Question

fill in two numbers that multiply to give the top number but add to give the bottom number.
①
48
14
②
-48
2
③
48
19
④
-48
-8
⑤
48
-16
⑥
-48
-13
⑦
48
-49
⑧
-48
22

Explanation:

Problem 1

Step1: Find two numbers \( x \) and \( y \) such that \( x \times y = 48 \) and \( x + y = 14 \).

We need to find factors of 48 that add up to 14. The factors of 48 are: 1 & 48, 2 & 24, 3 & 16, 4 & 12, 6 & 8. Checking the sum: \( 6 + 8 = 14 \) and \( 6 \times 8 = 48 \).

Step2: Verify the numbers.

\( 6 \times 8 = 48 \) and \( 6 + 8 = 14 \), which matches the top and bottom numbers.

Step1: Find two numbers \( x \) and \( y \) such that \( x \times y = -48 \) and \( x + y = 2 \).

We need to find two numbers where their product is -48 and sum is 2. Let's consider the factors of 48. We know that \( 8 \times (-6) = -48 \) and \( 8 + (-6) = 2 \).

Step2: Verify the numbers.

\( 8 \times (-6) = -48 \) and \( 8 + (-6) = 2 \), which matches the top and bottom numbers.

Step1: Find two numbers \( x \) and \( y \) such that \( x \times y = 48 \) and \( x + y = 19 \).

We need to find factors of 48 that add up to 19. The factors of 48: 1 & 48 (sum 49), 2 & 24 (sum 26), 3 & 16 (sum 19), 4 & 12 (sum 16), 6 & 8 (sum 14). So \( 3 \) and \( 16 \) work.

Step2: Verify the numbers.

\( 3 \times 16 = 48 \) and \( 3 + 16 = 19 \), which matches the top and bottom numbers.

Answer:

6 and 8

Problem 2