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Chapter 1: Problem 91

For each English sentence, write a mathematical expression and simplify. Divide 6 into 42.

Short Answer

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Step by step solution

01

Understand the Problem

The sentence 'Divide 6 into 42' means to see how many times 6 fits into 42 or mathematically divide 42 by 6.
02

Write the Mathematical Expression

The mathematical expression for dividing 42 by 6 is \( \frac{42}{6} \).
03

Simplify the Expression

Simplify the fraction \( \frac{42}{6} \) by dividing the numerator by the denominator: \( \frac{42}{6} = 7 \).

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Key Concepts

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

Basic Arithmetic
Basic arithmetic is the foundation of all math concepts. It includes addition, subtraction, multiplication, and division. These operations help you understand more complex math concepts in the future. To solve the exercise 'Divide 6 into 42,' you need to know about division, one of the four basic arithmetic operations. By using division, you can find out how many times one number fits into another. Think of division as a way to evenly split a number into smaller, equal parts. For instance, when you divide 42 by 6, you're figuring out how many groups of 6 can be made from 42.
Fractions and Division
Fractions and division are closely related. In fact, a fraction is another way of showing a division problem. The fraction \(\frac{42}{6}\) means that you are dividing 42 by 6. The number on top of the fraction (42) is called the numerator, and the number on the bottom (6) is the denominator. When you read a fraction, you're essentially reading a division problem. For example, \(\frac{1}{2}\) means 1 divided by 2, or one half of a whole. Fractions help make complex division problems more manageable. Knowing this can make division and other math operations easier to understand.
Simplifying Expressions
Simplifying expressions makes math problems less complicated and easier to solve. When you simplify \(\frac{42}{6}\), you're looking for the simplest form of that fraction. Begin by dividing the numerator (42) by the denominator (6). The result is 7 because 6 goes into 42 exactly 7 times. To simplify fractions, always look for common factors. For this example, the common factor is the number you are dividing by. Simplifying doesn't just apply to fractions鈥攊t's useful for various math problems. Once you simplify, your expression is easier to understand and work with, making your calculations smoother and more efficient.

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