Examples with solutions for Multiplication of Fractions: Complete the missing numbers

Exercise #1

23×?=16 \frac{2}{3}\times?=\frac{1}{6}

Video Solution

Step-by-Step Solution

To solve the equation 23×x=16\frac{2}{3} \times x = \frac{1}{6}, we need to find the value of xx by isolating it.

  • Step 1: Set the equation to solve for xx:
    23×x=16\frac{2}{3} \times x = \frac{1}{6}.
  • Step 2: Isolate xx by dividing both sides by 23\frac{2}{3}:
    x=16÷23x = \frac{1}{6} \div \frac{2}{3}.
  • Step 3: Performing the division by multiplying with the reciprocal:
    x=16×32x = \frac{1}{6} \times \frac{3}{2}.
  • Step 4: Simplify the expression:
    1×36×2=312=14\frac{1 \times 3}{6 \times 2} = \frac{3}{12} = \frac{1}{4}.

Thus, the number that satisfies the equation is 14 \frac{1}{4} .

Answer

14 \frac{1}{4}

Exercise #2

34×?=15 \frac{3}{4}\times?=\frac{1}{5}

Video Solution

Step-by-Step Solution

To solve the problem 34×?=15 \frac{3}{4} \times ? = \frac{1}{5} , we need to find the value of the question mark.

  • Step 1: Set up the equation for the unknown variable.
    We know 34×?=15 \frac{3}{4} \times ? = \frac{1}{5} . Thus, to isolate the question mark, we will divide both sides of the equation by 34 \frac{3}{4} .
  • Step 2: Perform the division.
    Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, ?=15÷34=15×43 ? = \frac{1}{5} \div \frac{3}{4} = \frac{1}{5} \times \frac{4}{3} .
  • Step 3: Simplify the multiplication.
    When multiplying fractions, multiply the numerators together and the denominators together:
    ?=1453=415 ? = \frac{1 \cdot 4}{5 \cdot 3} = \frac{4}{15} .

This calculation shows that the missing number is 415 \frac{4}{15} .

Therefore, the solution to the problem is 415 \frac{4}{15} .

Answer

415 \frac{4}{15}

Exercise #3

12×?=14 \frac{1}{2}\times?=\frac{1}{4}

Video Solution

Step-by-Step Solution

To solve the equation 12×?=14 \frac{1}{2} \times ? = \frac{1}{4} , we need to find the number that makes this equation true.

Let's perform the operations step-by-step:

  • Step 1: Start with the given equation: 12×x=14 \frac{1}{2} \times x = \frac{1}{4} .
  • Step 2: To isolate x x , divide both sides by 12 \frac{1}{2} . This gives us: x=14÷12 x = \frac{1}{4} \div \frac{1}{2} .
  • Step 3: Dividing by a fraction is the same as multiplying by its reciprocal. Thus, we have: x=14×21 x = \frac{1}{4} \times \frac{2}{1} .
  • Step 4: Multiply the fractions: x=1×24×1=24 x = \frac{1 \times 2}{4 \times 1} = \frac{2}{4} .
  • Step 5: Simplify the fraction: x=12 x = \frac{1}{2} .

Therefore, the missing number is 12\frac{1}{2}. This matches choice 4 from the given options.

Answer

12 \frac{1}{2}

Exercise #4

23×?=14 \frac{2}{3}\times?=\frac{1}{4}

Video Solution

Step-by-Step Solution

To solve this problem, we’ll follow the division of fractions method:

  • Step 1: Start with the given equation 23×?=14\frac{2}{3} \times ? = \frac{1}{4}.
  • Step 2: To isolate the unknown, divide both sides of the equation by 23\frac{2}{3}. This can be done by multiplying 14\frac{1}{4} by the reciprocal of 23\frac{2}{3}, which is 32\frac{3}{2}.
  • Step 3: The calculation becomes: 14×32=1×34×2=38\frac{1}{4} \times \frac{3}{2} = \frac{1 \times 3}{4 \times 2} = \frac{3}{8}.

Therefore, the solution to the problem is ?=38 ? = \frac{3}{8} . Hence, the correct choice is option 2.

Answer

38 \frac{3}{8}

Exercise #5

24×?=27 \frac{2}{4}\times?=\frac{2}{7}

Video Solution

Step-by-Step Solution

To solve the problem, let's use the equation provided:

24×x=27\frac{2}{4} \times x = \frac{2}{7}

Step 1: Isolate the missing fraction xx by dividing both sides by 24\frac{2}{4}.

x=2724x = \frac{\frac{2}{7}}{\frac{2}{4}}

Step 2: Simplify the division of the fractions. Recall that dividing by a fraction is the same as multiplying by its reciprocal.

x=27×42x = \frac{2}{7} \times \frac{4}{2}

Step 3: Simplify the multiplication by canceling common factors. Here, 42\frac{4}{2} simplifies to 2.

x=2×47×2=47x = \frac{2 \times 4}{7 \times 2} = \frac{4}{7}

Therefore, the missing fraction xx is 47\frac{4}{7}.

Thus, the correct answer is:

47 \frac{4}{7} (corresponds to choice 3)

Answer

47 \frac{4}{7}

Exercise #6

35×?=24 \frac{3}{5}\times?=\frac{2}{4}

Video Solution

Step-by-Step Solution

To solve this problem, we need to find the missing fraction x x such that 35×x=24 \frac{3}{5} \times x = \frac{2}{4} . We'll follow these steps:

  • Step 1: Simplify the fraction 24 \frac{2}{4} to 12 \frac{1}{2} .
  • Step 2: Set up the equation to solve for x x . This gives us 35×x=12 \frac{3}{5} \times x = \frac{1}{2} .
  • Step 3: Isolate x x by dividing both sides by 35 \frac{3}{5} , leading to x=1235 x = \frac{\frac{1}{2}}{\frac{3}{5}} .
  • Step 4: Simplify the complex fraction by multiplying by the reciprocal: x=12×53 x = \frac{1}{2} \times \frac{5}{3} .
  • Step 5: Calculate the multiplication: x=1×52×3=56 x = \frac{1 \times 5}{2 \times 3} = \frac{5}{6} .

Therefore, the solution to the problem is 56 \frac{5}{6} .

Answer

56 \frac{5}{6}

Exercise #7

56×?=13 \frac{5}{6}\times?=\frac{1}{3}

Video Solution

Step-by-Step Solution

To solve the equation 56×?=13 \frac{5}{6} \times ? = \frac{1}{3} , we need to find the missing number represented by "?".

We can solve this problem by using the following steps:

  • Step 1: Identify the equation we are working with:
    We have the equation 56×?=13 \frac{5}{6} \times ? = \frac{1}{3} .
  • Step 2: Isolate the unknown variable, "?":
    To do this, divide both sides of the equation by 56 \frac{5}{6} .
  • Perform the division:
    ?=1356=13×65? = \frac{\frac{1}{3}}{\frac{5}{6}} = \frac{1}{3} \times \frac{6}{5}
  • Step 3: Simplify the expression:
    Now, multiply 13 \frac{1}{3} by the reciprocal of 56 \frac{5}{6} :
    ?=1×63×5=615? = \frac{1 \times 6}{3 \times 5} = \frac{6}{15}
  • Simplify the fraction 615\frac{6}{15}:
    The greatest common divisor of 6 and 15 is 3, so divide both the numerator and the denominator by 3:
    ?=6÷315÷3=25? = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}

Therefore, the solution to the problem is 25 \frac{2}{5} .

Answer

25 \frac{2}{5}

Exercise #8

14×?=15 \frac{1}{4}\times?=\frac{1}{5}

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the known values and the variable to solve for.
  • Step 2: Rearrange the equation to isolate the unknown variable.
  • Step 3: Perform the arithmetic calculation to find the solution.

Now, let's work through each step:

Step 1: We have the equation 14×?=15 \frac{1}{4} \times ? = \frac{1}{5} . Our task is to find the value of the question mark (?).

Step 2: To isolate the question mark, we divide both sides of the equation by 14 \frac{1}{4} . This is equivalent to multiplying both sides by the reciprocal of 14 \frac{1}{4} , which is 4 4 . Thus, we have:

?=15×4 ? = \frac{1}{5} \times 4

Step 3: Perform the multiplication:

?=1×45×1=45 ? = \frac{1 \times 4}{5 \times 1} = \frac{4}{5}

Therefore, the number that satisfies the equation is 45 \frac{4}{5} .

The correct answer is choice 1: 45 \frac{4}{5} .

Answer

45 \frac{4}{5}

Exercise #9

57×?=13 \frac{5}{7}\times?=\frac{1}{3}

Video Solution

Step-by-Step Solution

To solve this problem, we'll proceed with the following steps:

  • Step 1: Set up the equation: 57×x=13 \frac{5}{7} \times x = \frac{1}{3} .
  • Step 2: Isolate x x by dividing both sides by 57 \frac{5}{7} , which is equivalent to multiplying both sides by the reciprocal, 75 \frac{7}{5} .
  • Step 3: Simplify the resulting expression to find x x .

Now, applying these steps:
Step 1: We have the equation 57×x=13 \frac{5}{7} \times x = \frac{1}{3} .
Step 2: Multiply both sides by 75 \frac{7}{5} to isolate x x :
x=13×75 x = \frac{1}{3} \times \frac{7}{5} .
Step 3: Simplify the calculation:
x=1×73×5=715 x = \frac{1 \times 7}{3 \times 5} = \frac{7}{15} .

Therefore, the solution to the problem is x=715 x = \frac{7}{15} .

Answer

715 \frac{7}{15}

Exercise #10

23×?=13 \frac{2}{3}\times?=\frac{1}{3}

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the equation 23×x=13\frac{2}{3} \times x = \frac{1}{3}.
  • Step 2: To isolate xx, we'll divide both sides by 23\frac{2}{3}.
  • Step 3: Perform the division by 23\frac{2}{3} by multiplying by its reciprocal.

Let's work through each step:

Step 1: We start with the equation 23×x=13\frac{2}{3} \times x = \frac{1}{3}.

Step 2: To solve for xx, divide both sides by 23\frac{2}{3}:

x=13÷23 x = \frac{1}{3} \div \frac{2}{3}

Step 3: Dividing by a fraction is equivalent to multiplying by the reciprocal:

x=13×32 x = \frac{1}{3} \times \frac{3}{2}

Calculate the multiplication:

x=1×33×2=36 x = \frac{1 \times 3}{3 \times 2} = \frac{3}{6}

x=12 x = \frac{1}{2}

Therefore, the solution to the problem is 12 \frac{1}{2} , which corresponds to choice .

Answer

12 \frac{1}{2}