/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 92 Write each word statement in sym... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 92

Write each word statement in symbols. One-third is less than or equal to three-ninths.

Short Answer

Expert verified
\frac{1}{3} \leq \frac{3}{9}

Step by step solution

01

Understand the given statement

The statement mentions 'one-third' and 'three-ninths' and that one-third is less than or equal to three-ninths. This needs to be translated into a mathematical inequality.
02

Translate 'one-third' into a fraction

'One-third' can be written as the fraction \(\frac{1}{3}\).
03

Translate 'three-ninths' into a fraction

'Three-ninths' can be written as the fraction \(\frac{3}{9}\).
04

Write the inequality

Combine the fractions into the given inequality: \(\frac{1}{3} \leq \frac{3}{9}\).
05

Simplify the fractions (optional)

Although not necessary for translation, simplifying \(\frac{3}{9} \) to \(\frac{1}{3} \) shows that \(\frac{1}{3} \leq \frac{1}{3} \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Fractions
Fractions are a way to express parts of a whole. A fraction consists of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction \(\frac{1}{3}\), the number 1 is the numerator, and the number 3 is the denominator.

Fractions represent division. So \(\frac{1}{3}\) can be thought of as 1 divided by 3. This means you take a whole and divide it into 3 equal parts, with 1 part being represented by the fraction.

Understanding fractions is essential for solving many mathematical problems, including those involving ratios, proportions, and sometimes inequalities.
Mathematical Symbols
Mathematical symbols are shorthand notations that simplify complex expressions. Using symbols makes it easier to write and understand mathematical statements.

In the given exercise, the symbol \( \leq \) is used to represent 'less than or equal to.' This means that the value on the left side is either smaller than or the same as the value on the right side.

Other common mathematical symbols include:
  • \( + \): Addition
  • \( - \): Subtraction
  • \( \times \): Multiplication
  • \( \div \): Division
  • \( = \): Equals
  • \( eq \): Not equal
  • \( > \): Greater than
  • \( < \): Less than
  • \( \geq \): Greater than or equal to


Knowing these symbols helps you translate word statements into mathematical ones and vice versa.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form. This often makes them easier to understand and compare.

To simplify a fraction, you find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number.

For example, in the fraction \(\frac{3}{9}\), both 3 and 9 can be divided by 3, their GCD. Dividing the numerator and the denominator by 3, we get:

\(\frac{3 \div 3}{9 \div 3} = \frac{1}{3}\).

So, \(\frac{3}{9}\) simplifies to \(\frac{1}{3}\). Simplification shows that sometimes different fractions can be equal, which is useful for understanding inequalities and other mathematical operations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A manufacturer has fixed costs of \(\$ 1000\) to produce widgets. Each widget costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the cost to make \(x\) widgets. (Hint: The cost will be the sum of the fixed cost and the cost per item times the number of items.)

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. Show that (a) \(4,114,107\) is divisible by \(9 \quad\) and \(\quad\) (b) \(2,287,321\) is not divisible by \(9 .\)

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(23,18,13,-4,\) and \(-8\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. See Example \(9 .\) 7 less than a number is 2

Perform each indicated operation. $$ \left(-\frac{3}{2}-0.75\right)-\left(0.5-\frac{1}{2}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.