/*! 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 49 Convert to a mixed numeral. $$... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 49

Convert to a mixed numeral. $$ \frac{757}{100} $$

Short Answer

Expert verified
The mixed numeral is 7\frac{57}{100}.

Step by step solution

01

Divide the Numerator by the Denominator

Divide 757 by 100 to find the whole number part. \[\frac{757}{100} = 7.57\] The whole number part is 7.
02

Find the Remainder

Calculate the remainder of the division. \[757 - (7 \times 100) = 757 - 700 = 57\] The remainder is 57.
03

Write as a Mixed Numeral

Combine the whole number part and the fractional part. Use the remainder as the numerator and the original denominator. \[7\frac{57}{100}\]So, \(\frac{757}{100}\) as a mixed numeral is \(7\frac{57}{100}\).

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Key Concepts

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

Division
Division is a fundamental arithmetic operation where one number (the dividend) is divided by another (the divisor). In this exercise, we divide 757 by 100.
First, identify how many times the divisor (100) fits into the dividend (757) without exceeding it. This gives us the whole number part of the quotient. So, we divide:
\[\frac{757}{100} = 7.57\]
The whole number part of the quotient is 7. This means that 100 goes into 757 exactly 7 times without exceeding it.
Mixed Numbers
Mixed numbers consist of a whole number and a fraction. In the exercise, after performing the division, we get a whole number part which is 7. This number represents the whole part of the mixed numeral.
Next, we need the fractional part, which is derived from the remainder of the division. By combining the whole number with the fraction, we get a mixed number. It is written as: \[ \text{whole number} \frac{\text{remainder}}{\text{divisor}} \].
In this case, the mixed number is \[ 7\frac{57}{100} \] where 7 is the whole number and \[ \frac{57}{100} \] is the fraction.
Fractions
Fractions represent parts of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). The exercise starts with the fraction \( \frac{757}{100} \) which represents 757 parts of a whole that is divided into 100 equal parts.
When we convert an improper fraction to a mixed number, proper understanding of fractions is crucial. The mixed number \[ 7\frac{57}{100} \] splits the improper fraction into a whole number plus a fraction. The numerator (57) is the leftover part of the division, and the denominator (100) remains the same.
Understanding fractions helps in simplifying and comparing various numerical values in mathematics.
Remainders
Remainders are the leftover part after performing division. They play an important role when converting improper fractions to mixed numbers. In our exercise, after dividing 757 by 100, we find the whole number 7 and then calculate the remainder.
To find the remainder, we subtract the product of the whole number and the divisor from the dividend: \[757 - (7 \times 100) = 57\].
This remainder becomes the numerator for the fractional part of the mixed number. Therefore, the remainder of 57 is used in the fractional part of \[ 7\frac{57}{100} \].
Understanding remainders is key to accurately converting and simplifying numbers in mathematics.

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Most popular questions from this chapter

For a community project, an earth science class volunteered one hour per day for three days on the state highway beautification project. The students collected trash along a \(\frac{4}{5}-\mathrm{mi}\) stretch of highway the first day, a \(\frac{5}{8}\) -mi stretch the second day, and a \(\frac{1}{2}\) -mi stretch the third day. How many miles along the highway did they clean?

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{1}{13} $$

Find the average of \(3 \frac{1}{2}\) and \(9 \frac{3}{8}\).

Simplify. $$ \frac{\frac{3}{8}-\frac{1}{4}}{\frac{7}{8}-\frac{1}{2}} $$

Subtract and simplify. $$ \frac{11}{12}-\frac{2}{12} $$
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