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Chapter 6: Problem 18

Perform the following operations. \(7+0.15 \div \frac{3}{30}\)

Short Answer

Expert verified
The result of the operation is 8.5.

Step by step solution

01

Simplify the Division

Begin by simplifying the division inside the expression \(0.15 \div \frac{3}{30}\). This can be rewritten as a multiplication: \(0.15 \times \frac{30}{3}\).
02

Calculate the Multiplication

Perform the multiplication inside the expression. \(0.15 \times \frac{30}{3} = 0.15 \times 10 = 1.5\).
03

Complete the Addition

Add the result of the multiplication to 7. \(7 + 1.5 = 8.5\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Division by Fractions
Division by fractions can initially seem challenging, but a helpful way to think about it is by changing division into multiplication. When dividing by a fraction, you multiply by its reciprocal (or upside-down version). For example, dividing by \(\frac{3}{30}\) becomes multiplying by \(\frac{30}{3}\). This creates a more straightforward problem, allowing easier computation.
To illustrate, consider the division \(0.15 \div \frac{3}{30}\):
  • Take the reciprocal of \(\frac{3}{30}\), which is \(\frac{30}{3}\).
  • Transform the division into multiplication: \(0.15 \times \frac{30}{3}\).
Breaking down complex operations into simpler multiplication steps often makes the math more manageable and less daunting.
Order of Operations
In mathematics, the order of operations is crucial for solving expressions accurately. The universally accepted method is known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). It dictates the sequence in which operations should be performed to ensure correct results.
In the given exercise:
  • First, handle the division: \(0.15 \div \frac{3}{30}\).
  • Then, move to other operations such as multiplication.
  • Finally, complete any addition or subtraction.
Always following the order of operations ensures every calculation step is logical and leads to the accurate solution, like in adding the final result (1.5) to 7, yielding 8.5.
Decimal Multiplication
Multiplying decimals may seem tricky due to decimal points, but it follows the same principles as integer multiplication, with one additional step: positioning the decimal point in the answer. A good approach is:
  • Ignore the decimal points initially and multiply the numbers as if they were whole.
  • Multiply: take \(0.15 \times 10\) which results in 1.5.
  • Count the total number of decimal places in the numbers being multiplied. In this case, it's two decimals (0.15 has two decimal places).
  • Place the decimal in the final answer so that it has the same number of decimal places.
These steps reveal that careful attention to decimal places will always lead to the correct answer.

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Most popular questions from this chapter

Convert each decimal to a proper fraction or a mixed number. 58.63

The decimal digit that appears three places to the right of the decimal point is in the ____________ position.

Perform each operation and simplify. \(57.51 \div 2.7\)

Perform each operation. $$ 0.21387 \div 0.19 $$

Perform each operation and simplify. \(14.007-5.061\)
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