/*! 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 11 Write a word problem that illust... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 11

Write a word problem that illustrates \(\frac{3}{4}+\frac{1}{5}\), and find the answer.

Short Answer

Expert verified
You have eaten \( \frac{19}{20} \) of the pizza.

Step by step solution

01

Present the Problem

Imagine you have a pizza that is divided into pieces of equal size. You eat \( \frac{3}{4} \) of the pizza, and later, you decide to eat \( \frac{1}{5} \) more of it. How much of the pizza have you eaten in total?
02

Find a Common Denominator

To add the fractions \( \frac{3}{4} \) and \( \frac{1}{5} \), we need to express them with a common denominator. The least common denominator of 4 and 5 is 20.
03

Convert the Fractions

Convert \( \frac{3}{4} \) to \( \frac{15}{20} \) by multiplying the numerator and denominator by 5. Convert \( \frac{1}{5} \) to \( \frac{4}{20} \) by multiplying the numerator and denominator by 4.
04

Add the Fractions

Add the converted fractions: \( \frac{15}{20} + \frac{4}{20} = \frac{19}{20} \). This is the total amount of the pizza that you have eaten.

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.

least common denominator
When adding fractions, it's essential to find a common base number that can comfortably work for both fractions. This number is called the 'least common denominator' or LCD. For example, if you are adding \( \frac{3}{4} \) and \( \frac{1}{5} \), it's like trying to combine pieces of a puzzle cut into 4 and 5 parts, which don't naturally fit together. To make them fit, we search for the smallest number that 4 and 5 both divide into evenly. This number is 20.

Thus:
  • List the multiples of each denominator.
  • Identify the smallest common multiple, which is 20 in this example.
Once you have the LCD, you can convert each fraction to make their denominators the same.
fraction conversion
After finding the least common denominator (LCD), the next step is to convert each fraction so they both share this common denominator. Here, our task is to express \( \frac{3}{4} \) and \( \frac{1}{5} \) in terms of the common denominator 20. By doing so, we ensure that each fraction fits perfectly together, just like perfectly fitting puzzle pieces.

To convert:
  • Multiply both the numerator and denominator of \( \frac{3}{4} \) by 5, transforming it into \( \frac{15}{20} \).
  • Then, multiply both the numerator and denominator of \( \frac{1}{5} \) by 4, converting it to \( \frac{4}{20} \).
This conversion makes it easy to add these fractions since they now have a common ground to be summed up upon.
word problems
Word problems provide us with a real-life context to apply mathematical concepts. Take, for instance, the problem where you eat a part of a pizza and then eat some more later. Word problems like these show us how fractions work outside textbooks, offering a relatable and concrete scenario.

When tackling word problems:
  • Identify the quantities involved, clearly understanding which fractions represent these parts.
  • Set up your fractions according to the problem's requirements, like \( \frac{3}{4} \) of a pizza already eaten and \( \frac{1}{5} \) more to add.
  • Follow logical steps to add the fractions, such as finding the least common denominator and converting fractions for addition.
Solving word problems involves not just understanding fractions but also interpreting real-life situations mathematically.

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

Draw a segment that is \(12 \mathrm{~cm}\) in length. Find and label a point that is two-thirds the distance from one of the endpoints.

Evaluate each expression. Write your answer as a fraction and as a decimal, rounded to the nearest hundredth. Remember, if the third digit to the right of the decimal is 5 or higher, round up. a. \(\frac{5^{3}}{2^{3}}\) b. \(\left(\frac{5}{3}\right)^{2}\) c. \(\left(\frac{7}{3}\right)^{4}\) d. \(\left(\frac{9}{4}\right)^{3}\)

Do these calculations. Check your results with a calculator. a. \(-2+5-(-7)\) b. \((-3)^{2}-(-2)^{3}\) c. \(\frac{3}{5}+\frac{-2}{3}\) d. \(-0.2 \cdot 20+15\) e. \(4-6(-2)\) f. \(7-4(2-5)\) g. \(-2 \frac{1}{3}-4 \frac{1}{6}\)

Use a ruler to draw a segment that fits each description. a. one-third of a segment \(8.4 \mathrm{~cm}\) long b. three-fourths of a segment \(7.6 \mathrm{~cm}\) long c. two-fifths of a segment \(12.7 \mathrm{~cm}\) long

What is \(\frac{3}{2}-\frac{1}{5}+\left(\frac{3}{2}\right)^{2}\) ?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.