Examples with solutions for Multiplication of Fractions: Solving the problem

Exercise #1

14×12= \frac{1}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this problem, we will multiply the two fractions given: 14 \frac{1}{4} and 12 \frac{1}{2} .

  • Step 1: Multiply the numerators: 1×1=1 1 \times 1 = 1 .
  • Step 2: Multiply the denominators: 4×2=8 4 \times 2 = 8 .
  • Step 3: Combine these results into a new fraction: 18 \frac{1}{8} .

Therefore, the product of the fractions 14 \frac{1}{4} and 12 \frac{1}{2} is 18 \frac{1}{8} . This matches choice 3 from the provided answer choices.

Answer

18 \frac{1}{8}

Exercise #2

34×12= \frac{3}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Simplify the resulting fraction if needed.

Now, let's work through each step:

Step 1: The fractions are given as 34 \frac{3}{4} and 12 \frac{1}{2} . Multiplying the numerators, we get:

3×1=3 3 \times 1 = 3

Step 2: Next, multiply the denominators:

4×2=8 4 \times 2 = 8

Step 3: Combine these results to write the product of the fractions:

34×12=3×14×2=38\frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}

The resulting fraction 38 \frac{3}{8} is already in its simplest form, so no further simplification is necessary.

Therefore, the solution to the problem is 38 \frac{3}{8} .

Answer

38 \frac{3}{8}

Exercise #3

16×13= \frac{1}{6}\times\frac{1}{3}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying two fractions 16 \frac{1}{6} and 13 \frac{1}{3} , we'll follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Simplify the resulting fraction if necessary.

Let's apply these steps to our problem:

Step 1: Multiply the numerators: 1×1=1 1 \times 1 = 1 .
Step 2: Multiply the denominators: 6×3=18 6 \times 3 = 18 .

Therefore, the product of 16 \frac{1}{6} and 13 \frac{1}{3} is 118 \frac{1}{18} .

The solution to the problem is 118 \frac{1}{18} , which corresponds to choice 4.

Answer

118 \frac{1}{18}

Exercise #4

14×32= \frac{1}{4}\times\frac{3}{2}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the fractions 14\frac{1}{4} and 32\frac{3}{2}, we will follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Write the result as a fraction and simplify if needed.

Now, let's work through each step:

Step 1: Multiply the numerators:
The numerators are 11 and 33. Thus, 1×3=31 \times 3 = 3.

Step 2: Multiply the denominators:
The denominators are 44 and 22. Thus, 4×2=84 \times 2 = 8.

Step 3: Write the result as a fraction and simplify:
The resulting fraction is 38\frac{3}{8}. This fraction is already in simplest form.

Therefore, the solution to the problem is 38\frac{3}{8}.

Among the choices provided, the correct answer is choice 3: 38\frac{3}{8}.

Answer

38 \frac{3}{8}

Exercise #5

23×57= \frac{2}{3}\times\frac{5}{7}=

Video Solution

Step-by-Step Solution

Let us solve the problem of multiplying the two fractions 23\frac{2}{3} and 57\frac{5}{7}.

  • Step 1: Identify the numerators and denominators. Here, the numerators are 22 and 55, and the denominators are 33 and 77.
  • Step 2: Multiply the numerators: 2×5=102 \times 5 = 10.
  • Step 3: Multiply the denominators: 3×7=213 \times 7 = 21.
  • Step 4: Put the results together in a new fraction: 1021\frac{10}{21}.
  • Step 5: Simplify the fraction if needed. In this case, 1021\frac{10}{21} is already in its simplest form as 1010 and 2121 have no common factors besides 11.

Therefore, the solution to the problem 23×57 \frac{2}{3} \times \frac{5}{7} is 1021\frac{10}{21}.

Answer

1021 \frac{10}{21}

Exercise #6

35×12= \frac{3}{5}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this problem, we need to multiply the fractions 35 \frac{3}{5} and 12 \frac{1}{2} .

  • Step 1: Multiply the numerators of the fractions. The numerators are 33 and 11, so 3×1=33 \times 1 = 3.
  • Step 2: Multiply the denominators of the fractions. The denominators are 55 and 22, so 5×2=105 \times 2 = 10.
  • Step 3: Combine the results from steps 1 and 2 to form the new fraction. The fraction becomes 310\frac{3}{10}.
  • Step 4: Simplify the fraction, if possible. In this case, 310\frac{3}{10} is already in its simplest form.

Therefore, the solution to 35×12\frac{3}{5} \times \frac{1}{2} is 310\frac{3}{10}.

Answer

310 \frac{3}{10}

Exercise #7

14×45= \frac{1}{4}\times\frac{4}{5}=

Video Solution

Step-by-Step Solution

To multiply fractions, we multiply numerator by numerator and denominator by denominator

1*4 = 4

4*5 = 20

4/20

Note that we can simplify this fraction by 4

4/20 = 1/5

Answer

15 \frac{1}{5}

Exercise #8

34×12= \frac{3}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the fractions 34 \frac{3}{4} and 12 \frac{1}{2} , follow these steps:

  • Step 1: Multiply the numerators.
    Multiply 3 3 and 1 1 , which gives 3 3 .
  • Step 2: Multiply the denominators.
    Multiply 4 4 and 2 2 , which gives 8 8 .
  • Step 3: Combine the results to form a new fraction.
    This results in 38 \frac{3}{8} .

The fraction 38 \frac{3}{8} is already in its simplest form, so we do not need to simplify further.

Therefore, the solution to the problem is 38 \frac{3}{8} .

Answer

38 \frac{3}{8}

Exercise #9

13×47= \frac{1}{3}\times\frac{4}{7}=

Video Solution

Step-by-Step Solution

To solve this problem, we need to multiply two fractions, 13 \frac{1}{3} and 47 \frac{4}{7} , by following these steps:

  • Step 1: Multiply the numerators:
    1×4=4 1 \times 4 = 4 .
  • Step 2: Multiply the denominators:
    3×7=21 3 \times 7 = 21 .
  • Step 3: Combine the results to form a new fraction:
    Thus, 13×47=421 \frac{1}{3} \times \frac{4}{7} = \frac{4}{21} .

This fraction, 421 \frac{4}{21} , is in its simplest form since there are no common factors between 4 and 21 other than 1.

Therefore, the solution to the problem is 421 \frac{4}{21} .

Answer

421 \frac{4}{21}

Exercise #10

25×12= \frac{2}{5}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this problem, let's multiply the fractions 25 \frac{2}{5} and 12 \frac{1}{2} .

Step 1: Multiply the numerators:
2×1=2 2 \times 1 = 2

Step 2: Multiply the denominators:
5×2=10 5 \times 2 = 10

Step 3: Construct the fraction using the products from steps 1 and 2:
210 \frac{2}{10}

Step 4: Simplify the fraction. We can divide both the numerator and the denominator by their greatest common divisor, which is 2:
2÷210÷2=15 \frac{2 \div 2}{10 \div 2} = \frac{1}{5}

Thus, the product of 25 \frac{2}{5} and 12 \frac{1}{2} is 15 \frac{1}{5} .

Therefore, the solution to the problem is 15 \frac{1}{5} .

Answer

15 \frac{1}{5}

Exercise #11

24×45= \frac{2}{4}\times\frac{4}{5}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the fractions 24\frac{2}{4} and 45\frac{4}{5}, follow these steps:

  • Step 1: Multiply the numerators. We have the numerators 22 and 44, so we calculate 2×4=82 \times 4 = 8.
  • Step 2: Multiply the denominators. We have the denominators 44 and 55, so we calculate 4×5=204 \times 5 = 20.
  • Step 3: Form the new fraction using the results from Steps 1 and 2. This gives us 820\frac{8}{20}.
  • Step 4: Simplify the fraction 820\frac{8}{20}. The greatest common divisor (GCD) of 88 and 2020 is 44.
  • Step 5: Divide both the numerator and the denominator by their GCD, 44: 8÷420÷4=25 \frac{8 \div 4}{20 \div 4} = \frac{2}{5}.

Therefore, the simplified product of 24\frac{2}{4} and 45\frac{4}{5} is 25\frac{2}{5}.

Answer

25 \frac{2}{5}

Exercise #12

23×14= \frac{2}{3}\times\frac{1}{4}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the fractions 23\frac{2}{3} and 14\frac{1}{4}, we will follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Simplify the resulting fraction if necessary.

Let's begin solving the problem:

Step 1: Multiply the numerators:
2×1=22 \times 1 = 2.

Step 2: Multiply the denominators:
3×4=123 \times 4 = 12.

Putting these together, the product of the fractions is:
212\frac{2}{12}.

Step 3: Simplify the fraction 212\frac{2}{12}. Both the numerator and the denominator are divisible by 2:
Divide the numerator and denominator by 2:
2÷212÷2=16 \frac{2 \div 2}{12 \div 2} = \frac{1}{6} .

Therefore, the product of 23\frac{2}{3} and 14\frac{1}{4} simplifies to 16\frac{1}{6}.

From the given choices, the correct answer is choice 3: 16 \frac{1}{6} .

Answer

16 \frac{1}{6}

Exercise #13

24×12= \frac{2}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this multiplication of fractions problem, we will follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Simplify the resulting fraction, if possible.

Now, let's carry out these steps:
Step 1: Multiply the numerators: 2×1=2 2 \times 1 = 2 .
Step 2: Multiply the denominators: 4×2=8 4 \times 2 = 8 .
Step 3: The resulting fraction is 28 \frac{2}{8} . We simplify by dividing the numerator and the denominator by their greatest common divisor, which is 2. So, 28=2÷28÷2=14\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}.

Therefore, the solution to the problem is 14 \frac{1}{4} .

Answer

14 \frac{1}{4}

Exercise #14

44×12= \frac{4}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

When we have a multiplication of fractions, we multiply numerator by numerator and denominator by denominator:

4*1 = 4
4*2 8

We can reduce the result, so we get:

4:4 = 1
8:4 2

And thus we arrived at the result, one half.

Similarly, we can see that the first fraction (4/4) is actually 1, because when the numerator and denominator are equal it means the fraction equals 1,
and since we know that any number multiplied by 1 remains the same number, we can conclude that the solution remains one half.

Answer

12 \frac{1}{2}

Exercise #15

23×34= \frac{2}{3}\times\frac{3}{4}=

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Multiply the numerators of the fractions. The numerators are 2 2 and 3 3 .
  • Step 2: Multiply the denominators of the fractions. The denominators are 3 3 and 4 4 .
  • Step 3: Simplify the resulting fraction if necessary.

Now, let us perform the multiplication:

Step 1: Multiply the numerators:

2×3=6 2 \times 3 = 6

Step 2: Multiply the denominators:

3×4=12 3 \times 4 = 12

So, the product of the fractions is:

612 \frac{6}{12}

Step 3: Simplify the fraction. To simplify, find the greatest common divisor (GCD) of 6 and 12, which is 6. Divide both numerator and denominator by 6:

6÷612÷6=12 \frac{6 \div 6}{12 \div 6} = \frac{1}{2}

Therefore, the simplified product of the fractions 23×34 \frac{2}{3} \times \frac{3}{4} is 12 \frac{1}{2} .

This matches choice 4, which is 12 \frac{1}{2} .

Answer

12 \frac{1}{2}

Exercise #16

68×56= \frac{6}{8}\times\frac{5}{6}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll multiply the fractions and simplify the result:

  • Step 1: Multiply the numerators together: 6×5=30 6 \times 5 = 30 .
  • Step 2: Multiply the denominators together: 8×6=48 8 \times 6 = 48 .
  • Step 3: Write the result as a single fraction: 3048 \frac{30}{48} .
  • Step 4: Simplify the fraction by finding the GCD of 30 and 48, which is 6.
  • Step 5: Divide both the numerator and the denominator by their GCD:

30÷648÷6=58 \frac{30 \div 6}{48 \div 6} = \frac{5}{8}

Therefore, the solution to the problem is 58 \frac{5}{8} .

Answer

58 \frac{5}{8}

Exercise #17

16×23= \frac{1}{6}\times\frac{2}{3}=

Video Solution

Step-by-Step Solution

To solve the problem, we will calculate the product of the fractions 16 \frac{1}{6} and 23 \frac{2}{3} using the standard method for multiplying fractions.

Step 1: Multiply the numerators.
The numerators are 1 and 2. Thus, the product of the numerators is 1×2=2 1 \times 2 = 2 .

Step 2: Multiply the denominators.
The denominators are 6 and 3. Thus, the product of the denominators is 6×3=18 6 \times 3 = 18 .

Step 3: Form the resulting fraction from the products obtained in the previous steps.
This gives us the fraction 218 \frac{2}{18} .

Step 4: Simplify the fraction.
To simplify 218 \frac{2}{18} , find the greatest common divisor (GCD) of 2 and 18, which is 2. Divide both the numerator and the denominator by their GCD:
2÷218÷2=19 \frac{2 \div 2}{18 \div 2} = \frac{1}{9}

Therefore, the simplified result of 16×23 \frac{1}{6} \times \frac{2}{3} is 19 \frac{1}{9} .

We compare this result with the multiple-choice options and confirm that the correct answer is:

19 \frac{1}{9}

Answer

19 \frac{1}{9}

Exercise #18

27×35= \frac{2}{7}\times\frac{3}{5}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Multiply the numerators.
  • Step 2: Multiply the denominators.
  • Step 3: Simplify the resulting fraction, if necessary.

Now, let's work through each step:
Step 1: Multiply the numerators: 2×3=6 2 \times 3 = 6 .
Step 2: Multiply the denominators: 7×5=35 7 \times 5 = 35 .
Thus, the product of the fractions is 635 \frac{6}{35} .

Therefore, the solution to the problem is 635 \frac{6}{35} .

Answer

635 \frac{6}{35}

Exercise #19

78×46= \frac{7}{8}\times\frac{4}{6}=

Video Solution

Step-by-Step Solution

The multiplication of fractions 78\frac{7}{8} and 46\frac{4}{6} requires the direct operation of multiplying numerators with numerators and denominators with denominators.

  • Multiply the numerators: 7×4=287 \times 4 = 28
  • Multiply the denominators: 8×6=488 \times 6 = 48
  • Form the resulting fraction: 2848\frac{28}{48}

Now, we need to simplify 2848\frac{28}{48}. Find the greatest common divisor (GCD) of 28 and 48, which is 4.

  • Divide both numerator and denominator by their GCD: 28÷448÷4=712\frac{28 \div 4}{48 \div 4} = \frac{7}{12}

Therefore, the solution to the problem is 712\frac{7}{12}.

Thus, the correct answer is 712\frac{7}{12}, which corresponds to choice 3.

Answer

712 \frac{7}{12}

Exercise #20

Solve the following exercise:

32×1×13= ? \frac{3}{2}\times1\times\frac{1}{3}=\text{ ?}

Video Solution

Step-by-Step Solution

According to the order of operations, we must solve the exercise from left to right since it contains only multiplication operations:

32×1=32 \frac{3}{2}\times1=\frac{3}{2}

32×13= \frac{3}{2}\times\frac{1}{3}=

Then, we will multiply the 3 by 3 to get:

12×1=12 \frac{1}{2}\times1=\frac{1}{2}

Answer

12 1\over2

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