Question

1. analyze and persevere how can you use 2s facts to find 4 × 8?
2. maria said 7 × 3 = 21. connie said 3 × 7 = 21. who is correct? explain.
3. five people bought tickets to a football game. they bought 3 tickets each. how many tickets were bought? draw an array.
4. higher order thinking mark is having a party. he invites 35 people. mark sets up 8 tables with 4 chairs at each table. does mark have enough tables and chairs for all of his guests? explain.
5. barney divides a rectangle into fourths. show two ways he could do this.
6. jillian buys 3 boxes of crayons. each box has the same number of crayons. which equation can be used to find the number of crayons jillian buys?

ⓐ (3×8)+(3×8)=?
ⓑ (3×4)+(3×4)=?
ⓒ (8×8)+(3×3)=?
ⓓ (3×3)+(8×8)=?

1. which of the following is not a way to use the distributive property to find 4 × 7?

ⓐ (4×3)+(4×3)
ⓑ (2×7)+(2×7)
ⓒ (4×3)+(4×4)
ⓓ (4×2)+(4×5)

Explanation:

Let's solve question 21: "Which of the following is NOT a way to use the Distributive Property to find \(4 \times 7\)?"

The Distributive Property states that \(a \times (b + c) = (a \times b) + (a \times c)\). We need to check each option:

Option A: \((4 \times 3) + (4 \times 3)\)

• Let's see if this relates to \(4 \times 7\). If we split 7 as \(3 + 3\), but \(3 + 3 = 6

eq 7\). Wait, no—wait, \(4 \times 7 = 4 \times (3 + 4)\)? Wait, no, let's compute:

• \(4 \times 7 = 28\)
• \((4 \times 3) + (4 \times 3) = 12 + 12 = 24

eq 28\). Wait, maybe I misread. Wait, no—wait, the Distributive Property is about splitting the second factor. Let's check each option:

Option B: \((2 \times 7) + (2 \times 7)\)

• Here, we split 4 as \(2 + 2\). So \(4 \times 7 = (2 + 2) \times 7 = (2 \times 7) + (2 \times 7)\) (by Distributive Property). Let's compute: \(14 + 14 = 28\), which is \(4 \times 7\). So this is valid.

Option C: \((4 \times 3) + (4 \times 4)\)

• Split 7 as \(3 + 4\). Then \(4 \times 7 = 4 \times (3 + 4) = (4 \times 3) + (4 \times 4)\) (by Distributive Property). Compute: \(12 + 16 = 28\), which is correct. So this is valid.

Option D: \((4 \times 2) + (4 \times 5)\)

• Split 7 as \(2 + 5\). Then \(4 \times 7 = 4 \times (2 + 5) = (4 \times 2) + (4 \times 5)\) (by Distributive Property). Compute: \(8 + 20 = 28\), which is correct. So this is valid.

Option A: \((4 \times 3) + (4 \times 3)\)

• As above, \( (4 \times 3) + (4 \times 3) = 12 + 12 = 24 \), which is not equal to \(4 \times 7 = 28\). Also, splitting 7 as \(3 + 3\) is incorrect because \(3 + 3 = 6

eq 7\). So this does not use the Distributive Property correctly for \(4 \times 7\).

So the answer is Option A.

Answer:

Let's solve question 21: "Which of the following is NOT a way to use the Distributive Property to find \(4 \times 7\)?"

The Distributive Property states that \(a \times (b + c) = (a \times b) + (a \times c)\). We need to check each option:

Option A: \((4 \times 3) + (4 \times 3)\)

• Let's see if this relates to \(4 \times 7\). If we split 7 as \(3 + 3\), but \(3 + 3 = 6

eq 7\). Wait, no—wait, \(4 \times 7 = 4 \times (3 + 4)\)? Wait, no, let's compute:

• \(4 \times 7 = 28\)
• \((4 \times 3) + (4 \times 3) = 12 + 12 = 24

eq 28\). Wait, maybe I misread. Wait, no—wait, the Distributive Property is about splitting the second factor. Let's check each option:

Option B: \((2 \times 7) + (2 \times 7)\)

• Here, we split 4 as \(2 + 2\). So \(4 \times 7 = (2 + 2) \times 7 = (2 \times 7) + (2 \times 7)\) (by Distributive Property). Let's compute: \(14 + 14 = 28\), which is \(4 \times 7\). So this is valid.

Option C: \((4 \times 3) + (4 \times 4)\)

• Split 7 as \(3 + 4\). Then \(4 \times 7 = 4 \times (3 + 4) = (4 \times 3) + (4 \times 4)\) (by Distributive Property). Compute: \(12 + 16 = 28\), which is correct. So this is valid.

Option D: \((4 \times 2) + (4 \times 5)\)

• Split 7 as \(2 + 5\). Then \(4 \times 7 = 4 \times (2 + 5) = (4 \times 2) + (4 \times 5)\) (by Distributive Property). Compute: \(8 + 20 = 28\), which is correct. So this is valid.

Option A: \((4 \times 3) + (4 \times 3)\)

• As above, \( (4 \times 3) + (4 \times 3) = 12 + 12 = 24 \), which is not equal to \(4 \times 7 = 28\). Also, splitting 7 as \(3 + 3\) is incorrect because \(3 + 3 = 6

eq 7\). So this does not use the Distributive Property correctly for \(4 \times 7\).

So the answer is Option A.