It looks like you've uploaded a worksheet titled
"GCF - Monomials" that asks students to find the
greatest common factor (GCF) for pairs of monomials. Since I can't view images directly, I'll help you solve this step by step based on the typical format of such worksheets.
Let’s assume the worksheet has problems like these (common types):
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Example Problems (Typical Format):
1. \( 6x^2 \) and \( 12x^3 \)
2. \( 18a^2b \) and \( 24ab^2 \)
3. \( 15m^3n^2 \) and \( 20m^2n^3 \)
4. \( 12x^2y \) and \( 18xy^2 \)
5. \( 24p^2q \) and \( 36pq^2 \)
6. \( 16r^3s \) and \( 24rs^2 \)
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How to Find the GCF of Two Monomials:
To find the
GCF of two monomials, follow these steps:
1.
Find the GCF of the coefficients (the numbers).
2.
For each variable, take the
lowest exponent that appears in both terms.
3. Multiply the GCF of the coefficients with the variables raised to their lowest exponents.
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Let's Solve Each Problem Step-by-Step
#### 1. \( 6x^2 \) and \( 12x^3 \)
- Coefficients: GCF of 6 and 12 =
6
- Variables: Both have \( x \), lowest exponent is \( x^2 \)
- GCF = \( 6x^2 \)
✔ Answer:
\( 6x^2 \)
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#### 2. \( 18a^2b \) and \( 24ab^2 \)
- Coefficients: GCF of 18 and 24 =
6
- \( a \): lowest exponent = \( a^1 \)
- \( b \): lowest exponent = \( b^1 \)
- GCF = \( 6ab \)
✔ Answer:
\( 6ab \)
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#### 3. \( 15m^3n^2 \) and \( 20m^2n^3 \)
- Coefficients: GCF of 15 and 20 =
5
- \( m \): min exponent = \( m^2 \)
- \( n \): min exponent = \( n^2 \)
- GCF = \( 5m^2n^2 \)
✔ Answer:
\( 5m^2n^2 \)
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#### 4. \( 12x^2y \) and \( 18xy^2 \)
- Coefficients: GCF of 12 and 18 =
6
- \( x \): min exponent = \( x^1 \)
- \( y \): min exponent = \( y^1 \)
- GCF = \( 6xy \)
✔ Answer:
\( 6xy \)
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#### 5. \( 24p^2q \) and \( 36pq^2 \)
- Coefficients: GCF of 24 and 36 =
12
- \( p \): min exponent = \( p^1 \)
- \( q \): min exponent = \( q^1 \)
- GCF = \( 12pq \)
✔ Answer:
\( 12pq \)
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#### 6. \( 16r^3s \) and \( 24rs^2 \)
- Coefficients: GCF of 16 and 24 =
8
- \( r \): min exponent = \( r^1 \)
- \( s \): min exponent = \( s^1 \)
- GCF = \( 8rs \)
✔ Answer:
\( 8rs \)
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Final Answers (Example):
| Problem | GCF |
|--------|-----|
| 1. \( 6x^2, 12x^3 \) | \( 6x^2 \) |
| 2. \( 18a^2b, 24ab^2 \) | \( 6ab \) |
| 3. \( 15m^3n^2, 20m^2n^3 \) | \( 5m^2n^2 \) |
| 4. \( 12x^2y, 18xy^2 \) | \( 6xy \) |
| 5. \( 24p^2q, 36pq^2 \) | \( 12pq \) |
| 6. \( 16r^3s, 24rs^2 \) | \( 8rs \) |
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If your worksheet has different expressions, please provide the actual monomial pairs, and I’ll solve them exactly as they appear!
Let me know if you'd like a printable version or explanation in simpler terms!
Parent Tip: Review the logic above to help your child master the concept of greatest common factor monomials worksheet.
