Examples with solutions for Division of Fractions: Using decimal fractions

Exercise #1

Solve the following:

69.510= \frac{69.5}{10}=

Step-by-Step Solution

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

  • Step 1: Understand the rule of division by 10

  • Step 2: Calculate by shifting the decimal point to the left

Now, let's work through each step:
Step 1: When dividing a number by 10, we shift the decimal point one position to the left.
Step 2: In the given fraction 69.510 \frac{69.5}{10} , we move the decimal point in 69.5 one place to the left, resulting in 6.95.

Therefore, the solution to the problem is 6.95 6.95 , which corresponds to choice 2.

Answer

6.95 6.95

Exercise #2

Solve the following:

99.933.3= \frac{99.9}{33.3}=

Step-by-Step Solution

To solve the problem 99.933.3 \frac{99.9}{33.3} , we will simplify it by transforming each decimal into a whole number to make calculation straightforward.

  • Step 1: Multiply both the numerator and the denominator by 1010 to eliminate decimals. This gives us:
    99.9×1033.3×10=999333 \frac{99.9 \times 10}{33.3 \times 10} = \frac{999}{333} .
  • Step 2: Notice that both 999999 and 333333 can be divided by 33 (a common factor). Divide each by 33:
    999÷3333÷3=333111 \frac{999 \div 3}{333 \div 3} = \frac{333}{111} .
  • Step 3: Notice again that 333333 and 111111 can be simplified further by dividing each by 111111 (another common factor).
    333÷111111÷111=31=3 \frac{333 \div 111}{111 \div 111} = \frac{3}{1} = 3 .

Therefore, the solution to the problem is 3 3 .

Answer

3 3

Exercise #3

Solve the following:

97.248.6= \frac{97.2}{48.6}=

Step-by-Step Solution

To solve the division 97.248.6 \frac{97.2}{48.6} , we will simplify by removing the decimals:

  • Step 1: Multiply both the numerator and denominator by 10 to eliminate the decimals since 97.2 and 48.6 each have one decimal place.
  • Step 2: The problem becomes equivalent to 972486 \frac{972}{486} .
  • Step 3: Simplifying 972486 \frac{972}{486} involves performing the division 972 ÷ 486.

By performing the division directly, we note that:

  • 972 divided by 486 equals 2 because 972 is exactly double 486.

Therefore, the solution to the problem is 2 2 .

Answer

2 2

Exercise #4

60.752×3= \frac{6}{0.75}-2\times3=

Video Solution

Step-by-Step Solution

To solve the expression 60.752×3 \frac{6}{0.75} - 2 \times 3 , we need to carefully follow the order of operations. The order of operations is often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, there are no parentheses or exponents, so we focus on multiplication, division, subtraction in the given order.

  • Step 1: Division
    First, perform the division: 60.75 \frac{6}{0.75} . To divide by a decimal, convert it to a fraction or adjust the dividend and divisor by a power of 10 to make the divisor a whole number. Here, 60.75 \frac{6}{0.75} becomes 6×1000.75×100=60075 \frac{6 \times 100}{0.75 \times 100} = \frac{600}{75} .
    Next, simplify 60075 \frac{600}{75} . Both numbers are divisible by 15:
    600÷15=40 600 \div 15 = 40 and 75÷15=5 75 \div 15 = 5 , so 60075=40÷5=8 \frac{600}{75} = 40 \div 5 = 8 .
  • Step 2: Multiplication
    Next, perform the multiplication: 2×3 2 \times 3 which equals 6 6 .
  • Step 3: Subtraction
    Finally, subtract the results of the previous operations: 86 8 - 6 . This gives 2 2 .

By carefully following the order of operations, the final answer to the expression 60.752×3 \frac{6}{0.75} - 2 \times 3 is 2 2 , which matches the correct answer provided.

Answer

2 2

Exercise #5

Solve the following:

2.45.1= \frac{2.4}{5.1}=

Step-by-Step Solution

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

  • Step 1: Convert each decimal number into a fraction
  • Step 2: Perform the division of these fractions using multiplication by the reciprocal
  • Step 3: Simplify the resulting fraction

Now, let's work through each step:

Step 1: Convert the decimals to fractions.

For the decimal 2.4, notice it is equal to 24 divided by 10, so it can be written as the fraction 2410\frac{24}{10}.

For the decimal 5.1, it is equal to 51 divided by 10, so it can be written as the fraction 5110\frac{51}{10}.

Step 2: Divide the fractions by multiplying by the reciprocal.

We have the division: 2410÷5110\frac{24}{10} \div \frac{51}{10}.

Instead of dividing, we multiply by the reciprocal: 2410×1051\frac{24}{10} \times \frac{10}{51}.

When multiplying, we multiply the numerators and the denominators:

24×1010×51=240510\frac{24 \times 10}{10 \times 51} = \frac{240}{510}.

Step 3: Simplify the resulting fraction.

Both 240 and 510 are divisible by 30:

240÷30510÷30=817\frac{240 \div 30}{510 \div 30} = \frac{8}{17}.

Thus, the fraction simplifies to 817\frac{8}{17}.

Therefore, the solution to the problem is 817 \frac{8}{17} .

Answer

817 \frac{8}{17}

Exercise #6

Solve the following:

11.33.8= \frac{11.3}{3.8}=

Step-by-Step Solution

To solve the problem 11.33.8 \frac{11.3}{3.8} , follow these steps:

  • Step 1: Convert 11.3 and 3.8 into fractions.
  • Step 2: Conduct the division using these fractions.
  • Step 3: Simplify and convert to a mixed number if appropriate.

Step 1: Convert 11.3 and 3.8 to fractions:
11.3=11310 11.3 = \frac{113}{10} since the decimal point signifies tenths place.
3.8=3810 3.8 = \frac{38}{10}

Step 2: Use the rule for fraction division, which is to multiply by the reciprocal:
11310÷3810=11310×1038=11338 \frac{113}{10} \div \frac{38}{10} = \frac{113}{10} \times \frac{10}{38} = \frac{113}{38} .

Step 3: Simplify 11338 \frac{113}{38} by performing the division:
113 divided by 38 gives a quotient of 2 and a remainder of 37.
Thus, 11338=23738 \frac{113}{38} = 2\frac{37}{38} .

Therefore, the division of 11.33.8 \frac{11.3}{3.8} results in 23738 2\frac{37}{38} .

Therefore, the solution to 11.33.8 \frac{11.3}{3.8} is 23738 \mathbf{2\frac{37}{38}} , which matches the second choice provided.

Answer

23738 2\frac{37}{38}