Problem 69 - Prealgebra

Question

Write each fraction or mixed number as a decimal. \(\frac{3}{4}\)

Step-by-Step Solution

Answer

\(\frac{3}{4}\) is 0.75 as a decimal.

Step 1: Understanding the Fraction

The fraction given is \(\frac{3}{4}\), which means 3 divided by 4. We need to convert this fraction into a decimal form.

Step 2: Setting up the Division

To convert \(\frac{3}{4}\) into a decimal, set up a division problem where 3 is divided by 4. This can be set up as 3 ÷ 4.

Step 3: Performing the Division

Divide 3 by 4. Since 3 is less than 4, you add a decimal point and a zero to make it 30. 4 goes into 30 seven times (since 4 × 7 = 28).

Step 4: Finding the Remainder

Subtract 28 from 30 to get a remainder of 2. Bring down another 0 to make it 20. Divide 20 by 4.

Step 5: Completing the Division

4 goes into 20 exactly five times (since 4 × 5 = 20). Subtract 20 from 20 to get a remainder of 0, completing the division.

Step 6: Writing the Decimal

Combine the results of the division: 0.75. So, \(\frac{3}{4}\) as a decimal is 0.75.

Key Concepts

Division

Division is a fundamental mathematical operation that involves splitting a number (the dividend) into equal parts specified by another number (the divisor). In the context of fractions, division is used to convert a fraction into a decimal. When we have a fraction like \(\frac{3}{4}\), it means "3 divided by 4."

To carry out the division of 3 by 4:

• Set up the division by determining how many times the divisor (4) fits into the dividend (3).
• Since 3 is less than 4, you initially have a quotient of 0, but you can proceed by introducing a decimal point and a zero, turning 3 into 30.
• Practically, this changes the task to figuring out how many times 4 can fit into 30 evenly.

Now that we've expanded the problem with a decimal, continue dividing until you can no longer. Performing such small steps allow you to dive deeper into decimals when dividing fractions, making the conversion easier and more comprehendible.

Mixed Numbers

Mixed numbers are a combination of whole numbers and fractions, often used to express values between whole numbers. For example, if you had "1 and 3/4," it's a mixed number because it combines the whole number 1 with the fraction \(\frac{3}{4}\).

To convert mixed numbers to decimals, you follow a simple process:

• Convert the fractional part of the mixed number into a decimal, just as you would with a simple fraction. For instance, you'll convert \(\frac{3}{4}\) to 0.75.
• Add this decimal result to the whole number part of the mixed number. So 1 + 0.75 results in 1.75.

Understanding mixed numbers is essential for many real-life applications, such as measuring ingredients in recipes or determining distances where whole numbers are only part of the story.

Decimal Representation

Decimal representation makes it easier to visualize and compare values because it uses a base-10 system. This system is similar to how we naturally count and handle numbers in everyday math. Converting fractions to decimal representation involves using division to create a number with a more standardized form.

Why use decimal representations?

• Fractions like \(\frac{3}{4}\) can be converted into decimals (0.75), offering a clearer picture of size or proportion.
• Decimals are extremely useful when it comes to precise calculations, especially for financial transactions, scientific measurements, and statistics.

To convert any fraction to a decimal, perform the division of the numerator by the denominator, continuing until you reach a remainder of zero or a repeating pattern. Decimals allow for easier comparison and arithmetic operations, integrating seamlessly with percentages and whole numbers.