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Chapter 2: Problem 103

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

Short Answer

Expert verified
After evaluating the fraction \(\frac{18}{3}\), the simplification results in 6.

Step by step solution

01

Simplify the numerator

Add the fractions in the numerator which are \(2 + \frac{1}{4}\). As 2 is equivalent to \(\frac{8}{4}\), the sum becomes \(\frac{8}{4} + \frac{1}{4} = \frac{9}{4}\).
02

Divide the numerator by the denominator

Now divide the simplified numerator \(\frac{9}{4}\) by the denominator which is \(\frac{3}{8}\). In dividing fractions, you multiply the first fraction by the reciprocal of the second fraction. So, the equation becomes \(\frac{9}{4} \times \frac{8}{3}\). The 8 in the numerator and 4 in the denominator can be simplified to 2 and 1 respectively. So the equation simplifies to \(\frac{9 \times 2}{1 \times 3}\).
03

Evaluate the multiplication

Conduct the multiplication in the numerator and the denominator and the equation becomes \(\frac{18}{3}\).

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Key Concepts

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

Fraction Addition
Understanding how to add fractions is an essential skill in mathematics. When you come across a problem that involves the sum of a whole number and a fraction, such as in the exercise \(2 + \frac{1}{4}\), the key is to have both numbers represented as fractions with the same denominator. Here's how to approach it:

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Most popular questions from this chapter

For Exercises 172 to \(177,\) insert \(+,-, \times,\) or \(\div\) into the square so that the statement is true. $$3.46 \square 0.24=0.8304$$

Convert the decimal to a fraction. $$0.125$$

Convert the fraction to a decimal. Place a bar over repeating digits of a repeating decimal. $$\frac{7}{12}$$

Convert the fraction to a decimal. Place a bar over repeating digits of a repeating decimal. $$1 \frac{1}{2}$$

A long-haul truck driver earns \(\$ .43\) for each mile driven. How much will a truck driver earn for driving \(1507 \mathrm{mi}\) from Boston to Miami?
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