Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Insert a digit to make the number divisible by 15 if possible:

[tex]\[ 8\_30 \][/tex]

It is [tex]\(\square\)[/tex].

All possible digits are:

[tex]\(\square\)[/tex]
[tex]\(\square\)[/tex]
[tex]\(\square\)[/tex]
[tex]\(\square\)[/tex]
[tex]\(\square\)[/tex]

Sagot :

GinnyAnswer
To determine the digits that can be inserted into the blank space in the number [tex]\(8\_30\)[/tex] to make it divisible by 15, we follow these steps:

1. Understanding Divisibility by 15:
- A number must be divisible by both 3 and 5 to be divisible by 15.

2. Divisibility by 5:
- A number is divisible by 5 if its last digit is either 0 or 5.

3. Divisibility by 3:
- A number is divisible by 3 if the sum of its digits is divisible by 3.

Given the number [tex]\(8\_30\)[/tex]:

1. Check for Divisibility by 5:
- Since the last digit is 0, the number will always be divisible by 5 regardless of the blank position.

2. Check for Divisibility by 3:
- We explore different digits (0 through 9) to replace the blank and check if the resulting number is divisible by 3.

We try each digit from 0 to 9 in place of the blank:

### Calculation:
- Insert 0: [tex]\(8030\)[/tex], sum of digits: [tex]\(8 + 0 + 3 + 0 = 11\)[/tex] (not divisible by 3)
- Insert 1: [tex]\(8130\)[/tex], sum of digits: [tex]\(8 + 1 + 3 + 0 = 12\)[/tex] (divisible by 3)
- Insert 2: [tex]\(8230\)[/tex], sum of digits: [tex]\(8 + 2 + 3 + 0 = 13\)[/tex] (not divisible by 3)
- Insert 3: [tex]\(8330\)[/tex], sum of digits: [tex]\(8 + 3 + 3 + 0 = 14\)[/tex] (not divisible by 3)
- Insert 4: [tex]\(8430\)[/tex], sum of digits: [tex]\(8 + 4 + 3 + 0 = 15\)[/tex] (divisible by 3)
- Insert 5: [tex]\(8530\)[/tex], sum of digits: [tex]\(8 + 5 + 3 + 0 = 16\)[/tex] (not divisible by 3)
- Insert 6: [tex]\(8630\)[/tex], sum of digits: [tex]\(8 + 6 + 3 + 0 = 17\)[/tex] (not divisible by 3)
- Insert 7: [tex]\(8730\)[/tex], sum of digits: [tex]\(8 + 7 + 3 + 0 = 18\)[/tex] (divisible by 3)
- Insert 8: [tex]\(8830\)[/tex], sum of digits: [tex]\(8 + 8 + 3 + 0 = 19\)[/tex] (not divisible by 3)
- Insert 9: [tex]\(8930\)[/tex], sum of digits: [tex]\(8 + 9 + 3 + 0 = 20\)[/tex] (not divisible by 3)

The digits that make the sum divisible by 3 are:
[tex]\[ 1, 4, 7 \][/tex]

### Answer:
All possible digits to replace the blank that make the number divisible by 15 are:
[tex]\[ 1, 4, 7 \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.