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Chapter 4: Problem 35

In the following exercises, rewrite the improper fraction as a mixed number. $$\frac{47}{15}$$

Short Answer

Expert verified
3 \(\frac{2}{15}\)

Step by step solution

01

鈥� Divide the numerator by the denominator

Divide 47 by 15. The quotient will be the whole number part of the mixed number, and the remainder will be the numerator of the fractional part.
02

鈥� Calculate the whole number part

47 divided by 15 equals 3 with a remainder of 2. So, the whole number part of our mixed number is 3.
03

鈥� Form the fractional part

The remainder from the division is 2, and the original denominator is 15. Therefore, the fractional part is \(\frac{2}{15}\).
04

鈥� Combine the whole number and the fraction

Combine the whole number part from Step 2 and the fractional part from Step 3. Therefore, \(\frac{47}{15}\) as a mixed number is 3 \(\frac{2}{15}\).

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Key Concepts

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

Understanding Division in Fractions
To grasp improper fractions and mixed numbers, it's essential to understand how division works in the context of fractions. An improper fraction like \(\frac{47}{15}\) has a numerator (the top number) that is larger than the denominator (the bottom number). When we divide 47 by 15, we are essentially trying to see how many whole groups of 15 can fit into 47.
For this exercise, 47 divided by 15 equals 3 whole parts with a remainder. So, the 3 becomes our whole number part of the mixed number.
Always remember:
  • The quotient (the result of division) gives us the whole number part of the mixed number.
  • The remainder tells us how much is left over, forming the new numerator of the fraction.
  • The original denominator remains the same.
Mixed Number Conversion
Converting an improper fraction to a mixed number involves a few straightforward steps. First, divide the given numerator by the denominator. For our example of \(\frac{47}{15}\), the division is 47 梅 15. This yields a quotient of 3, indicating that 15 fits into 47 three whole times.
The remainder of the division (47 - 3 * 15 = 2) becomes the new numerator, and our denominator stays as 15. Thus, our mixed number combines the whole number and the fraction: 3 \(\frac{2}{15}\).
Here is a summary of the process:
  • Divide the numerator by the denominator to get the whole number.
  • The remainder of this division becomes the new numerator of the fractional part.
  • The denominator remains unchanged from the original fraction.
Fraction Simplification Explained
After converting an improper fraction to a mixed number, it's important to check if the fractional part can be simplified. While \(\frac{2}{15}\) is already in its simplest form (since 2 and 15 have no common factors other than 1), it's good practice to always check.
To simplify a fraction:
  • Find the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by this GCD.
Simplification helps in reducing the fraction to its simplest form, making it easier to understand and work with in further calculations.
Remember: Not all fractions need simplification, but it鈥檚 always good practice to check!

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Most popular questions from this chapter

In the following exercises, simplify. $$ \frac{\frac{p}{2}}{\frac{q}{5}} $$

Convert the mixed number to an improper fraction. $$ 3 \frac{2}{7} $$

In the following exercises, determine whether the each number is a solution of the given equation. $$ y+\frac{3}{5}=\frac{5}{9} $$ $$ (a)y=\frac{1}{2} $$ $$ (b)y=\frac{52}{45} $$ $$ (c)y=-\frac{2}{45} $$

In the following exercises, simplify. $$ -\frac{3}{4} \div \frac{x}{3} $$

In the following exercises, perform the indicated operations and simplify. $$\frac{1}{5}+\frac{2}{3}$$
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