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Chapter 5: Problem 250

Simplify. \(\frac{9}{16}(21.96-9.8)\)

Short Answer

Expert verified
6.84

Step by step solution

01

- Simplify Inside the Parentheses

First, subtract 9.8 from 21.96. 21.96 - 9.8 = 12.16
02

- Multiply the Fraction by the Result

Now, multiply \(\frac{9}{16}\) by 12.16. \(\frac{9}{16} \times 12.16 \)
03

- Perform the Multiplication

Calculate \(\frac{9}{16} \times 12.16\): \(9 \times 12.16 = 109.44\) and \(109.44 \div 16 = 6.84\) Therefore, \(\frac{9}{16} \times 12.16 = 6.84\)

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Key Concepts

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

fraction multiplication
Fraction multiplication is a key concept in arithmetic. When you multiply fractions, you multiply the numerators (top numbers) together and the denominators (bottom numbers) together. If you are multiplying by a whole number or a decimal, you convert the whole number or decimal into a fraction first.

In this exercise, you multiply \(\frac{9}{16}\) by 12.16. To do this multiplication, you treat 12.16 as a whole number, convert it into a fraction, and then proceed.
  • Step 1: Convert 12.16 into a fraction. It's \(\frac{1216}{100}\).
  • Step 2: Simplify if necessary.
  • Step 3: Multiply the numerators: \(9 \times 1216 = 10944\).
  • Step 4: Multiply the denominators: \(16 \times 100 = 1600\).
  • Step 5: Simplify the resulting fraction \(\frac{10944}{1600}\) to get the final answer.
order of operations
Order of operations is crucial when solving mathematical expressions. It dictates the order in which you should perform different operations to correctly solve expressions. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) helps us remember the correct order.

In our exercise, the order of operations tells us to simplify inside the parentheses first. Here's a quick breakdown:
  • First, handle parentheses: \(21.96 - 9.8\). This gives us 12.16.
  • Next, move on to multiplication: \(\frac{9}{16} \times 12.16\).
Following PEMDAS ensures you get the correct solution!
basic arithmetic operations
Arithmetic operations are the fundamental building blocks of math. They include addition, subtraction, multiplication, and division. Understanding these operations is essential for simplifying expressions.

In our problem:
  • Subtraction: We first subtract 9.8 from 21.96 to get 12.16.
  • Multiplication: Then we multiply \(\frac{9}{16}\) by 12.16.
Simplifying involves breaking down complex problems using these basic operations step by step. Once you master these operations, solving math problems becomes a lot easier!

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Most popular questions from this chapter

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Describe a situation in your life in which you might need to find the area or circumference of a circle.

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