Question

3 7/16 + 2 5/32= 1 1/12 + 3 4/9= 4 1/6 + 5 3/14 + 6 2/21 5 16/21 - 2 5/9 = 9 5/6 - 4 9/16 =

Answer 1

3 7/16 + 2 5/32=(3+2)+(7/16+5/32)=5 19/32

1 1/12 + 3 4/9=(1+3)+(1/12+4/9)=4 19/36

4 1/6 + 5 3/14 + 6 2/21=(4+6+5)+(1/6+3/14+2/21)=15 10/21

5 16/21 - 2 5/9 =(5-2)+(16/21-5/9)=3 13/63

9 5/6 - 4 9/16 =(9-4)+(5/6-9/16)=5 13/48

Answer 2

Let's solve each of these step by step:

1. 3 7/16 + 2 5/32:

   • Convert the mixed numbers to improper fractions:
     $3 \frac{7}{16} = \frac{3 \cdot 16 + 7}{16} = \frac{55}{16}$ $2 \frac{5}{32} = \frac{2 \cdot 32 + 5}{32} = \frac{69}{32}$
   • Add the fractions: $\frac{55}{16} + \frac{69}{32} = \frac{110}{32} + \frac{69}{32} = \frac{179}{32}$
   • Simplify the fraction if possible: $\frac{179}{32} = 5 \frac{19}{32}$

2. 1 1/12 + 3 4/9:

   • Convert the mixed numbers to improper fractions:
     $1 \frac{1}{12} = \frac{1 \cdot 12 + 1}{12} = \frac{13}{12}$ $3 \frac{4}{9} = \frac{3 \cdot 9 + 4}{9} = \frac{31}{9}$
   • Add the fractions: $\frac{13}{12} + \frac{31}{9}$
   • Find a common denominator, which is 36: $\frac{13}{12} \cdot \frac{3}{3} = \frac{39}{36}$ $\frac{31}{9} \cdot \frac{4}{4} = \frac{124}{36}$
   • Add the fractions: $\frac{39}{36} + \frac{124}{36} = \frac{163}{36}$
   • Convert the improper fraction back to a mixed number: $163 \div 36 = 4 \frac{19}{36}$

3. 4 1/6 + 5 3/14 + 6 2/21:

   • Convert the mixed numbers to improper fractions:
     $4 \frac{1}{6} = \frac{4 \cdot 6 + 1}{6} = \frac{25}{6}$ $5 \frac{3}{14} = \frac{5 \cdot 14 + 3}{14} = \frac{73}{14}$ $6 \frac{2}{21} = \frac{6 \cdot 21 + 2}{21} = \frac{128}{21}$
   • Add the fractions: $\frac{25}{6} + \frac{73}{14} + \frac{128}{21}$
   • Find a common denominator, which is $6 \cdot 14 \cdot 21 = 1764$: Adjust the fractions accordingly.
   • Add the fractions once they have the same denominator.

4. 5 16/21 - 2 5/9:

   • Convert the mixed numbers to improper fractions:
     $5 \frac{16}{21} = \frac{5 \cdot 21 + 16}{21} = \frac{121}{21}$ $2 \frac{5}{9} = \frac{2 \cdot 9 + 5}{9} = \frac{23}{9}$