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Chapter 6: Problem 82

Write as a percent. Write the remainder in fractional form. $$1 \frac{1}{4}$$

Short Answer

Expert verified
So, \(1 \frac{1}{4}\) as a percent with remainder in fractional form is \(125\%\).

Step by step solution

01

Convert the mixed number to an improper fraction

A mixed number consists of a whole number and a proper fraction. To convert it to an improper fraction, multiply the denominator of the fractional part (which is 4 in this case) by the whole number (1 here) and then add the numerator of the fractional part (1 here). This gives the numerator of the improper fraction. The denominator remains the same. So, \(1 \frac{1}{4}\) turns into \(\frac{5}{4}\).
02

Convert the improper fraction to a decimal

To convert an improper fraction to a decimal, divide the numerator by the denominator. Here, divide 5 by 4. The result is 1.25.
03

Convert the decimal to a percentage

To convert a decimal to a percentage, multiply by 100. Here, \(1.25*100 = 125\%\).

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Key Concepts

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

Mixed Numbers
A mixed number combines a whole number with a proper fraction. It is often seen as a combination of a full set with a part of an additional set. For example, with the mixed number \(1 \frac{1}{4}\), the whole number is 1, and the fraction is \(\frac{1}{4}\). This means you have one whole and one out of four parts of another whole.
When you work with mixed numbers, it's crucial to understand the difference between the whole portion and the fractional part. Mixed numbers can be very handy in day-to-day life, like measuring ingredients in cooking or calculating distances in mixed units.
Improper Fractions
Improper fractions might seem strange at first, but they're just fractions where the numerator is greater than or equal to the denominator. This means the fraction represents a whole number or more.
To convert a mixed number like \(1 \frac{1}{4}\) into an improper fraction, you multiply the denominator by the whole number and add the numerator. For \(1 \frac{1}{4}\), you calculate \(1 \times 4 + 1 = 5\), resulting in the improper fraction \(\frac{5}{4}\).
Understanding improper fractions is critical because it allows them to be easily converted to decimals and other forms, facilitating various mathematical operations.
Decimal Conversion
Decimal conversion involves turning fractions, whether proper or improper, into a decimal form. This form is often easier to understand and compare because it aligns with the base-10 system used in everyday counting.
To convert a fraction like \(\frac{5}{4}\) to a decimal, you divide the numerator by the denominator. In this case, dividing 5 by 4 gives you 1.25. This shows that \(\frac{5}{4}\) is equivalent to 1.25 in decimal form.
Decimals are highly useful because they can easily be added, subtracted, and used in various calculations more seamlessly than fractions.
Percentage Conversion
Converting decimals to percentages is a straightforward process that makes it easier to understand proportions in a relatable way. A percentage represents a fraction out of 100, allowing people to intuitively grasp and compare quantities.
To turn a decimal like 1.25 into a percentage, multiply by 100. Calculating \(1.25 \times 100\) gives 125%.
This means our original mixed number, \(1 \frac{1}{4}\), which converted to an improper fraction of \(\frac{5}{4}\) and then to a decimal of 1.25, is equal to 125%. Using percentages is familiar in many contexts, such as sales, interest rates, and exam scores, making it an invaluable skill.

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Most popular questions from this chapter

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