/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 76 Calculate. \(55 \frac{3}{5}-12... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 76

Calculate. \(55 \frac{3}{5}-12.22\)

Short Answer

Expert verified
43.38

Step by step solution

01

Convert Mixed Fraction to Decimal

First, convert the mixed number \(55 \frac{3}{5}\) to a decimal. The fraction \(\frac{3}{5}\) can be written as 0.6. So, \(55 \frac{3}{5} = 55 + 0.6 = 55.6\).
02

Perform the Subtraction

Subtract 12.22 from 55.6. This can be set up as: \(55.6 - 12.22\).
03

Calculate the Result

Perform the subtraction: \(55.6 - 12.22 = 43.38\).

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Key Concepts

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

Mixed Fractions
Mixed fractions are numbers made up of a whole number and a fraction. For example, in the exercise, the mixed fraction is written as \(55 \frac{3}{5}\).
To work with mixed fractions, especially in arithmetic operations, it's often easier to convert them to decimals.
In our example, the fraction part \(\frac{3}{5}\) is converted to a decimal by dividing the numerator (3) by the denominator (5) resulting in 0.6.
Therefore, \(55 \frac{3}{5} = 55 + 0.6 = 55.6\).
This is useful because decimals are sometimes simpler to handle in basic arithmetic operations like addition, subtraction, multiplication, and division.
Decimal Conversion
Decimal conversion involves changing a fraction or a mixed fraction into a decimal form. This makes solving problems easier.
To convert a fraction like \(\frac{3}{5}\) to a decimal, divide the top number (3) by the bottom number (5), which gives 0.6.
So, \(55 \frac{3}{5}\) can be written as 55.6.
This step is crucial as it simplifies the calculation process in arithmetic operations like subtraction, ensuring accuracy and ease.
Once you have all numbers in decimal form, you can proceed with standard subtraction, addition, multiplication, or division processes.
Basic Arithmetic
Basic arithmetic refers to the fundamental operations of mathematics: addition, subtraction, multiplication, and division.
In our exercise, we are performing a subtraction.
First, we converted the mixed fraction to a decimal: \(55.6\).
Next, we subtract another decimal number: \(12.22\).
Set up the operation as \(55.6 - 12.22\).
Align the decimal points and subtract as you would with whole numbers:
  • Borrow if needed
  • Subtract each column from right to left
  • The result is \(43.38\)

Following these steps carefully will ensure you get the correct result and understand the arithmetic involved.

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