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Chapter 5: Problem 17

\(\operatorname{Add} \frac{3}{4}+0.625\) (a) 1.375 (b) 1.875 (c) 0.46875 (d) 0.575

Short Answer

Expert verified
1.375 (option a)

Step by step solution

01

Convert Fraction to Decimal

First, convert the fraction \( \frac{3}{4} \) to a decimal. Divide the numerator by the denominator: \( 3 \div 4 = 0.75 \). So, \( \frac{3}{4} = 0.75 \).
02

Perform the Addition

Add the decimal representation of the fraction to the other given decimal value: \( 0.75 + 0.625 \).
03

Add Decimal Values

When adding the decimals \(0.75\) and \(0.625\), align the decimal points and add:\[\begin{array}{c}0.750 \+0.625 \\hline1.375\end{array}\]
04

Select the Correct Answer

The result of the addition is \(1.375\). Therefore, the correct answer is option (a) 1.375.

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Key Concepts

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

Decimal Addition
Adding decimals is similar to adding whole numbers. However, it involves careful alignment of the decimal points. Let's break down the process to make it simple:
  • Line up the numbers vertically, ensuring the decimal points are directly under one another.
  • If needed, fill in zeros to make sure both numbers have the same number of decimal places.
  • Add each column starting from the rightmost digit. Move to the left, carrying over any extra to the next column if necessary.
Imagine adding 0.75 and 0.625. Arrange them as follows:\[\begin{array}{c}0.750 \+0.625 \\hline\end{array}\]Start adding from the rightmost decimal place. This meticulous alignment ensures accuracy and helps avoid errors.
Numerator and Denominator
A fraction is made up of two main parts: the numerator and the denominator. Understanding these is essential for converting fractions to decimals.
  • The numerator is the top number, representing how many parts we have.
  • The denominator is the bottom number, showing into how many total parts the whole is divided.
In the fraction \(\frac{3}{4}\), 3 is the numerator and 4 is the denominator. To convert a fraction like \(\frac{3}{4}\) to a decimal, you divide the numerator by the denominator:\[3 \div 4 = 0.75\]This conversion is crucial for our calculations because it transforms the fraction into a form that is easier to work with when adding decimals.
Align Decimal Points
Aligning decimal points is a key step in performing accurate addition of decimal numbers. It ensures that each digit is correctly positioned by place value.
  • Start by writing the decimal numbers in a column format.
  • Make sure the decimal points of the numbers to be added are directly aligned, forming a vertical line.
  • If necessary, add zeros to ensure equal decimal places.
This step eliminates confusion and errors, as each digit is properly accounted for in its respective column. For example, when we align the numbers 0.750 and 0.625, it looks like this:\[\begin{array}{c}0.750 \+0.625 \\hline1.375\end{array}\]Not having aligned decimal points can lead to mistakes in addition, so always check before proceeding to add.

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Most popular questions from this chapter

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