Lesson Worksheet: Simplifying Monomials: Quotient Rule Mathematics

In this worksheet, we will practice dividing monomials involving single and multiple variables.

Q1:

What is the length of a rectangle whose area is 10๐‘ฅ๐‘ฆ๏Šฌ cm2 and whose width is 5๐‘ฅ๐‘ฆ cm?

  • A2๐‘ฅ๐‘ฆ๏Šฌ cm
  • B2๐‘ฅ๐‘ฆ๏Šซ cm
  • C2๐‘ฅ๏Šซ cm
  • D5๐‘ฅ๏Šซ cm

Q2:

What must 3๐‘ฆ be multiplied by to get 18๐‘ฅ๐‘ฆ๐‘ง๏Šจ?

  • A6๐‘ฅ๐‘ฆ๐‘ง
  • B6๐‘ฅ๐‘ง
  • C6๐‘ฆ๐‘ฅ๐‘ง๏Šจ
  • D6๐‘ฅ๐‘ง๏Šจ
  • E6๐‘ฅ๐‘ง๏Šจ

Q3:

What must 3๐‘ฆ be multiplied by to get 18๐‘ฅ๐‘ฆ๐‘ง๏Šจ?

  • A6๐‘ฅ๐‘ง๏Šจ
  • B6๐‘ฅ๐‘ง๏Šจ
  • C6๐‘ฅ๐‘ง
  • D6๐‘ฅ๐‘ฆ๐‘ง
  • E6๐‘ฆ๐‘ฅ๐‘ง๏Šจ

Q4:

The diagram shows a unit square of side ๐‘ข. The blue rectangle has an area of 12๐‘ข๏Šจ.

Express 12๐‘ข๏Šจ in terms of quarters of ๐‘ข๏Šจ.

  • A43๐‘ข๏Šจ
  • B34๐‘ข๏Šจ
  • C14๐‘ข๏Šจ
  • D54๐‘ข๏Šจ
  • E24๐‘ข๏Šจ

Which of the following is a multiplication equality giving the area of the blue rectangle?

  • A34๐‘ขร—?๐‘ข=24๐‘ข๏Šจ
  • B34๐‘ขร—?๐‘ข=43๐‘ข๏Šจ
  • C34๐‘ขร—?๐‘ข=34๐‘ข๏Šจ
  • D34๐‘ขร—?๐‘ข=54๐‘ข๏Šจ
  • E34๐‘ขร—?๐‘ข=14๐‘ข๏Šจ

What is the unknown length of the blue rectangle?

  • A23๐‘ข
  • B169๐‘ข
  • C๐‘ข
  • D13๐‘ข
  • E53๐‘ข

Q5:

Simplify ๐‘ฅรท๐‘ฅ๏Šจ, given that ๐‘ฅโ‰ 0.

  • A๐‘ฅ๏Šฑ๏Šง
  • B๐‘ฅ๏Šจ
  • C๐‘ฅ๏Ž ๏Žก
  • Dโˆ’๐‘ฅ
  • E๐‘ฅ๏Šฉ

Q6:

Which of the following is equal to ๐‘ฅ+1๐‘ฅ๏Šฉ๏Šฉ, where ๐‘ฅโ‰ 0?

  • A1+๐‘ฅ๏Šฉ
  • B๐‘ฅโˆ’๐‘ฅ๏Šฉ๏Šฑ๏Šฉ
  • C1+๐‘ฅ
  • D๐‘ฅ+๐‘ฅ๏Šฉ๏Šฑ๏Šฉ
  • E1+๐‘ฅ๏Šฑ๏Šฉ

Q7:

Simplify ๐‘ฅ๐‘ฅ๏Šฉ๏Šฌ.

  • A๐‘ฅ๏Šฉ
  • B๐‘ฅ๏Šฑ๏Šฏ
  • C๐‘ฅ๏Šฏ
  • D๐‘ฅ๏Šฑ๏Šจ
  • E๐‘ฅ๏Šฑ๏Šฉ

Q8:

Simplify ๐‘ฅรท๐‘ฅ๏Šฌ๏Šช.

  • A๐‘ฅ๏Šจ๏Šช
  • B2๐‘ฅ
  • C๐‘ฅ๏Šจ
  • D2๐‘ฅ๏Šจ

Q9:

Simplify ๏€น6๐‘ฅโˆ’3๐‘ฅ๏…รท3๐‘ฅ๏Šฉ๏Šฉ๏Šจ.

  • A๐‘ฅ๏Šฉ
  • Bโˆ’6๐‘ฅ๏Šช
  • Cโˆ’6๐‘ฅ
  • D๐‘ฅ๏Šช
  • E๐‘ฅ

Q10:

Simplify ๐‘ฅร—๐‘ฅ๐‘ฅ๏Šจ๏Šฉ๏Šฉ๏Šซ๏Šง๏Šญ, where ๐‘ฅโ‰ 0.

  • A๐‘ฅ๏Šซ
  • B๐‘ฅ๏Šง๏Šง
  • C๐‘ฅ๏Šช๏Šญ
  • D๐‘ฅ๏Šช๏Šง

This lesson includes 15 additional questions and 180 additional question variations for subscribers.

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