To solve the given expression:
\[
9 - 3 \div \frac{1}{3} + 1
\]
we need to follow the
order of operations, often remembered by the acronym
PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Step-by-Step Solution:
1.
Identify the operations in the expression:
\[
9 - 3 \div \frac{1}{3} + 1
\]
The operations present are subtraction, division, and addition.
2.
Apply the order of operations:
-
Division comes before subtraction and addition.
- The division operation is \( 3 \div \frac{1}{3} \).
3.
Solve the division \( 3 \div \frac{1}{3} \):
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of \( \frac{1}{3} \) is \( 3 \). Therefore:
\[
3 \div \frac{1}{3} = 3 \times 3 = 9
\]
4.
Substitute the result back into the expression:
Replace \( 3 \div \frac{1}{3} \) with \( 9 \):
\[
9 - 9 + 1
\]
5.
Perform the subtraction and addition from left to right:
- First, subtract \( 9 \) from \( 9 \):
\[
9 - 9 = 0
\]
- Then, add \( 1 \) to the result:
\[
0 + 1 = 1
\]
Final Answer:
\[
\boxed{1}
\]
Parent Tip: Review the logic above to help your child master the concept of basic math problems.
