Question

fill in two numbers that multiply to give the top number but add to give the bottom number.
ex
-30
1
=
-30
6
-5
1
6·(-5) = -30
6 + (-5) = 1
①
12
7
②
-12
-4
③
12
8
④
-12
11
⑤
12
-8
⑥
-12
1

Explanation:

Problem ①

Step1: Find two numbers that multiply to 12 and add to 7.

Let the numbers be \( x \) and \( y \). So \( x \times y = 12 \) and \( x + y = 7 \). We need to find factors of 12 that add up to 7. The factors of 12 are 1 & 12, 2 & 6, 3 & 4. Checking their sums: \( 3 + 4 = 7 \).

Step2: Verify the multiplication and addition.

\( 3 \times 4 = 12 \) and \( 3 + 4 = 7 \).

Step1: Find two numbers that multiply to -12 and add to -4.

Let the numbers be \( x \) and \( y \). So \( x \times y = -12 \) and \( x + y = -4 \). We need to find two numbers where one is positive and one is negative (since product is negative) and their sum is -4. Let's list factor pairs of 12: (1,12), (2,6), (3,4). Now assign signs: Let's try -6 and 2. \( -6 \times 2 = -12 \) and \( -6 + 2 = -4 \).

Step2: Verify the multiplication and addition.

\( -6 \times 2 = -12 \) and \( -6 + 2 = -4 \).

Step1: Find two numbers that multiply to 12 and add to 8.

Let the numbers be \( x \) and \( y \). So \( x \times y = 12 \) and \( x + y = 8 \). Factors of 12: 1 & 12 (sum 13), 2 & 6 (sum 8), 3 & 4 (sum 7). So 2 and 6.

Step2: Verify the multiplication and addition.

\( 2 \times 6 = 12 \) and \( 2 + 6 = 8 \).

Answer:

3 and 4

Problem ②