Problem 36 - Prealgebra

Question

Divide. Write your answers as decimals. $$\frac{115}{0.1}$$

Step-by-Step Solution

Answer

1150

Step 1: Understand the Problem

We need to divide the number 115 by 0.1 and express the answer as a decimal.

Step 2: Convert the Division Problem

Dividing by a decimal can be tricky. To simplify, remember that dividing by 0.1 is the same as multiplying by 10. Therefore, \( \frac{115}{0.1} = 115 \times 10 \).

Step 3: Perform the Multiplication

Now, multiply 115 by 10. \( 115 \times 10 = 1150 \).

Step 4: Write the Result as a Decimal

The product, 1150, is already a decimal number. Thus, \( \frac{115}{0.1} = 1150 \).

Key Concepts

Multiplication

Multiplication is one of the basic arithmetic operations that involves combining groups of equal quantities. It is essentially repeated addition. For example, when we multiply 115 by 10, it is similar to adding 115 ten times. Mathematically, this operation is expressed as \( 115 \times 10 \).When solving problems that involve multiplying by 10 or any other multiple of 10, there's a simple trick: you can add zeros to the end of the number you're multiplying. For instance, multiplying by 10 will shift the digits to the left on a number line, making the number 10 times larger. In this case, \( 115 \times 10 = 1150 \), where we've added one zero at the end of 115 to arrive at the solution.Multiplication is fundamental in arithmetic and plays a critical role when dividing by decimals, as it helps to simplify calculations by converting them into whole number operations.

Fractions

Fractions represent a part of a whole and are written in the form \( \frac{a}{b} \), where \( a \) is the numerator and \( b \) is the denominator. The exercise requires us to divide 115 by 0.1, which can initially be expressed as a fraction: \( \frac{115}{0.1} \).Dividing by a fraction is similar to multiplying by its reciprocal. The reciprocal of \( 0.1 \) is 10, because \( 0.1 \) represents \( \frac{1}{10} \). Thus, when we divide by \( 0.1 \), it is equivalent to multiplying by 10. This simplifies the fraction problem to a straightforward multiplication exercise: \( \frac{115}{0.1} = 115 \times 10 = 1150 \).Understanding fractions and the concept of reciprocals is essential for simplifying division problems involving decimals. It transforms complex operations into simpler ones, enhancing accuracy in calculations.

Prealgebra

Prealgebra is an introductory math level where foundational concepts are laid out to ease the transition into algebra. It includes operations with whole numbers, decimals, fractions, and introduces basic principles that will be used in algebra.In our exercise, understanding how to convert a division by a decimal into a multiplication problem is a key prealgebra skill. It involves conceptualizing the decimal \( 0.1 \) as a fraction and recognizing that dividing by \( 0.1 \) or any decimal is the same as multiplying by its reciprocal.Prealgebra teaches:- Arithmetic operations like addition, subtraction, multiplication, and division.- Fractions and decimals as numbers that describe parts of wholes.- Basic problem-solving skills that include translation of worded problems into mathematical equations.For example, converting \( \frac{115}{0.1} \) to \( 115 \times 10 \) shows the prealgebra ability to manipulate numbers to simplify operations, setting a foundation for more complex mathematical understanding.