/*! 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 17 $$8+12 \cdot \frac{3}{4}$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 17

$$8+12 \cdot \frac{3}{4}$$

Short Answer

Expert verified
The simplified expression for \(8 + 12 \cdot \frac{3}{4}\) is 17.

Step by step solution

01

Perform the multiplication

First, we need to perform the multiplication operation between 12 and the fraction \(\frac{3}{4}\). To do this, we simply multiply 12 by the numerator (3) and keep the same denominator (4): $$12 \cdot \frac{3}{4} = \frac{12 \cdot 3}{4}$$
02

Simplify the multiplication

Now, we can simplify the multiplication: $$\frac{12 \cdot 3}{4} = \frac{36}{4}$$
03

Simplify the fraction

Next, we can simplify the fraction \(\frac{36}{4}\) by dividing the numerator and denominator by their greatest common divisor, which is 4: $$\frac{36}{4} = \frac{36 \div 4}{4 \div 4} = \frac{9}{1} = 9$$
04

Perform the addition

Finally, we can perform the addition operation between 8 and 9: $$8 + 9 = 17$$ So, the simplified expression is equal to 17.

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.

Multiplication in Fractions
When multiplying a whole number with a fraction, like 12 and \( \frac{3}{4} \), it's important to focus on the numerator first. Here's how it works:
  • Multiply the whole number by the numerator of the fraction: \( 12 \cdot 3 = 36 \).
  • The denominator remains the same: \( \frac{36}{4} \).
After finding the product, you get a new fraction. By keeping the denominator unchanged during multiplication, you make the calculation manageable.
This step sets up the fraction for the simplification process, which is crucial for solving problems involving fractions.
Simplifying Fractions
Simplifying fractions is about reducing them to their simplest form, where the numerator and denominator have no common factors other than 1. Here鈥檚 how:
  • Identify the greatest common divisor (GCD) of the numerator and denominator. For \( \frac{36}{4} \), the GCD is 4.
  • Divide both the numerator and the denominator by the GCD: \( \frac{36 \div 4}{4 \div 4} = \frac{9}{1} \).
  • Simplifying gives you a whole number if the denominator becomes 1. Here it simplifies to 9.
The purpose of simplifying is to make calculations easier and solutions more understandable. It ensures that fractions are as simple as they can be, making further operations more straightforward.
Addition of Integers
Addition of integers is often the final step in solving arithmetic expressions. After simplifying fractions, the integers can be combined:
  • Consider each integer in the equation. In our example, they are 8 and 9.

  • Add them up: \( 8 + 9 = 17 \).
Adding integers is straightforward: just combine the numbers to get the sum. This is especially easy once fractions have been simplified to whole numbers. Understanding this basic operation is essential, as it is frequently used in algebra and everyday math calculations.

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

Decide if each statement is true or false. $$-8.1>-8.5$$

Write a mathematical expression for each and simplify. The product of \(-12\) and 6

Write a mathematical expression for each and simplify. The quotient of \(-100\) and 4 decreased by the sum of \(-7\) and 2

Applications of Perimeter, Area, and Volume: Use 3.14 for \(\pi\) and include the correct units. The Florida Highway Department must order four concrete columns for a bridge. Each column is a right circular cylinder with a radius of \(2 \mathrm{ft}\) and a height of \(14 \mathrm{ft}\). The cost of the concrete is \(\$ 3.10 / \mathrm{ft}^{3}\). Find the cost of the four columns. (Round to the nearest dollar.)

Write an expression for each and simplify. Answer the question with a complete sentence. The median income for a male 25 years or older with a bachelor's degree in 2004 was \(\$ 51,081 .\) In \(2005,\) the median income was \(\$ 51,700 .\) What was the difference in the median income from 2004 to \(2005 ?\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.