Question 3 of 19intermediate🔧 ApplyNumerical3 marks

Find a few numbers that leave a remainder of 2 when divided by 3 and a remainder of 2 when divided by 4. Write an algebraic expression to describe all such numbers.

Correct Answer

Step 1: Numbers with remainder 2 when divided by 3: 3a + 2

Step 2: Numbers with remainder 2 when divided by 4: 4b + 2

Step 3: Equate: 3a + 2 = 4b + 2, so 3a = 4b

Step 4: Since 3 and 4 are coprime, a = 4k for some integer k

Step 5: Substitute: 3(4k) + 2 = 12k + 2

Step 6: Numbers are 2, 14, 26, 38, 50, ...

Answer: Numbers: 2, 14, 26, 38, 50, ... Algebraic expression: 12k + 2, where k is a non-negative integer.

Exercise: Figure it Out (Section 1) | Q: 4 | (Page Page 11)
For More Understanding

Explanation

A number that leaves remainder 2 when divided by 3 is of the form 3a + 2. A number that leaves remainder 2 when divided by 4 is of the form 4b + 2. For both conditions to be satisfied, we need 3a + 2 = 4b + 2, which means 3a = 4b. Since 3 and 4 are coprime, a must be a multiple of 4 and b must be a multiple of 3. So a = 4k, giving the number as 3(4k) + 2 = 12k + 2.

Solution Steps

  1. Step 1: Numbers with remainder 2 when divided by 3: 3a + 2

  2. Step 2: Numbers with remainder 2 when divided by 4: 4b + 2

  3. Step 3: Equate: 3a + 2 = 4b + 2, so 3a = 4b

  4. Step 4: Since 3 and 4 are coprime, a = 4k for some integer k

  5. Step 5: Substitute: 3(4k) + 2 = 12k + 2

  6. Step 6: Numbers are 2, 14, 26, 38, 50, ...

PreviousNext