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Chapter 4: Problem 59

How many thirds are in 10?

Short Answer

Expert verified
There are 30 thirds in 10.

Step by step solution

01

Understand the Problem

The goal is to determine how many one-third portions can fit into the number 10. This requires dividing the number 10 by one third.
02

Convert the Division of Fractions

To divide by a fraction, multiply by its reciprocal. The reciprocal of \(\frac{1}{3}\) is 3. Thus, the problem becomes: \(\frac{10}{\frac{1}{3}} = 10 \times 3\).
03

Perform the Multiplication

Multiply 10 by 3 to get \(\text{10} \times 3 = 30\).

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Key Concepts

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

Fraction Division
When dividing fractions, you are essentially figuring out how many times one fraction fits into another. In the given exercise, you are working with a whole number and a fraction.
For instance, you need to find out how many \(\frac{1}{3}\)s are in 10.
If you visualize a whole number, think of it divided into smaller parts, just like slicing a pizza into smaller pieces.
Reciprocal Multiplication
One essential trick in fraction division is to use reciprocal multiplication. The reciprocal of a fraction is simply flipping the numerator and the denominator.
For example, the reciprocal of \(\frac{1}{3}\) is 3/1, or just 3.
When dividing a number by a fraction like \(\frac{1}{3}\), you multiply that number by the reciprocal of the fraction. So, \(\frac{10}{\frac{1}{3}}\) converts to \(\frac{10}{1} \times \frac{3}{1} = 10 \times 3\).
This switch makes the math much easier to handle!
Basic Arithmetic
Now let's get into basic arithmetic.
Multiplication is straightforward: just multiply the numbers directly. From the problem, you learned to multiply 10 by 3.
The result is \(\text{10} \times 3 = 30\).
So, 10 divided by \(\frac{1}{3}\) equals 30.
Basic arithmetic skills like addition, subtraction, multiplication, and division are crucial for solving fraction problems easily and efficiently.

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Most popular questions from this chapter

Raymond read 720 pages of a 792 -page book. His roommate, Travis, read 540 pages from a 660 -page book. a. What fractional part of the book did each person read? b. Which of the roommates read a greater fraction of his book?

Convert the improper fraction to a mixed number. $$\frac{51}{10}$$

Divide. Write the quotient as a mixed number. $$4257 \div 23$$

Simplify. $$-\left(-\frac{1}{4}\right)$$

Which expressions are equivalent to \(\frac{-9}{10} ?\) \(\begin{array}{cccc}\text { a. } \frac{9}{10} & \text { b. }-\frac{9}{10} & \text { c. } \frac{9}{-10} & \text { d. } \frac{-9}{-10}\end{array}\)
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