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Chapter 3: Problem 98

Evaluate. \(\frac{4}{3} \cdot 15\)

Short Answer

Expert verified
20

Step by step solution

01

Understand the Problem

The problem asks to evaluate the expression \(\frac{4}{3} \cdot 15\). This means we need to multiply the fraction \(\frac{4}{3}\) by the whole number 15.
02

Simplify the Multiplication

To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number. In this case, multiply 4 by 15:\(\frac{4}{3} \cdot 15 = \frac{4 \cdot 15}{3}\)
03

Perform the Multiplication

Calculate the multiplication of numbers in the numerator: \(4 \cdot 15 = 60\)
04

Simplify the Resulting Fraction

Now, place the result of the multiplication over the original denominator. Simplify if necessary.\(\frac{60}{3}\)
05

Divide and Simplify

Finally, divide the numerator by the denominator to get the final answer: \( \frac{60}{3} = 20 \)

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Key Concepts

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

Evaluating Expressions
When we are asked to evaluate an expression such as \(\frac{4}{3} \cdot 15\), we need to perform a series of steps to find the value of the expression. Evaluating expressions involves understanding the mathematical operations required and correctly applying them.
In this case, the operation is multiplication. We have a fraction and a whole number that need to be multiplied.
Multiplie fractions and whole numbers by following these steps:
  • Multiply the numerator (the top number of the fraction) by the whole number.
  • Keep the same denominator (the bottom number of the fraction).
  • Simplify the resulting fraction if necessary.
Understanding these steps will help you confidently approach similar problems and correctly evaluate expressions involving fractions and whole numbers.
Simplifying Fractions
Simplifying fractions is an important skill in mathematics. It involves reducing a fraction to its simplest form, where the numerator and denominator are the smallest possible whole numbers that retain the same value as the original fraction.
To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both by this number.
  • For example, if we have \(\frac{60}{3}\), our goal is to simplify this fraction.
  • First, check if the numerator (60) and the denominator (3) have any common factors. Since 3 divides 60 evenly, we use 3 as the GCD.
  • Divide both the numerator and the denominator by their GCD: \(\frac{60 \/ 3}{3 \/ 3}\).
  • The simplified fraction is \(\frac{20}{1} = 20\).
Simplifying makes fractions easier to understand and work with.
Whole Numbers
Whole numbers are the simple numbers that we use in everyday counting and operations. They are non-negative integers, including zero (0, 1, 2, 3, and so on).
In many mathematical expressions, whole numbers are often involved, and understanding their properties helps in computations.
When multiplying a fraction by a whole number:
  • Start with the numerator of the fraction.
  • Multiply it by the whole number directly.
  • The denominator stays the same, maintaining the fractional part of the expression until any necessary simplifications.
In our example \(\frac{4}{3} \cdot 15\), 15 is a whole number.
We multiply 4 by 15 to get 60, keeping the denominator 3 until we simplify \(\frac{60}{3}\), resulting in 20.
This understanding of whole numbers and their interaction with fractions is crucial for solving complex mathematical problems.

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Most popular questions from this chapter

Use the slope formula to find the slope of the line that passes through the points. \((1,8) ;(3,15)\)

(a) find the \(y\)-intercept. (b) find the \(x\)-intercept. (c) use the slope formula to find the slope of the line. \(-8 x+3 y=48\)

(a) find the \(y\)-intercept. (b) find the \(x\)-intercept. (c) use the slope formula to find the slope of the line. \(x-3 y=27\)

(a) find three solutions of the equation. (b) graph the equation. \(y=\frac{2}{5} x-3\)

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