State how the divisibility tests for 3 and 9 are similar.
wses Determine whether or not the results of the fo

Ask by Clark Turnbull. in Australia

Mar 18,2025

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State how the divisibility tests for 3 and 9 are similar. wses Determine whether or not the results of the fo $$ \begin{array}{ll}	ext { a. } 54 \div 2 & 	ext { b. } 150 \div 9\end{array} $$

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**Divisibility Tests for 3 and 9**

Both divisibility tests rely on the sum of the digits of the integer. Specifically:  
- A number is divisible by $$3$$ if the sum of its digits is divisible by $$3$$.  
- A number is divisible by $$9$$ if the sum of its digits is divisible by $$9$$.

Thus, both tests simplify the divisibility problem by reducing a large number to the sum of its digits.

**Determining the Division Results**

**a. $$54 \div 2$$**

1. Compute the division:
   $$
   54 \div 2 = 27
   $$
2. Since $$27$$ is a whole number, the division $$54 \div 2$$ results in an integer.

**b. $$150 \div 9$$**

1. Compute the division:
   $$
   150 \div 9 \approx 16.67
   $$
   More precisely, $$9 \times 16 = 144$$ and $$9 \times 17 = 153$$. Since $$150$$ lies between these values, $$150$$ is not exactly divisible by $$9$$.
2. The remainder can also be computed:
   $$
   150 - (9 \times 16) = 150 - 144 = 6
   $$
3. Since there is a nonzero remainder, $$150 \div 9$$ does not result in a whole number.

**Summary:**
- The divisibility tests for $$3$$ and $$9$$ are similar because they both check whether the sum of the digits of a number is divisible by $$3$$ or $$9$$ respectively.
- $$54 \div 2 = 27$$ is a whole number.
- $$150 \div 9$$ does not result in a whole number because it leaves a remainder of $$6$$.
**Divisibility Tests for 3 and 9** Both tests check if the sum of a number's digits is divisible by 3 or 9. **Division Results** - $$54 \div 2 = 27$$ (whole number) - $$150 \div 9$$ leaves a remainder of 6 (not a whole number) **Summary:** - Both tests use the sum of digits. - $$54 \div 2$$ is exact. - $$150 \div 9$$ is not exact.

State how the divisibility tests for 3 and 9 are similar.
wses Determine whether or not the results of the fo

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