Certainly! Let's rewrite each numeric expression using the Distributive Property and the Greatest Common Factor (GCF).
1. Expression: [tex]\( 56 + 35 \)[/tex]
- Given GCF: [tex]\( 7 \)[/tex]
- We can factor out the GCF from each term in the expression.
- [tex]\( 56 = 7 \times 8 \)[/tex]
- [tex]\( 35 = 7 \times 5 \)[/tex]
- Therefore, [tex]\( 56 + 35 = 7 \times 8 + 7 \times 5 = 7(8 + 5) \)[/tex]
Written in the distributive form using the GCF:
[tex]\[ 7(8 + 5) \][/tex]
2. Expression: [tex]\( 90 + 27 \)[/tex]
- Given GCF: [tex]\( 9 \)[/tex]
- We can factor out the GCF from each term in the expression.
- [tex]\( 90 = 9 \times 10 \)[/tex]
- [tex]\( 27 = 9 \times 3 \)[/tex]
- Therefore, [tex]\( 90 + 27 = 9 \times 10 + 9 \times 3 = 9(10 + 3) \)[/tex]
Written in the distributive form using the GCF:
[tex]\[ 9(10 + 3) \][/tex]
3. Expression: [tex]\( 54 + 72 \)[/tex]
- Given GCF: [tex]\( 18 \)[/tex]
- We can factor out the GCF from each term in the expression.
- [tex]\( 54 = 18 \times 3 \)[/tex]
- [tex]\( 72 = 18 \times 4 \)[/tex]
- Therefore, [tex]\( 54 + 72 = 18 \times 3 + 18 \times 4 = 18(3 + 4) \)[/tex]
Written in the distributive form using the GCF:
[tex]\[ 18(3 + 4) \][/tex]
4. Expression: [tex]\( 36 + 60 \)[/tex]
- Find the GCF: [tex]\( 12 \)[/tex]
- We can factor out the GCF from each term in the expression.
- [tex]\( 36 = 12 \times 3 \)[/tex]
- [tex]\( 60 = 12 \times 5 \)[/tex]
- Therefore, [tex]\( 36 + 60 = 12 \times 3 + 12 \times 5 = 12(3 + 5) \)[/tex]
Written in the distributive form using the GCF:
[tex]\[ 12(3 + 5) \][/tex]
5. Expression: [tex]\( 32 + 28 \)[/tex]
- Find the GCF: [tex]\( 4 \)[/tex]
- We can factor out the GCF from each term in the expression.
- [tex]\( 32 = 4 \times 8 \)[/tex]
- [tex]\( 28 = 4 \times 7 \)[/tex]
- Therefore, [tex]\( 32 + 28 = 4 \times 8 + 4 \times 7 = 4(8 + 7) \)[/tex]
Written in the distributive form using the GCF:
[tex]\[ 4(8 + 7) \][/tex]
6. Expression: [tex]\( 88 + 66 \)[/tex]
- Find the GCF: [tex]\( 22 \)[/tex]
- We can factor out the GCF from each term in the expression.
- [tex]\( 88 = 22 \times 4 \)[/tex]
- [tex]\( 66 = 22 \times 3 \)[/tex]
- Therefore, [tex]\( 88 + 66 = 22 \times 4 + 22 \times 3 = 22(4 + 3) \)[/tex]
Written in the distributive form using the GCF:
[tex]\[ 22(4 + 3) \][/tex]
By following the steps above, you can see how the numeric expressions are rewritten using the Distributive Property and their respective Greatest Common Factors.
