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Chapter 3: Problem 69

Determine whether the first number is divisible by the second. $$ 2345 \text { by } 9 $$

Short Answer

Expert verified
2345 is not divisible by 9.

Step by step solution

01

- Sum the Digits of the Number

Add the digits of 2345. This means calculating: 2 + 3 + 4 + 5.
02

- Simplify the Sum

Simplify the sum from Step 1: 2 + 3 + 4 + 5 = 14.
03

- Check Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9. Check if 14 is divisible by 9. Since 14 梅 9 equals about 1.56, 14 is not divisible by 9.
04

Conclusion

Since the sum of the digits (14) is not divisible by 9, 2345 is not divisible by 9.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Divisibility by 9
In this section, we will discuss the rule for checking whether a number is divisible by 9. The rule is simple and involves basic arithmetic. A number is divisible by 9 if the sum of its digits is also divisible by 9. For example, let's consider the number 2345 and check its divisibility by 9.
First, add the digits of the number: 2 + 3 + 4 + 5. This equals 14.
Next, see if 14 is divisible by 9. Since 14 divided by 9 equals approximately 1.56, 14 is not divisible by 9, and thus 2345 is not divisible by 9.
Sum of Digits
To apply the divisibility rule for 9, we need to find the sum of the digits of the number. The sum of digits is simply the result of adding each digit of the number together.
For example, the digits of the number 2345 are 2, 3, 4, and 5. When we add these digits, we get: 2 + 3 + 4 + 5 = 14.
This sum (14) helps in determining whether the initial number (2345) is divisible by 9. The key task here is to add all the digits correctly to find the sum.
Basic Arithmetic
Arithmetic operations such as addition, subtraction, multiplication, and division are fundamental to solving math problems. In our example, we used addition to sum the digits of the number 2345.
Here is how addition works:
2 + 3 = 5
5 + 4 = 9
9 + 5 = 14
Finally, checking if a number is divisible involves a simple division operation. We divided the sum of the digits (14) by 9, getting approximately 1.56. Since this is not a whole number, 14 is not divisible by 9.
Basic arithmetic is essential for performing these operations accurately.

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Most popular questions from this chapter

Use a calculator to arrange the following in order from smallest to largest. $$ \frac{3}{4}, \frac{17}{21}, \frac{13}{15}, \frac{7}{9}, \frac{15}{17}, \frac{13}{12}, \frac{19}{22} $$

Estimate each of the following by estimating each mixed numeral as a whole number or as a mixed numeral where the fraction part is \(\frac{1}{2}\) and by estimating each fraction as \(0, \frac{1}{2},\) or 1 . $$ 16 \frac{1}{5} \div 2 \frac{1}{11}+25 \frac{9}{10}-4 \frac{11}{23} $$

Simplify. $$ \frac{\frac{3}{8}}{12} $$

A triathlete runs \(\frac{7}{8} \mathrm{mi}\), canoes \(\frac{1}{3} \mathrm{mi},\) and swims \(\frac{1}{6}\) mi. How many miles does the triathlete cover?

Simplify. $$ \frac{7}{8} \div \frac{1}{2} \cdot \frac{1}{4} $$
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