Question

1. add a sign.

2 6 9 1 2 = 23,712

1. add a sign.

4 6 3 2 8 = 579

1. what are all the common factors of 6 and 8?
2. how many quarts are in 8 gallons?
3. a country’s flag has three horizontal strips, one red, one blue, and one green. how many different ways can the colors be arranged on the flag?

Explanation:

Step1: Solve Q1: Form 23712 with signs

$26 \times 912 = 23712$

Step2: Solve Q2: Form 579 with signs

$463 + 2 \times 8 = 579$

Step3: Solve Q3: Find common factors

Factors of 6: $1,2,3,6$; Factors of 8: $1,2,4,8$. Common factors: $1,2$

Step4: Solve Q4: Convert gallons to quarts

1 gallon = 4 quarts, so $8 \times 4 = 32$

Step5: Solve Q5: Calculate permutations

3 distinct colors: $3! = 3 \times 2 \times 1 = 6$

Answer:

1. $26 \times 912 = 23712$
2. $463 + 2 \times 8 = 579$
3. 1, 2
4. 32
5. 6