Multiplying and Dividing Mixed Numbers: By multiplication only

Examples with solutions for Multiplying and Dividing Mixed Numbers: By multiplication only

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

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}

Exercise #9

517×134= 5\frac{1}{7}\times1\frac{3}{4}=

Video Solution

Step-by-Step Solution

To solve the problem 517×1345 \frac{1}{7} \times 1 \frac{3}{4}, we will first convert both mixed numbers into improper fractions and then multiply them.

  • Convert each mixed number to an improper fraction:
    For 5175 \frac{1}{7}: Multiply the whole number 5 by the denominator 7 and add the numerator 1: 5×7+1=365 \times 7 + 1 = 36. Therefore, 5175 \frac{1}{7} becomes 367\frac{36}{7}.
    For 1341 \frac{3}{4}: Multiply the whole number 1 by the denominator 4 and add the numerator 3: 1×4+3=71 \times 4 + 3 = 7. Therefore, 1341 \frac{3}{4} becomes 74\frac{7}{4}.
  • Multiply the improper fractions:
    Multiply the numerators: 36×7=25236 \times 7 = 252.
    Multiply the denominators: 7×4=287 \times 4 = 28.
    Thus, 367×74=25228\frac{36}{7} \times \frac{7}{4} = \frac{252}{28}.
  • Simplify the resulting fraction, 25228\frac{252}{28}:
    Divide both the numerator and denominator by their greatest common divisor, which is 28:
    252÷28=9252 \div 28 = 9 and 28÷28=128 \div 28 = 1.
    So, 25228=9\frac{252}{28} = 9.

Therefore, the solution to the problem is 99.

Answer

9 9

Exercise #10

447×212= 4\frac{4}{7}\times2\frac{1}{2}=

Video Solution

Step-by-Step Solution

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

  • Convert each mixed number to an improper fraction.
  • Multiply the two improper fractions.
  • Convert the result back to a mixed number.

Now, let's work through each step:

Step 1: Convert the mixed numbers to improper fractions.
For 447 4\frac{4}{7} :
Multiply the whole number by the denominator: 4×7=284 \times 7 = 28.
Add the numerator to this product: 28+4=3228 + 4 = 32.
Thus, 447=327 4\frac{4}{7} = \frac{32}{7} .

For 212 2\frac{1}{2} :
Multiply the whole number by the denominator: 2×2=42 \times 2 = 4.
Add the numerator: 4+1=54 + 1 = 5.
Thus, 212=52 2\frac{1}{2} = \frac{5}{2} .

Step 2: Multiply the two improper fractions:
327×52=32×57×2=16014\frac{32}{7} \times \frac{5}{2} = \frac{32 \times 5}{7 \times 2} = \frac{160}{14}.

Step 3: Simplify 16014\frac{160}{14} and convert to a mixed number:
First, simplify the fraction by finding the greatest common divisor of 160 and 14, which is 2.
16014=160÷214÷2=807\frac{160}{14} = \frac{160 \div 2}{14 \div 2} = \frac{80}{7}.

Convert 807\frac{80}{7} to a mixed number:
Divide 80 by 7, which gives a quotient of 11 and a remainder of 3.
Thus, 807=1137\frac{80}{7} = 11\frac{3}{7}.

Therefore, the solution to the problem is 1137 11\frac{3}{7} .

Answer

1137 11\frac{3}{7}

Exercise #11

227×134= 2\frac{2}{7}\times1\frac{3}{4}=

Video Solution

Step-by-Step Solution

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

  • Convert each mixed number into an improper fraction.
  • Multiply the two improper fractions.
  • Simplify the resulting fraction if necessary.
  • Convert the final product back to a mixed number if desired.

Now, let's work through each step:

Step 1: Convert the mixed numbers into improper fractions.
For 227 2\frac{2}{7} : 227=2×7+27=14+27=167 2\frac{2}{7} = \frac{2 \times 7 + 2}{7} = \frac{14 + 2}{7} = \frac{16}{7} For 134 1\frac{3}{4} : 134=1×4+34=4+34=74 1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}

Step 2: Multiply the improper fractions.
167×74=16×77×4=11228 \frac{16}{7} \times \frac{7}{4} = \frac{16 \times 7}{7 \times 4} = \frac{112}{28}

Step 3: Simplify the resulting fraction.
Since 112÷28=4 112 \div 28 = 4 , 11228=4 \frac{112}{28} = 4

The final result is a whole number, so there is no need for conversion back to a mixed number.

Therefore, the solution to the problem is 4 4 .

Answer

4 4

Exercise #12

145×112= 1\frac{4}{5}\times1\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying 145 1\frac{4}{5} and 112 1\frac{1}{2} , we will follow these detailed steps:

  • Step 1: Convert both mixed numbers to improper fractions.
  • Step 2: Multiply the improper fractions.
  • Step 3: Simplify the result and convert back to a mixed number.

Now let's go through each step in detail:

Step 1: Convert to Improper Fractions
For the number 145 1\frac{4}{5} :
- Multiply the whole number by the denominator: 1×5=51 \times 5 = 5.
- Add the numerator: 5+4=95 + 4 = 9.
- The improper fraction is 95\frac{9}{5}.

For the number 112 1\frac{1}{2} :
- Multiply the whole number by the denominator: 1×2=21 \times 2 = 2.
- Add the numerator: 2+1=32 + 1 = 3.
- The improper fraction is 32\frac{3}{2}.

Step 2: Multiply the Improper Fractions
Multiply 95\frac{9}{5} by 32\frac{3}{2}:
95×32=9×35×2=2710\frac{9}{5} \times \frac{3}{2} = \frac{9 \times 3}{5 \times 2} = \frac{27}{10}.

Step 3: Simplify and Convert Back to Mixed Number
- The fraction 2710\frac{27}{10} is already in simplest form.
- Convert it to a mixed number: Divide 27 by 10, which is 2 with a remainder of 7.
- Therefore, 2710=2710\frac{27}{10} = 2\frac{7}{10}.

Thus, the product of 145 1\frac{4}{5} and 112 1\frac{1}{2} is 2710 2\frac{7}{10} .

Answer

2710 2\frac{7}{10}