When a number is divided by 8, it leaves a remainder of 5. If this number is mul
Practice Questions
Q1
When a number is divided by 8, it leaves a remainder of 5. If this number is multiplied by 3, what will be the remainder when the result is divided by 8? (2023)
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Questions & Step-by-Step Solutions
When a number is divided by 8, it leaves a remainder of 5. If this number is multiplied by 3, what will be the remainder when the result is divided by 8? (2023)
Step 1: Understand that when a number is divided by 8 and leaves a remainder of 5, we can express this number as '8k + 5', where 'k' is some integer.
Step 2: Multiply the entire expression '8k + 5' by 3. This gives us '3 * (8k + 5)'.
Step 3: Distribute the 3: '3 * 8k + 3 * 5' which simplifies to '24k + 15'.
Step 4: Now, we need to find the remainder when '24k + 15' is divided by 8.
Step 5: Notice that '24k' is a multiple of 8 (since 24 is divisible by 8), so it leaves a remainder of 0 when divided by 8.
Step 6: Now, focus on the '15'. When we divide 15 by 8, we get 15 = 8 * 1 + 7, which means the remainder is 7.
Step 7: Therefore, the remainder when '24k + 15' is divided by 8 is the same as the remainder of 15 divided by 8, which is 7.
