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Chapter 2: Problem 1

Convert these improper fractions to mixed numbers. $$ \frac{21}{15} $$

Short Answer

Expert verified
Question: Convert the improper fraction 21/15 to a mixed number. Answer: The mixed number equivalent of the improper fraction 21/15 is 1 6/15.

Step by step solution

01

Divide the numerator by the denominator

Divide 21 by 15: $$ 21 \div 15 = 1 \text{ remainder } 6 $$
02

Write down the whole number quotient as the integer part

The whole number quotient is 1, so this will be the integer part of the mixed number.
03

Write down the remainder as the numerator of the fractional part

The remainder is 6, so this will be the numerator of the fractional part of the mixed number.
04

The denominator of the fraction remains the same

The denominator is 15, so it remains the same in the mixed number.
05

Result

The mixed number equivalent of the improper fraction \(\frac{21}{15}\) is \(1\frac{6}{15}\).

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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 is a number that combines both a whole number and a fraction. It's a practical way to express quantities that are not whole, making them easier to visualize and understand. For example, when you turn an improper fraction like \(\frac{21}{15}\) into \(1\frac{6}{15}\), you create a mixed number. This means you have 1 whole part plus a fractional part, \(\frac{6}{15}\).

Mixed numbers are helpful in everyday situations where you deal with quantities that are not quite whole, like when measuring ingredients for a recipe or dividing items among a group.
Numerator and Denominator
The terms 'numerator' and 'denominator' are key in understanding fractions. The numerator is the top number in a fraction, showing how many parts we have. The denominator is the bottom number, indicating how many parts make a whole.

In our example, the improper fraction \(\frac{21}{15}\) has 21 as the numerator and 15 as the denominator. When converting to a mixed number, the numerator (in this case the remainder of 6) becomes the numerator of the fractional part of the mixed number. Meanwhile, the denominator stays the same, maintaining its role as the total number of equal parts.
Division in Fractions
Converting improper fractions to mixed numbers involves division. You divide the numerator by the denominator. So, for the fraction \(\frac{21}{15}\), you divide 21 by 15. The result of this division tells us the whole number part of the mixed number, which is 1, because 15 fits into 21 once completely.

The remainder of the division, which is the leftover part after dividing, becomes the new numerator of the fractional part. In our example, 21 divided by 15 leaves a remainder of 6. The denominator remains unchanged, keeping the original value of 15. This way, you create a mixed number with a strong understanding of each component.

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Most popular questions from this chapter

Convert these improper fractions to mixed numbers. $$ \frac{16}{8} $$

Multiply or divide these fractions as indicated. Reduce the result to its lowest form. If the result is an improper fraction, convert it to a mixed number. $$ \frac{1}{2} \times \frac{3}{4} $$

Multiply or divide these fractions as indicated. Reduce the result to its lowest form. If the result is an improper fraction, convert it to a mixed number. $$ \frac{5}{8} \div \frac{1}{4} $$

Fill in the blank between each pair of fractions using greater than \((>)\), less than \((<)\), or equals \((=)\) symbols. \frac{1}{5} \quad \frac{2}{9}

Add or subtract these fractions as indicated. If the result is an improper fraction, convert it to a mixed number. $$ \frac{2}{3}-\frac{1}{3} $$
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