Math Problem Statement

3 OVER 4 /1 OVER 4 + (3X7+7)

Solution

Let's break down the expression step-by-step.

You have:

34÷14+(3×7+7)\frac{3}{4} \div \frac{1}{4} + (3 \times 7 + 7)

Step 1: Simplifying 34÷14\frac{3}{4} \div \frac{1}{4}

Dividing fractions involves multiplying by the reciprocal of the second fraction:

34÷14=34×41=3×44×1=124=3\frac{3}{4} \div \frac{1}{4} = \frac{3}{4} \times \frac{4}{1} = \frac{3 \times 4}{4 \times 1} = \frac{12}{4} = 3

Step 2: Simplifying the parentheses (3×7+7)(3 \times 7 + 7)

First, multiply:

3×7=213 \times 7 = 21

Then, add 7:

21+7=2821 + 7 = 28

Step 3: Putting it all together

Now, add the results from the two parts:

3+28=313 + 28 = 31

So, the value of the expression is 31.


If you need any clarifications or further details, feel free to ask!

Here are 5 related questions you might find interesting:

  1. How do you divide fractions in general?
  2. What is the order of operations (PEMDAS)?
  3. What are some common algebraic simplifications for fractions?
  4. How do parentheses affect the calculation in an expression?
  5. Can you solve an expression like this one using decimal approximations?

Tip: When dividing fractions, always remember to multiply by the reciprocal of the divisor!

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Math Problem Analysis

Mathematical Concepts

Fractions
Division of Fractions
Basic Algebra
Order of Operations

Formulas

Dividing fractions: a/b ÷ c/d = a/b × d/c
Order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)

Theorems

Reciprocal of a fraction

Suitable Grade Level

Grades 5-7