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Chapter 1: Problem 7

Solve these multiplication and division problems. \(8 x y\) divided by \(y\)

Short Answer

Expert verified
8x

Step by step solution

01

Identify the expression

Start by identifying the expression given in the problem: \(8 x y \) divided by \(y\).
02

Write the division in fraction form

Rewrite the division problem as a fraction: \[ \frac{8xy}{y} \].
03

Simplify the fraction

Simplify the fraction by canceling out the common variable \(y\) in the numerator and the denominator. This gives: \[ \frac{8xy}{y} = 8x \].
04

Write the simplified result

The simplified result of the expression \(8xy\) divided by \(y\) is \(8x\).

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Key Concepts

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

Multiplication and Division in Algebra
Understanding how to handle multiplication and division in algebra is crucial. When you encounter a problem like multiplying or dividing algebraic expressions, follow these steps:
  • Identify the terms in the expression.
  • Rewrite the expression in an easier form, such as fraction for division.
  • Simplify where possible, using properties of algebra.
For instance, in the problem \(8xy divided by y\), we first rewrite it as a fraction \[\frac{8xy}{y}\].
By recognizing that dividing by a variable is the same as reducing the fraction, we see the expression can be simplified.
Simplifying Fractions
Simplifying fractions helps to make equations more manageable. To simplify:
  • Identify and label the numerator and the denominator.
  • Find common factors in both the numerator and the denominator.
  • Cancel those common factors to simplify the fraction.

For example, when simplifying \[\frac{8xy}{y}\], \(y\) is a common factor. Canceling \(y\) from both the numerator and the denominator results in \[\frac{8xy}{y} = 8x\]. This makes our equation simpler to work with.
Simplification can change a complex fraction into an easier algebraic expression.
Canceling Common Factors
Canceling common factors is a straightforward but powerful method. Here's how:
  • Determine the common factors in the numerator and the denominator.
  • Divide both the numerator and the denominator by these common factors.
  • Write the simplified fraction.
In the exercise \[\frac{8xy}{y}\], the variable \(y\) is present in both parts.
By canceling \(y\), we see that the expression reduces to \[8x\]. This method ensures we handle the algebraic terms correctly and keep our calculations accurate.

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Most popular questions from this chapter

Add or subtract each of these algebraic expressions. $$ 3 x-3 x $$

Using the abbreviations below, circle the number system or systems to which each number belongs. Some numbers belong to more than one number system. \(\mathrm{N}=\) Natural numbers \(\mathrm{W}=\) Whole numbers \(\ln =\) Integers \(\mathrm{Ra}=\) Rational numbers \(Ir =\) Irrational numbers \(Re =\) Real numbers $$ \frac{3}{8} $$

Compute the values of the following expressions. Keep in mind the Order of Operations. Remember: "Please Excuse My Dear Aunt Sally." $$ 3+12-5 \cdot 2 $$

Use the following abbreviations as instructed below. \(\mathrm{CA}=\) The Commutative Property of Addition \(\mathrm{CM}=\) The Commutative Property of Multiplication \(\mathrm{AA}=\) The Associative Property of Addition \(\mathrm{AM}=\) The Associative Property of Multiplication \(\mathrm{DM} / \mathrm{A}=\) The Distributive Property of Multiplication over Addition Next to each mathematical equation, write the abbreviation for the property the equation represents. Be careful-some of the problems are tricky. $$ 6(5+1)=6(5)+6(1) $$

Using the abbreviations below, circle the number system or systems to which each number belongs. Some numbers belong to more than one number system. \(\mathrm{N}=\) Natural numbers \(\mathrm{W}=\) Whole numbers \(\ln =\) Integers \(\mathrm{Ra}=\) Rational numbers \(Ir =\) Irrational numbers \(Re =\) Real numbers $$ 0 $$
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