Worksheet: Simplifying Monomials: Quotient Rule

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

Q11:

Simplify ๐‘ฅ๐‘ฅ๏Šญ๏Šฌ.

  • A๐‘ฅ๏Šง๏Šฉ
  • B1๐‘ฅ
  • C๐‘ฅ๏Šจ
  • D๐‘ฅ
  • E๐‘ฅ๏Šฉ

Q12:

Simplify ๐‘ฅ๐‘ฆร—๐‘ฅ๐‘ฆ๐‘ฅ๐‘ฆ๏Šช๏Šช๏Šจ๏Šช๏Šช๏Šฉ.

  • A๐‘ฅ๐‘ฆ๏Šจ๏Šซ
  • B(๐‘ฅ๐‘ฆ)๏Šง๏Šจ
  • C๐‘ฅ๐‘ฆ๏Šจ๏Ž ๏Žฅ๏Žข
  • D๐‘ฅ๐‘ฆ๏Šฌ๏Šฉ
  • E(๐‘ฅ๐‘ฆ)๏Šญ

Q13:

Simplify ๏€น14๐‘ฅรท7๐‘ฅ๏…+4๐‘ฅ๏Šง๏Šฆ๏Šช๏Šฌ, where ๐‘ฅโ‰ 0.

  • A6๐‘ฅ๏Šจ
  • B6๐‘ฅ๏Šฌ
  • C11๐‘ฅ๏Šฌ
  • D11๐‘ฅ๏Šจ
  • E6๐‘ฅ๏Šง๏Šช

Q14:

Simplify โˆ’4๐‘ฅ๐‘ฆร—๐‘ฅ๐‘ฆโˆ’2๐‘ฅ๐‘ฆ๏Šซ๏Šฉ๏Šฉ๏Šซ๏Šจ๏Šฉ.

  • A4๐‘ฅ๐‘ฆ๏Šฌ๏Šซ
  • B2๐‘ฅ๐‘ฆ๏Šง๏Šฆ๏Šซ
  • Cโˆ’4๐‘ฅ๐‘ฆ๏Šฌ๏Šซ
  • D2๐‘ฅ๐‘ฆ๏Šฌ๏Šง๏Šง
  • E2๐‘ฅ๐‘ฆ๏Šฌ๏Šซ

Q15:

Find the quotient of 21๐‘Ž๐‘7๐‘Ž๐‘๏Šฌ.

  • A3๐‘Ž๏Šซ
  • B3๐‘Ž๐‘๏Šซ
  • C3๐‘Ž๏Šฌ
  • D3๐‘Ž๐‘๏Šญ๏Šจ
  • E3๐‘Ž๐‘๏Šฌ

Q16:

Complete ๏€นโˆ’๐‘š๐‘›๏…=3๐‘š๐‘›โˆ’๐‘š๐‘›๏Šช๏Šช๏Šฎ๏Šจ๏Šฎ.

  • A๐‘š๐‘›๏Šช, 3๐‘š๐‘›๏Šช๏Šฉ
  • B๐‘š๐‘›๏Šช, 3๐‘š๐‘›๏Šฉ๏Šช
  • C๐‘š๐‘›๏Šช, 3๐‘š๐‘›๏Šฉ๏Šช
  • D3๐‘š๐‘›๏Šช, ๐‘š๐‘›๏Šช๏Šฉ

Q17:

Complete 4๐‘ฅ๐‘ฆ๏€น+โˆ’2๐‘ฅ๏…=โˆ’12๐‘ฅ๐‘ฆ+12๐‘ฅ๐‘ฆ+๏Šจ๏Šฉ๏Šฉ๏Šช๏Šฌ๏Šจ๏Šฌ.

  • A3๐‘ฅ๐‘ฆ๏Šจ๏Šฉ, โˆ’3๐‘ฆ๏Šฉ, โˆ’8๐‘ฅ๐‘ฆ๏Šซ๏Šฉ
  • Bโˆ’3๐‘ฅ๐‘ฆ๏Šฉ๏Šจ, 3๐‘ฆ๏Šฉ, โˆ’8๐‘ฅ๐‘ฆ๏Šฉ๏Šซ
  • Cโˆ’3๐‘ฅ๐‘ฆ๏Šจ๏Šฉ, 3๐‘ฆ๏Šฉ, โˆ’8๐‘ฅ๐‘ฆ๏Šซ๏Šฉ
  • Dโˆ’3๐‘ฅ๐‘ฆ๏Šจ๏Šฉ, 3๐‘ฆ, โˆ’8๐‘ฅ๐‘ฆ๏Šซ๏Šฉ

Q18:

Simplify ๐‘ฅ๐‘ฆ๐‘ฆร—๏€พ๐‘ฆ๐‘ฅ๏Š๏Šช๏Šจ๏Šญ๏Šช๏Šฉ.

  • A๐‘ฅ๐‘ฆ๏Šง๏Šช
  • B๐‘ฅ๐‘ฆ๏Šญ
  • C๐‘ฅ๐‘ฆ๏Šฉ๏Šญ
  • D๐‘ฅ๐‘ฆ๏Šฉ

Q19:

Simplify (โˆ’2๐‘)ร—๏€ผ23๐‘๏ˆ๏Šฉ๏Šจ.

  • Aโˆ’4๐‘3
  • Bโˆ’32๐‘9๏Žข๏Žก
  • Cโˆ’32๐‘9
  • Dโˆ’32๐‘3
  • Eโˆ’16๐‘9

Q20:

Simplify ๏€ป๐‘Ž๐‘๏‡ร—๐‘๐‘๏Šช๏Šฎ๏Šฌ.

  • A๐‘Ž๐‘๐‘๏Šง๏Šจ๏Šจ๏Šง๏Šฆ
  • B๐‘Ž๐‘๐‘๏Šช๏Šง๏Šจ๏Šฌ
  • C๐‘Ž๐‘๐‘๏Šช๏Šจ๏Šฌ
  • D๐‘Ž๐‘๐‘๏Šช๏Šช๏Šฌ
  • E๐‘Ž๐‘๐‘๏Šช๏Šญ๏Šฌ

Q21:

โˆ’40๐‘ฅรท=โˆ’5๐‘ฅ๏Šฏ๏Šญ.

  • A18๐‘ฅ๏Šจ
  • B8๐‘ฅ๏Šง๏Šฌ
  • C200๐‘ฅ๏Šง๏Šฌ
  • D8๐‘ฅ๏Šจ

Q22:

Simplify โˆ’20๐‘ฅโˆ’10๐‘ฅ.

Q23:

Simplify (3๐‘ฅ๐‘ฆ)(โˆ’๐‘ฅ๐‘ฆ)๏Šฉ๏Šจ๏Šฉ, where ๐‘ฅ๐‘ฆโ‰ 0, and evaluate this expression when ๐‘ฅ=โˆ’1 and ๐‘ฆ=โˆ’2.

  • Aโˆ’27๐‘ฅ๏Šฑ๏Šฉ, 27
  • Bโˆ’27๐‘ฅ๏Šฑ๏Šซ, 27
  • Cโˆ’3๐‘ฅ๏Šฑ๏Šฉ, 3
  • D27๐‘ฅ๏Šฑ๏Šฉ, โˆ’27

Q24:

Simplify โˆ’12๐‘ฅ๐‘ฆ6๐‘ฅ๐‘ฆ๏Šฌ๏Šซ๏Šช.

  • Aโˆ’2๐‘ฅ๐‘ฆ๏Šง๏Šฆ๏Šฌ
  • Bโˆ’2
  • Cโˆ’2๐‘ฅ๐‘ฆ๏Šฌ๏Šซ
  • Dโˆ’2๐‘ฅ๐‘ฆ๏Šจ๏Šช

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.