Multiplication and Division of Mixed Numbers

First step:
Let's reduce the fractions if possible.
Second step:
Let's convert the mixed numbers into fractions.

In multiplications

We will operate according to the method of numerator by numerator and denominator by denominator.

In divisions:

We will change the operation from division to multiplication and swap the locations between the numerator and the denominator in the second fraction -that is, the fraction that is after the sign.
Then we will solve by multiplying numerator by numerator and denominator by denominator.

Suggested Topics to Practice in Advance

  1. Mixed Numbers and Fractions Greater Than 1
  2. Remainder and Mixed Number
  3. Remainders
  4. Remainder of a fraction
  5. Addition and Subtraction of Mixed Numbers
  6. Multiplication of Integers by a Fraction and a Mixed Number

Practice Multiplying and Dividing Mixed Numbers

Examples with solutions for Multiplying and Dividing Mixed Numbers

Exercise #1

114×168= 1\frac{1}{4}\times1\frac{6}{8}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert each mixed number to an improper fraction.
  • Step 2: Multiply the improper fractions.
  • Step 3: Convert the result back to a mixed number.

Now, let's work through each step:

Step 1: Convert each mixed number to an improper fraction.
For 1141\frac{1}{4}:
- Whole number is 1, denominator is 4, and numerator is 1.
- Convert to improper fraction: 114=4×1+14=541\frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4}.

For 1681\frac{6}{8}:
- Whole number is 1, denominator is 8, and numerator is 6.
- Convert to improper fraction: 168=8×1+68=1481\frac{6}{8} = \frac{8 \times 1 + 6}{8} = \frac{14}{8}.
- Simplify 148\frac{14}{8} to 74\frac{7}{4} by dividing both the numerator and the denominator by 2.

Step 2: Multiply the improper fractions:
54×74=5×74×4=3516\frac{5}{4} \times \frac{7}{4} = \frac{5 \times 7}{4 \times 4} = \frac{35}{16}.

Step 3: Convert the improper fraction back to a mixed number:
Divide 35 by 16. This gives 2 as the quotient with a remainder of 3.
Thus, 3516=2316\frac{35}{16} = 2\frac{3}{16}.

Therefore, the product of 114×1681\frac{1}{4} \times 1\frac{6}{8} is 23162\frac{3}{16}.

Answer

2316 2\frac{3}{16}

Exercise #2

256×114= 2\frac{5}{6}\times1\frac{1}{4}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the mixed numbers 2562\frac{5}{6} and 1141\frac{1}{4}, we will follow these steps:

  • Step 1: Convert mixed numbers to improper fractions.

For 2562\frac{5}{6}:
Multiply the whole number 2 by the denominator 6, resulting in 12. Add the numerator 5 to get 17.
Thus, 256=1762\frac{5}{6} = \frac{17}{6}.

For 1141\frac{1}{4}:
Multiply the whole number 1 by the denominator 4, resulting in 4. Add the numerator 1 to get 5.
Thus, 114=541\frac{1}{4} = \frac{5}{4}.

  • Step 2: Multiply the improper fractions.

Multiply 176\frac{17}{6} by 54\frac{5}{4}:
The result is 17×56×4=8524\frac{17 \times 5}{6 \times 4} = \frac{85}{24}.

  • Step 3: Convert the result back to a mixed number.

To convert 8524\frac{85}{24} to a mixed number, divide 85 by 24:
85 divided by 24 is 3, with a remainder of 13.
Hence, 8524=31324\frac{85}{24} = 3\frac{13}{24}.

Therefore, the product of the mixed numbers 2562\frac{5}{6} and 1141\frac{1}{4} is 31324 3\frac{13}{24} .

Answer

31324 3\frac{13}{24}

Exercise #3

145×212= 1\frac{4}{5}\times2\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert each mixed number to an improper fraction.
  • Step 2: Multiply the improper fractions.
  • Step 3: Simplify the resulting fraction, if needed, and convert it back to a mixed number.

Now, let's work through each step:
Step 1: Convert the mixed numbers to improper fractions.
For 1451\frac{4}{5}:
145=1×5+45=951\frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5}.
For 2122\frac{1}{2}:
212=2×2+12=522\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}.

Step 2: Multiply the improper fractions:
95×52=9×55×2=4510\frac{9}{5} \times \frac{5}{2} = \frac{9 \times 5}{5 \times 2} = \frac{45}{10}.

Step 3: Simplify the fraction and convert it back to a mixed number:
4510=92=412\frac{45}{10} = \frac{9}{2} = 4\frac{1}{2}.

Therefore, the product of 145×2121\frac{4}{5} \times 2\frac{1}{2} is 4124\frac{1}{2}, which corresponds to choice 2.

Answer

412 4\frac{1}{2}

Exercise #4

214×123= 2\frac{1}{4}\times1\frac{2}{3}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the mixed numbers 214 2\frac{1}{4} and 123 1\frac{2}{3} , we proceed as follows:

  • Step 1: Convert Mixed Numbers to Improper Fractions

    • Convert 214 2\frac{1}{4} to an improper fraction: 214=2×4+14=94 2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}

    • Convert 123 1\frac{2}{3} to an improper fraction: 123=1×3+23=53 1\frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}

  • Step 2: Multiply the Improper Fractions

  • Now, multiply 94\frac{9}{4} by 53\frac{5}{3}: 94×53=9×54×3=4512 \frac{9}{4} \times \frac{5}{3} = \frac{9 \times 5}{4 \times 3} = \frac{45}{12}

  • Step 3: Simplify the Fraction

  • Simplify 4512\frac{45}{12} by finding the greatest common divisor of 45 and 12, which is 3: 45÷312÷3=154 \frac{45 \div 3}{12 \div 3} = \frac{15}{4}

  • Step 4: Convert Back to a Mixed Number

  • Convert 154\frac{15}{4} into a mixed number: 15÷4=3remainder3 15 \div 4 = 3 \quad \text{remainder} \quad 3 So, 154=334\frac{15}{4} = 3\frac{3}{4}.

Based on the calculations, the product of 214 2\frac{1}{4} and 123 1\frac{2}{3} is 334 3\frac{3}{4} .

Therefore, the solution to the problem is 334 3\frac{3}{4} .

Answer

334 3\frac{3}{4}

Exercise #5

145×113= 1\frac{4}{5}\times1\frac{1}{3}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll convert the mixed numbers into improper fractions, multiply them, and simplify the result:

  • Step 1: Convert mixed numbers to improper fractions.
    • 1451\frac{4}{5} becomes 1×5+45=95\frac{1 \times 5 + 4}{5} = \frac{9}{5}.
    • 1131\frac{1}{3} becomes 1×3+13=43\frac{1 \times 3 + 1}{3} = \frac{4}{3}.
  • Step 2: Multiply the improper fractions.
    • 95×43=9×45×3=3615\frac{9}{5} \times \frac{4}{3} = \frac{9 \times 4}{5 \times 3} = \frac{36}{15}.
  • Step 3: Simplify the fraction 3615\frac{36}{15}.
    • The greatest common divisor of 36 and 15 is 3.
    • 36÷315÷3=125\frac{36 \div 3}{15 \div 3} = \frac{12}{5}.
  • Step 4: Convert the improper fraction 125\frac{12}{5} back to a mixed number.
    • 12÷512 \div 5 is 2 with a remainder of 2.
    • The mixed number is 2252\frac{2}{5}.

Therefore, the product of 145×113 1\frac{4}{5} \times 1\frac{1}{3} is 225 2\frac{2}{5} .

Answer

225 2\frac{2}{5}

Exercise #6

423×115 4\frac{2}{3}\times1\frac{1}{5}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert 4234\frac{2}{3} and 1151\frac{1}{5} to improper fractions.
  • Step 2: Multiply these improper fractions.
  • Step 3: Simplify the result, if necessary, and convert it back to a mixed number.

Now, let's work through each step:
Step 1: Convert mixed numbers to improper fractions:
For 4234\frac{2}{3}:
Multiply the whole number 4 by the denominator 3 and add the numerator 2:
4×3+2=12+2=144 \times 3 + 2 = 12 + 2 = 14.
Thus, 423=1434\frac{2}{3} = \frac{14}{3}.
For 1151\frac{1}{5}:
Multiply the whole number 1 by the denominator 5 and add the numerator 1:
1×5+1=5+1=61 \times 5 + 1 = 5 + 1 = 6.
Thus, 115=651\frac{1}{5} = \frac{6}{5}.

Step 2: Multiply the improper fractions 143\frac{14}{3} and 65\frac{6}{5}:
143×65=14×63×5=8415\frac{14}{3} \times \frac{6}{5} = \frac{14 \times 6}{3 \times 5} = \frac{84}{15}.

Step 3: Simplify the resulting fraction 8415\frac{84}{15} and convert it to a mixed number if necessary:
Find the greatest common divisor (GCD) of 84 and 15, which is 3.
Divide both numerator and denominator by their GCD:
84÷315÷3=285\frac{84 \div 3}{15 \div 3} = \frac{28}{5}.

Convert the improper fraction 285\frac{28}{5} to a mixed number:
Divide 28 by 5: Quotient is 5, remainder is 3.
Thus, 285=535\frac{28}{5} = 5\frac{3}{5}.

Therefore, the solution to the problem is 5355\frac{3}{5}.

Answer

535 5\frac{3}{5}

Exercise #7

325×116= 3\frac{2}{5}\times1\frac{1}{6}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying 3253 \frac{2}{5} by 1161 \frac{1}{6}, follow these steps:

  • Step 1: Convert Mixed Numbers to Improper Fractions.
    - For 3253 \frac{2}{5}, convert by multiplying 3 (the whole number) by 5 (the denominator) and adding 2 (the numerator):
    (3×5)+2=15+2=17(3 \times 5) + 2 = 15 + 2 = 17. Thus, 325=1753 \frac{2}{5} = \frac{17}{5}.
    - For 1161 \frac{1}{6}, convert by multiplying 1 (the whole number) by 6 (the denominator) and adding 1 (the numerator):
    (1×6)+1=6+1=7(1 \times 6) + 1 = 6 + 1 = 7. Thus, 116=761 \frac{1}{6} = \frac{7}{6}.
  • Step 2: Multiply the Improper Fractions.
    Multiply 175\frac{17}{5} by 76\frac{7}{6}:
    175×76=17×75×6=11930\frac{17}{5} \times \frac{7}{6} = \frac{17 \times 7}{5 \times 6} = \frac{119}{30}.
  • Step 3: Convert the Result to a Mixed Number.
    Divide 119 by 30. The quotient is 3 with a remainder of 29, so the mixed number is 329303 \frac{29}{30}.

Conclusion: 325×116=32930 3 \frac{2}{5} \times 1 \frac{1}{6} = 3 \frac{29}{30} .

The correct choice from the options provided is Choice 4: 32930 3 \frac{29}{30} .

Answer

32930 3\frac{29}{30}

Exercise #8

139×224= 1\frac{3}{9}\times2\frac{2}{4}=

Video Solution

Step-by-Step Solution

To solve the problem 139×224 1\frac{3}{9} \times 2\frac{2}{4} , we will follow these steps:

  • Step 1: Convert each mixed number to an improper fraction.
  • Step 2: Multiply the improper fractions.
  • Step 3: Convert the resulting improper fraction back into a mixed number.

Let’s begin with each step in detail:

Step 1: Convert 139 1\frac{3}{9} and 224 2\frac{2}{4} to improper fractions.
- For 139 1\frac{3}{9} : Convert the fraction 39 \frac{3}{9} to its simplest form, which is 13 \frac{1}{3} . Then, the mixed number 113 1\frac{1}{3} becomes 1+13=33+13=43 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} .
- For 224 2\frac{2}{4} : The fraction 24 \frac{2}{4} simplifies to 12 \frac{1}{2} . Then, the mixed number 212 2\frac{1}{2} becomes 2+12=42+12=52 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} .

Step 2: Multiply the improper fractions:
43×52=4×53×2=206\frac{4}{3} \times \frac{5}{2} = \frac{4 \times 5}{3 \times 2} = \frac{20}{6}.

Simplify 206\frac{20}{6}:
Find the greatest common divisor (GCD) of 20 and 6, which is 2. Then 206=20÷26÷2=103\frac{20}{6} = \frac{20 \div 2}{6 \div 2} = \frac{10}{3}.

Step 3: Convert the improper fraction 103\frac{10}{3} back to a mixed number:
Divide 10 by 3 to get 3 with a remainder of 1, thus 103=313\frac{10}{3} = 3\frac{1}{3}.

Therefore, the product is 313 3\frac{1}{3} .

Answer

313 3\frac{1}{3}

Exercise #9

146×128= 1\frac{4}{6}\times1\frac{2}{8}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll convert the given mixed numbers to improper fractions, multiply them, and simplify the result. Let's proceed step by step:

  • Step 1: Convert the mixed numbers to improper fractions.
    For 1461\frac{4}{6}: Multiply the whole number by the denominator and add the numerator: 146=1×6+46=1061\frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{10}{6}.
    For 1281\frac{2}{8}: Similarly, multiply the whole number by the denominator and add the numerator: 128=1×8+28=1081\frac{2}{8} = \frac{1 \times 8 + 2}{8} = \frac{10}{8}.
  • Step 2: Multiply the improper fractions.
    106×108=10×106×8=10048 \frac{10}{6} \times \frac{10}{8} = \frac{10 \times 10}{6 \times 8} = \frac{100}{48}.
  • Step 3: Simplify the resulting fraction.
    Find the GCD of 100 and 48, which is 4. Divide both the numerator and the denominator by 4:
    10048=100÷448÷4=2512 \frac{100}{48} = \frac{100 \div 4}{48 \div 4} = \frac{25}{12}.
  • Step 4: Convert the simplified improper fraction back to a mixed number.
    Divide 25 by 12: 25 divided by 12 is 2 with a remainder of 1. So, 2512=2112\frac{25}{12} = 2\frac{1}{12}.

Therefore, the solution to the problem is 2112 2\frac{1}{12} . This matches the correct answer choice 2.

Answer

2112 2\frac{1}{12}

Exercise #10

2412×124= 2\frac{4}{12}\times1\frac{2}{4}=

Video Solution

Step-by-Step Solution

To solve the given problem, we'll follow these steps:

  • Convert the mixed numbers to improper fractions.
  • Multiply the improper fractions.
  • Simplify the result and convert back to a mixed number if necessary.

Let's work through these steps:

1. Convert each mixed number to an improper fraction:

  • For 24122\frac{4}{12}, first simplify the fraction 412\frac{4}{12} to 13\frac{1}{3}. So, 2132\frac{1}{3} becomes:
  • 2×3+13=73\frac{2 \times 3 + 1}{3} = \frac{7}{3}.

  • For 1241\frac{2}{4}, first simplify the fraction 24\frac{2}{4} to 12\frac{1}{2}. So, 1121\frac{1}{2} becomes:
  • 1×2+12=32\frac{1 \times 2 + 1}{2} = \frac{3}{2}.

2. Multiply the improper fractions:

The multiplication of 73\frac{7}{3} and 32\frac{3}{2} is:

73×32=216\frac{7}{3} \times \frac{3}{2} = \frac{21}{6}.

3. Simplify the resulting fraction 216\frac{21}{6}:

216=72\frac{21}{6} = \frac{7}{2} after dividing the numerator and denominator by 3.

4. Convert the improper fraction back to a mixed number:

72=312\frac{7}{2} = 3\frac{1}{2}.

Thus, the solution to the problem is 312\boxed{3\frac{1}{2}}.

Answer

312 3\frac{1}{2}

Exercise #11

226×1410= 2\frac{2}{6}\times1\frac{4}{10}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert each mixed number to an improper fraction.
  • Step 2: Multiply the improper fractions.
  • Step 3: Simplify the resulting fraction, if necessary.
  • Step 4: Convert the result back to a mixed number.

Now, let's work through each step:

Step 1: Convert each mixed number to an improper fraction.

For 2262\frac{2}{6}:

226=2×6+26=12+26=146 2\frac{2}{6} = \frac{2 \times 6 + 2}{6} = \frac{12 + 2}{6} = \frac{14}{6}

Simplifying 146\frac{14}{6} by dividing the numerator and the denominator by 2, we get 146=73\frac{14}{6} = \frac{7}{3}.

For 14101\frac{4}{10}:

1410=1×10+410=10+410=1410 1\frac{4}{10} = \frac{1 \times 10 + 4}{10} = \frac{10 + 4}{10} = \frac{14}{10}

Simplifying 1410\frac{14}{10} by dividing the numerator and the denominator by 2, we get 1410=75\frac{14}{10} = \frac{7}{5}.

Step 2: Multiply the improper fractions:

73×75=7×73×5=4915 \frac{7}{3} \times \frac{7}{5} = \frac{7 \times 7}{3 \times 5} = \frac{49}{15}

Step 3: Simplify the resulting fraction, if necessary. In this case, 4915\frac{49}{15} is already in its simplest form.

Step 4: Convert the result back to a mixed number:

4915 \frac{49}{15} can be rewritten as 34153\frac{4}{15}, since 49 divided by 15 is 3 with a remainder of 4.

Therefore, the solution to the problem is 3415 3\frac{4}{15} .

Answer

3415 3\frac{4}{15}

Exercise #12

168×226= 1\frac{6}{8}\times2\frac{2}{6}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert each mixed number to an improper fraction.
  • Step 2: Multiply the improper fractions.
  • Step 3: Simplify the resulting fraction.
  • Step 4: Convert the improper fraction back to a mixed number if necessary.

Let's begin:

Step 1: Convert to improper fractions
Convert 1681\frac{6}{8} to an improper fraction:
8×1+68=148\frac{8 \times 1 + 6}{8} = \frac{14}{8}.

Convert 2262\frac{2}{6} to an improper fraction:
6×2+26=146\frac{6 \times 2 + 2}{6} = \frac{14}{6}.

Step 2: Multiply the fractions
Multiply 148\frac{14}{8} and 146\frac{14}{6}:
148×146=19648\frac{14}{8} \times \frac{14}{6} = \frac{196}{48}.

Step 3: Simplify the fraction
Find the greatest common divisor (GCD) of 196 and 48, which is 4. Simplify 19648\frac{196}{48}:
196÷448÷4=4912\frac{196 \div 4}{48 \div 4} = \frac{49}{12}.

Step 4: Convert to a mixed number
4912\frac{49}{12} as a mixed number is 41124\frac{1}{12} since 49 divided by 12 is 4 with a remainder of 1.

Therefore, the solution to the problem is 4112 4\frac{1}{12} .

Answer

4112 4\frac{1}{12}

Exercise #13

1412×1414= 1\frac{4}{12}\times1\frac{4}{14}=

Video Solution

Step-by-Step Solution

Let's solve the problem by following these steps:

  • Step 1: Convert the mixed numbers to improper fractions.
  • Step 2: Multiply the improper fractions.
  • Step 3: Simplify the resulting fraction and convert back to a mixed number if needed.

Step 1:
Convert 14121\frac{4}{12} to an improper fraction.

Calculate the improper fraction: 1412=1×12+412=1612 1\frac{4}{12} = \frac{1 \times 12 + 4}{12} = \frac{16}{12}

Convert 14141\frac{4}{14} to an improper fraction.

Calculate the improper fraction: 1414=1×14+414=1814 1\frac{4}{14} = \frac{1 \times 14 + 4}{14} = \frac{18}{14}

Step 2:
Multiply the two improper fractions:

1612×1814=16×1812×14 \frac{16}{12} \times \frac{18}{14} = \frac{16 \times 18}{12 \times 14}

Simplify the multiplication:

  • Numerator: 16×18=28816 \times 18 = 288
  • Denominator: 12×14=16812 \times 14 = 168

The resulting fraction is 288168\frac{288}{168}.

Step 3:
Simplify 288168\frac{288}{168}.

Find the greatest common divisor (GCD) of 288 and 168, which is 24.

  • Divide numerator by GCD: 288÷24=12288 \div 24 = 12
  • Divide denominator by GCD: 168÷24=7168 \div 24 = 7

The simplified fraction is 127\frac{12}{7}.

Convert 127\frac{12}{7} back to a mixed number:

12 divided by 7 is 1 with a remainder of 5, so the mixed number is 1571\frac{5}{7}.

Thus, the solution to the problem is 157\boxed{1\frac{5}{7}}.

Answer

157 1\frac{5}{7}

Exercise #14

21020×1416= 2\frac{10}{20}\times1\frac{4}{16}=

Video Solution

Step-by-Step Solution

To solve this problem, we will convert the mixed numbers to improper fractions and multiply them.

  • Step 1: Convert Mixed Numbers to Improper Fractions

For the first mixed number 210202\frac{10}{20}:
- Convert 210202\frac{10}{20} to an improper fraction:
Initially, 10/2010/20 can be simplified to 1/21/2 (since gcd(10,20)=10\gcd(10, 20) = 10). Therefore, the mixed number 2122\frac{1}{2} is equal to:
2×2+1=4+1=52 \times 2 + 1 = 4 + 1 = 5
Thus, 2122\frac{1}{2} becomes 52\frac{5}{2}.

For the second mixed number 14161\frac{4}{16}:
- Simplify 4/164/16 to 1/41/4 (since gcd(4,16)=4\gcd(4, 16) = 4). Hence, 14161\frac{4}{16} simplifies to 1141\frac{1}{4}:
1×4+1=4+1=51 \times 4 + 1 = 4 + 1 = 5
Thus, 1141\frac{1}{4} becomes 54\frac{5}{4}.

  • Step 2: Multiply the Improper Fractions

Multiply the fractions 52×54\frac{5}{2} \times \frac{5}{4}:
5×52×4=258\frac{5 \times 5}{2 \times 4} = \frac{25}{8}

  • Step 3: Simplify and Convert to Mixed Number

Convert 258\frac{25}{8} back to a mixed number by dividing:
- Divide 25 by 8, which goes 3 times (remainder 1).
Thus, 258=318\frac{25}{8} = 3\frac{1}{8}.

Therefore, the solution to the problem is 3183\frac{1}{8}.

Answer

318 3\frac{1}{8}

Exercise #15

345×212= 3\frac{4}{5}\times2\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve the problem, we'll use the following steps:

  • Step 1: Convert both mixed numbers into improper fractions.

  • Step 2: Multiply the improper fractions.

  • Step 3: Convert the product back to a mixed number.

Now, let’s work through each step:

Step 1: Convert 3453\frac{4}{5} and 2122\frac{1}{2} into improper fractions.
For 3453\frac{4}{5}: Multiply the whole number 3 by the denominator 5, and add the numerator 4:
3×5+4=15+4=193 \times 5 + 4 = 15 + 4 = 19.
The improper fraction is 195\frac{19}{5}.
For 2122\frac{1}{2}: Multiply the whole number 2 by the denominator 2, and add the numerator 1:
2×2+1=4+1=52 \times 2 + 1 = 4 + 1 = 5.
The improper fraction is 52\frac{5}{2}.

Step 2: Multiply the improper fractions.
195×52=19×55×2=9510\frac{19}{5} \times \frac{5}{2} = \frac{19 \times 5}{5 \times 2} = \frac{95}{10}.

Step 3: Simplify 9510\frac{95}{10} and convert to a mixed number.
Divide 95 by 10. The quotient is 9 with a remainder of 5, so:
9510=9510\frac{95}{10} = 9\frac{5}{10}.
Since 510\frac{5}{10} simplifies to 12\frac{1}{2}, we get:
9129\frac{1}{2} as the final answer.

Therefore, the solution to the problem is 9129\frac{1}{2}.

Answer

912 9\frac{1}{2}