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Chapter 5: Problem 86

For Exercises \(83-88\) simplify by $$(78.2-60.2) \div \frac{9}{13}$$

Short Answer

Expert verified
26

Step by step solution

01

Subtract the numbers in the parentheses

Calculate the difference between 78.2 and 60.2:\[ 78.2 - 60.2 = 18 \]
02

Simplify the division with a fraction

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \( \frac{9}{13} \) is \( \frac{13}{9} \). So, the equation becomes:\[ 18 \times \frac{13}{9} \]
03

Perform the multiplication

Multiply 18 by \( \frac{13}{9} \):\[ 18 \times \frac{13}{9} = 18 \times 1.4444 = 26 \]
04

Final answer

The simplified expression is 26.

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Key Concepts

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

Basic Arithmetic
Understanding basic arithmetic is essential.
Arithmetic deals with basic number operations like addition, subtraction, multiplication, and division.
In this exercise, we start with subtraction:
  • Subtracting 60.2 from 78.2 is the first step.
  • When you subtract these numbers, you get 18.

Mastering basic arithmetic operations helps you handle more complex expressions effectively.
Always pay attention to the order of operations in arithmetic calculations.
Follow BODMAS/BIDMAS rules (Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication, Addition and Subtraction).
This ensures you perform operations in the correct sequence.
Fractions
Fractions are a big part of mathematics.
They represent a portion of a whole.
A fraction has a numerator (top number) and a denominator (bottom number).
In the given exercise, we deal with a fraction during division.
Dividing by a fraction means multiplying by its reciprocal.
The reciprocal of a fraction is obtained by swapping its numerator and denominator.
  • For the fraction \(\frac{9}{13}\), the reciprocal is \(\frac{13}{9}\).
  • This step changes our operation from division to multiplication.

Changing fractions into reciprocals and understanding these concepts are crucial skills.
They allow you to simplify expressions more easily and accurately.
Always remember to check if the fraction can be simplified further.
Multiplication
Multiplication is another key arithmetic operation.
It involves finding the product of two numbers.
When you multiply fractions, you multiply the numerators together and the denominators together.
  • In the step where we multiply 18 by \(\frac{13}{9}\), think about 18 as \(\frac{18}{1}\).
  • Multiply the numerators: \ 18 \times 13 = 234 \
  • Multiply the denominators: \ 1 \times 9 = 9 \
  • You get \(\frac{234}{9}\).
  • Simplify to get 26.

When working with fractions and multiplication, always simplify the fraction at the end.
This ensures the solution is as simple as possible.

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Most popular questions from this chapter

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