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?

  • A 2 ๐‘ฅ ๐‘ฆ ๏Šฌ cm
  • B 2 ๐‘ฅ ๐‘ฆ ๏Šซ cm
  • C 2 ๐‘ฅ ๏Šซ cm
  • D 5 ๐‘ฅ ๏Šซ cm

Q2:

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

  • A 6 ๐‘ฅ ๐‘ฆ ๐‘ง
  • B 6 ๐‘ฅ ๐‘ง
  • C 6 ๐‘ฆ ๐‘ฅ ๐‘ง ๏Šจ
  • D 6 ๐‘ฅ ๐‘ง ๏Šจ
  • E 6 ๐‘ฅ ๐‘ง ๏Šจ

Q3:

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

  • A 6 ๐‘ฅ ๐‘ง ๏Šจ
  • B 6 ๐‘ฅ ๐‘ง ๏Šจ
  • C 6 ๐‘ฅ ๐‘ง
  • D 6 ๐‘ฅ ๐‘ฆ ๐‘ง
  • E 6 ๐‘ฆ ๐‘ฅ ๐‘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.

  • A 4 3 ๐‘ข ๏Šจ
  • B 3 4 ๐‘ข ๏Šจ
  • C 1 4 ๐‘ข ๏Šจ
  • D 5 4 ๐‘ข ๏Šจ
  • E 2 4 ๐‘ข ๏Šจ

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

  • A 3 4 ๐‘ข ร— ? ๐‘ข = 2 4 ๐‘ข ๏Šจ
  • B 3 4 ๐‘ข ร— ? ๐‘ข = 4 3 ๐‘ข ๏Šจ
  • C 3 4 ๐‘ข ร— ? ๐‘ข = 3 4 ๐‘ข ๏Šจ
  • D 3 4 ๐‘ข ร— ? ๐‘ข = 5 4 ๐‘ข ๏Šจ
  • E 3 4 ๐‘ข ร— ? ๐‘ข = 1 4 ๐‘ข ๏Šจ

What is the unknown length of the blue rectangle?

  • A 2 3 ๐‘ข
  • B 1 6 9 ๐‘ข
  • C ๐‘ข
  • D 1 3 ๐‘ข
  • E 5 3 ๐‘ข

Q5:

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

  • A ๐‘ฅ ๏Šฑ ๏Šง
  • B ๐‘ฅ ๏Šจ
  • C ๐‘ฅ ๏Ž  ๏Žก
  • D โˆ’ ๐‘ฅ
  • E ๐‘ฅ ๏Šฉ

Q6:

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

  • A 1 + ๐‘ฅ ๏Šฉ
  • B ๐‘ฅ โˆ’ ๐‘ฅ ๏Šฉ ๏Šฑ ๏Šฉ
  • C 1 + ๐‘ฅ
  • D ๐‘ฅ + ๐‘ฅ ๏Šฉ ๏Šฑ ๏Šฉ
  • E 1 + ๐‘ฅ ๏Šฑ ๏Šฉ

Q7:

Simplify ๐‘ฅ๐‘ฅ๏Šฉ๏Šฌ.

  • A ๐‘ฅ ๏Šฉ
  • B ๐‘ฅ ๏Šฑ ๏Šฏ
  • C ๐‘ฅ ๏Šฏ
  • D ๐‘ฅ ๏Šฑ ๏Šจ
  • E ๐‘ฅ ๏Šฑ ๏Šฉ

Q8:

Simplify ๐‘ฅรท๐‘ฅ๏Šฌ๏Šช.

  • A ๐‘ฅ ๏Šจ ๏Šช
  • B 2 ๐‘ฅ
  • C ๐‘ฅ ๏Šจ
  • D 2 ๐‘ฅ ๏Šจ

Q9:

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

  • A ๐‘ฅ ๏Šฉ
  • B โˆ’ 6 ๐‘ฅ ๏Šช
  • C โˆ’ 6 ๐‘ฅ
  • D ๐‘ฅ ๏Šช
  • E ๐‘ฅ

Q10:

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

  • A ๐‘ฅ ๏Šซ
  • B ๐‘ฅ ๏Šง ๏Šง
  • C ๐‘ฅ ๏Šช ๏Šญ
  • D ๐‘ฅ ๏Šช ๏Šง

Q11:

Simplify ๐‘ฅ๐‘ฅ๏Šญ๏Šฌ.

  • A ๐‘ฅ ๏Šง ๏Šฉ
  • B 1 ๐‘ฅ
  • C ๐‘ฅ ๏Šจ
  • D ๐‘ฅ
  • E ๐‘ฅ ๏Šฉ

Q12:

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

  • A ๐‘ฅ ๐‘ฆ ๏Šจ ๏Šซ
  • B ( ๐‘ฅ ๐‘ฆ ) ๏Šง ๏Šจ
  • C ๐‘ฅ ๐‘ฆ ๏Šจ ๏Ž  ๏Žฅ ๏Žข
  • D ๐‘ฅ ๐‘ฆ ๏Šฌ ๏Šฉ
  • E ( ๐‘ฅ ๐‘ฆ ) ๏Šญ

Q13:

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

  • A 6 ๐‘ฅ ๏Šจ
  • B 6 ๐‘ฅ ๏Šฌ
  • C 1 1 ๐‘ฅ ๏Šฌ
  • D 1 1 ๐‘ฅ ๏Šจ
  • E 6 ๐‘ฅ ๏Šง ๏Šช

Q14:

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

  • A 4 ๐‘ฅ ๐‘ฆ ๏Šฌ ๏Šซ
  • B 2 ๐‘ฅ ๐‘ฆ ๏Šง ๏Šฆ ๏Šซ
  • C โˆ’ 4 ๐‘ฅ ๐‘ฆ ๏Šฌ ๏Šซ
  • D 2 ๐‘ฅ ๐‘ฆ ๏Šฌ ๏Šง ๏Šง
  • E 2 ๐‘ฅ ๐‘ฆ ๏Šฌ ๏Šซ

Q15:

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

  • A 3 ๐‘Ž ๏Šซ
  • B 3 ๐‘Ž ๐‘ ๏Šซ
  • C 3 ๐‘Ž ๏Šฌ
  • D 3 ๐‘Ž ๐‘ ๏Šญ ๏Šจ
  • E 3 ๐‘Ž ๐‘ ๏Šฌ

Q16:

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

  • A ๐‘š ๐‘› ๏Šช , 3 ๐‘š ๐‘› ๏Šช ๏Šฉ
  • B ๐‘š ๐‘› ๏Šช , 3 ๐‘š ๐‘› ๏Šฉ ๏Šช
  • C ๐‘š ๐‘› ๏Šช , 3 ๐‘š ๐‘› ๏Šฉ ๏Šช
  • D 3 ๐‘š ๐‘› ๏Šช , ๐‘š ๐‘› ๏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.

  • A 3 ๐‘ฅ ๐‘ฆ ๏Šจ ๏Šฉ , โˆ’ 3 ๐‘ฆ ๏Šฉ , โˆ’ 8 ๐‘ฅ ๐‘ฆ ๏Šซ ๏Šฉ
  • B โˆ’ 3 ๐‘ฅ ๐‘ฆ ๏Šฉ ๏Šจ , 3 ๐‘ฆ ๏Šฉ , โˆ’ 8 ๐‘ฅ ๐‘ฆ ๏Šฉ ๏Šซ
  • C โˆ’ 3 ๐‘ฅ ๐‘ฆ ๏Šจ ๏Šฉ , 3 ๐‘ฆ ๏Šฉ , โˆ’ 8 ๐‘ฅ ๐‘ฆ ๏Šซ ๏Šฉ
  • D โˆ’ 3 ๐‘ฅ ๐‘ฆ ๏Šจ ๏Šฉ , 3 ๐‘ฆ , โˆ’ 8 ๐‘ฅ ๐‘ฆ ๏Šซ ๏Šฉ

Q18:

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

  • A ๐‘ฅ ๐‘ฆ ๏Šง ๏Šช
  • B ๐‘ฅ ๐‘ฆ ๏Šญ
  • C ๐‘ฅ ๐‘ฆ ๏Šฉ ๏Šญ
  • D ๐‘ฅ ๐‘ฆ ๏Šฉ

Q19:

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

  • A โˆ’ 4 ๐‘ 3
  • B โˆ’ 3 2 ๐‘ 9 ๏Žข ๏Žก
  • C โˆ’ 3 2 ๐‘ 9
  • D โˆ’ 3 2 ๐‘ 3
  • E โˆ’ 1 6 ๐‘ 9

Q20:

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

  • A ๐‘Ž ๐‘ ๐‘ ๏Šง ๏Šจ ๏Šจ ๏Šง ๏Šฆ
  • B ๐‘Ž ๐‘ ๐‘ ๏Šช ๏Šง ๏Šจ ๏Šฌ
  • C ๐‘Ž ๐‘ ๐‘ ๏Šช ๏Šจ ๏Šฌ
  • D ๐‘Ž ๐‘ ๐‘ ๏Šช ๏Šช ๏Šฌ
  • E ๐‘Ž ๐‘ ๐‘ ๏Šช ๏Šญ ๏Šฌ

Q21:

โˆ’ 4 0 ๐‘ฅ รท = โˆ’ 5 ๐‘ฅ ๏Šฏ ๏Šญ .

  • A 1 8 ๐‘ฅ ๏Šจ
  • B 8 ๐‘ฅ ๏Šง ๏Šฌ
  • C 2 0 0 ๐‘ฅ ๏Šง ๏Šฌ
  • D 8 ๐‘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.

  • A โˆ’ 2 7 ๐‘ฅ ๏Šฑ ๏Šฉ , 27
  • B โˆ’ 2 7 ๐‘ฅ ๏Šฑ ๏Šซ , 27
  • C โˆ’ 3 ๐‘ฅ ๏Šฑ ๏Šฉ , 3
  • D 2 7 ๐‘ฅ ๏Šฑ ๏Šฉ , โˆ’ 2 7

Q24:

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

  • A โˆ’ 2 ๐‘ฅ ๐‘ฆ ๏Šง ๏Šฆ ๏Šฌ
  • B โˆ’ 2
  • C โˆ’ 2 ๐‘ฅ ๐‘ฆ ๏Šฌ ๏Šซ
  • D โˆ’ 2 ๐‘ฅ ๐‘ฆ ๏Šจ ๏Šช

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