}{6} = \frac{12 \times 6 + 1}{6} = \frac{72 + 1}{6} = \frac{73}{6}$

Step 2: Multiply the improper fractions

$\frac{62}{9} \times \frac{73}{6} = \frac{62 \times 73}{9 \times 6}$
Calculate the numerator: $62 \times 73 = 4526$
Calculate the denominator: $9 \times 6 = 54$
So, $\frac{4526}{54}$

Step 3: Simplify the fraction

Divide numerator and denominator by 2: $\frac{4526 \div 2}{54 \div 2} = \frac{2263}{27}$
Convert back to mixed number: $2263 \div 27 = 83$ with a remainder of $2263 - 27 \times 83 = 2263 - 2241 = 22$
So, $83\frac{22}{27}$

Problem 2: $4\frac{3}{8} \times 11\frac{7}{12}$

Step 1: Convert mixed numbers to improper fractions

$4\frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8}$
$11\frac{7}{12} = \frac{11 \times 12 + 7}{12} = \frac{132 + 7}{12} = \frac{139}{12}$

Step 2: Multiply the improper fractions

$\frac{35}{8} \times \frac{139}{12} = \frac{35 \times 139}{8 \times 12}$
Calculate the numerator: $35 \times 139 = 4865$
Calculate the denominator: $8 \times 12 = 96$
So, $\frac{4865}{96}$

Step 3: Simplify the fraction

Convert to mixed number: $4865 \div 96 = 50$ with a remainder of $4865 - 96 \times 50 = 4865 - 4800 = 65$
So, $50\frac{65}{96}$

Problem 3: $3\frac{3}{8} \times 1\frac{1}{5}$

Step 1: Convert mixed numbers to improper fractions

$3\frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8}$
$1\frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{5 + 1}{5} = \frac{6}{5}$

Step 2: Multiply the improper fractions

$\frac{27}{8} \times \frac{6}{5} = \frac{27 \times 6}{8 \times 5}$
Calculate the numerator: $27 \times 6 = 162$
Calculate the denominator: $8 \times 5 = 40$
So, $\frac{162}{40}$

Step 3: Simplify the fraction

Divide numerator and denominator by 2: $\frac{162 \div 2}{40 \div 2} = \frac{81}{20}$
Convert to mixed number: $81 \div 20 = 4$ with a remainder of $81 - 20 \times 4 = 81 - 80 = 1$
So, $4\frac{1}{20}$

Problem 4: $\frac{7}{9} \times 6\frac{2}{5}$

Step 1: Convert mixed number to improper fraction

$6\frac{2}{5} = \frac{6 \times 5 + 2}{5} = \frac{30 + 2}{5} = \frac{32}{5}$

Step 2: Multiply the fractions

$\frac{7}{9} \times \frac{32}{5} = \frac{7 \times 32}{9 \times 5}$
Calculate the numerator: $7 \times 32 = 224$
Calculate the denominator: $9 \times 5 = 45$
So, $\frac{224}{45}$

Step 3: Simplify the fraction

Convert to mixed number: $224 \div 45 = 4$ with a remainder of $224 - 45 \times 4 = 224 - 180 = 44$
So, $4\frac{44}{45}$

Problem 5: $\frac{4}{5} \times 6\frac{3}{4}$

Step 1: Convert mixed number to improper fraction

$6\frac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4}$

Step 2: Multiply the fractions

$\frac{4}{5} \times \frac{27}{4} = \frac{4 \times 27}{5 \times 4}$

Step 3: Simplify (cancel common factors)

The 4 in the numerator and denominator cancels: $\frac{27}{5}$

Step 4: Convert to mixed number

$27 \div 5 = 5$ with a remainder of $27 - 5 \times 5 = 27 - 25 = 2$
So, $5\frac{2}{5}$

Problem 6: $\frac{4}{10} \times 4\frac{1}{3}$

Step 1: Simplify $\frac{4}{10}$ to $\frac{2}{5}$

$\frac{4}{10} = \frac{4 \div 2}{10 \div 2} = \frac{2}{5}$

Step 2: Convert mixed number to improper fraction

$4\frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3}$

Step 3: Multiply the fractions

$\frac{2}{5} \times \frac{13}{3} = \frac{2 \times 13}{5 \times 3} = \frac{26}{15}$

Step 4: Convert to mixed number

$26 \div 15 = 1$ with a remainder of $26 - 15 \times 1 = 26 - 15 = 11$
So, $1\frac{11}{15}$

Problem 7: $\frac{4}{8} \times \frac{43}{7}$

Step 1: Simplify $\frac{4}{8}$ to $\frac{1}{2}$

$\frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}$

Step 2: Multiply the fractions

$\frac{1}{2} \times \frac{43}{7} = \frac{1 \times 43}{2 \times 7} = \frac{43}{14}$

Step 3: Convert to mixed number

$43 \div 14 = 3$ with a remainder of $43 - 14 \times 3 = 43 - 42 = 1$
So, $3\frac{1}{14}$

Problem 8: $\frac{4}{12} \times \frac{19}{3}$

Step 1: Simplify $\frac{4}{12}$ to $\frac{1}{3}$

$\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}$

Step 2: Multiply the fractions

$\frac{1}{3} \times \frac{19}{3} = \frac{1 \times 19}{3 \times 3} = \frac{19}{9}$

Step 3: Convert to mixed number

$19 \div 9 = 2$ with a remainder of $19 - 9 \times 2 = 19 - 18 = 1$
So, $2\frac{1}{9}$

Problem 9: $\frac{2}{5} \times \frac{19}{4}$

Step 1: Multiply the fractions

$\frac{2}{5} \times \frac{19}{4} = \frac{2 \times 19}{5 \times 4}$

Step 2: Simplify (cancel common factors)

The 2 in the numerator and 4 in the denominator can be simplified: $\frac{19}{5 \times 2} = \frac{19}{10}$

Step 3: Convert to mixed number

$19 \div 10 = 1$ with a remainder of $19 - 10 \times 1 = 19 - 10 = 9$
So, $1\frac{9}{10}$

Problem 10: $\frac{1}{4} \times 9$

Step 1: Multiply the fraction and the whole number

$\frac{1}{4} \times 9 = \frac{1 \times 9}{4} = \frac{9}{4}$

Step 2: Convert to mixed number

$9 \div 4 = 2$ with a remainder of $9 - 4 \times 2 = 9 - 8 = 1$
So, $2\frac{1}{4}$

Problem 11: $\frac{8}{11} \times 6$

Step 1: Multiply the fraction and the whole number

$\frac{8}{11} \times 6 = \frac{8 \times 6}{11} = \frac{48}{11}$

Step 2: Convert to mixed number

$48 \div 11 = 4$ with a remainder of $48 - 11 \times 4 = 48 - 44 = 4$
So, $4\frac{4}{11}$

Problem 12: $\frac{8}{9} \times 11$

Step 1: Multiply the fraction and the whole number

$\frac{8}{9} \times 11 = \frac{8 \times 11}{9} = \frac{88}{9}$

Step 2: Convert to mixed number

$88 \div 9 = 9$ with a remainder of $88 - 9 \times 9 = 88 - 81 = 7$
So, $9\frac{7}{9}$

Problem 13: $7\frac{8}{11} \times 6$

Step 1: Convert mixed number to improper fraction

$7\frac{8}{11} = \frac{7 \times 11 + 8}{11} = \frac{77 + 8}{11} = \frac{85}{11}$

Step 2: Multiply the improper fraction and the whole number

$\frac{85}{11} \times 6 = \frac{85 \times 6}{11} = \frac{510}{11}$

Step 3: Convert to mixed number

$510 \div 11 = 46$ with a remainder of $510 - 11 \times 46 = 510 - 506 = 4$
So, $46\frac{4}{11}$

Problem 14: $2\frac{1}{2} \times 8$

Step 1: Convert mixed number to improper fraction

$2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$

Step 2: Multiply the improper fraction and the whole number

$\frac{5}{2} \times 8 = \frac{5 \times 8}{2}$

Step 3: Simplify

$5 \times 4 = 20$ (since 8 ÷ 2 = 4)
So, $20$

Problem 15: $7\frac{3}{6} \times 5$

Step 1: Simplify the mixed number

$7\frac{3}{6} = 7\frac{1}{2}$ (since 3 ÷ 3 = 1 and 6 ÷ 3 = 2)

Step 2: Convert to improper fraction

$7\frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2}$

Step 3: Multiply the improper fraction and the whole number

$\frac{15}{2} \times 5 = \frac{15 \times 5}{2} = \frac{75}{2}$

Step 4: Convert to mixed number

$75 \div 2 = 37$ with a remainder of $75 - 2 \times 37 = 75 - 74 = 1$
So, $37\frac{1}{2}$

Problem 16: $6 \times 2$

Step 1: Multiply the whole numbers

$6 \times 2 = 12$

Problem 17: $15 \times 2$

Step 1: Multiply the whole numbers

$15 \times 2 = 30$

Problem 18: $9 \times 14$

Step 1: Multiply the whole numbers

$9 \times 14 = 126$

Final Answers:

1. $83\frac{22}{27}$
2. $50\frac{65}{96}$
3. $4\frac{1}{20}$
4. $4\frac{44}{45}$
5. $5\frac{2}{5}$
6. $1\frac{11}{15}$
7. $3\frac{1}{14}$
8. $2\frac{1}{9}$
9. $1\frac{9}{10}$
10. $2\frac{1}{4}$
11. $4\frac{4}{11}$
12. $9\frac{7}{9}$
13. $46\frac{4}{11}$
14. $20$
15. $37\frac{1}{2}$
16. $12$
17. $30$
18. $126$