Math Problem Statement

Given the expression 2/9 ÷ 5/6 + 3/4 × 3/5, insert parentheses into the expression so that (a) the first operation to be performed is addition; (b) the second operation to be performed is multiplication; (c) the third operation to be performed is division.

Solution

The given expression is:

29÷56+34×35\frac{2}{9} \div \frac{5}{6} + \frac{3}{4} \times \frac{3}{5}

We need to insert parentheses so that:

  1. The first operation is addition.
  2. The second operation is multiplication.
  3. The third operation is division.

Let's break down the solution:

To ensure that the first operation is addition, the addition part of the expression must be in parentheses:

(29÷56)+(34×35)\left( \frac{2}{9} \div \frac{5}{6} \right) + \left( \frac{3}{4} \times \frac{3}{5} \right)

This setup ensures that:

  • First: The multiplication 34×35\frac{3}{4} \times \frac{3}{5} is done because it is inside parentheses.
  • Second: The addition is done after the result of multiplication.
  • Third: The division 29÷56\frac{2}{9} \div \frac{5}{6} is performed after multiplication and addition.

Thus, the correct expression is:

(29÷56)+(34×35)\left( \frac{2}{9} \div \frac{5}{6} \right) + \left( \frac{3}{4} \times \frac{3}{5} \right)

This satisfies the condition that:

(a) The first operation is addition.

(b) The second operation is multiplication.

(c) The third operation is division.


Do you want further details on how this solution was derived or any clarifications?

5 Related Questions:

  1. How do you apply the order of operations (PEMDAS) to an expression with fractions?
  2. How do you divide fractions, such as 29÷56\frac{2}{9} \div \frac{5}{6}?
  3. What is the process for multiplying fractions?
  4. How do parentheses change the order of operations in a mathematical expression?
  5. How would the result differ if parentheses were not included?

Tip: Always resolve the operations inside parentheses first to avoid mistakes in complex expressions!

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Fractions
Arithmetic Operations

Formulas

PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

Theorems

Order of Operations

Suitable Grade Level

Grades 6-8