Calculating Brick Weight Using Fractions

This problem involves understanding fractions and how they relate to quantities. We are given information about a fraction of the weight of a brick and asked to find a different fraction of that same brick's weight. To solve this, we first need to determine the total weight of the brick.

Understanding the Problem: Brick Weight Fractions

We are told that \(\frac{3}{4}\) of the weight of a brick is equal to \(\frac{7}{8}\) kg. We need to calculate what \(\frac{5}{7}\) of the weight of the same brick is.

• Given: \(\frac{3}{4} \times \text{Weight of Brick} = \frac{7}{8}\) kg
• To find: \(\frac{5}{7} \times \text{Weight of Brick}\)

Steps to Solve the Brick Weight Problem

Here's how we can break down the problem:

1. Let the total weight of the brick be represented by a variable, say \(W\).
2. Set up an equation based on the information given: \(\frac{3}{4} \times W = \frac{7}{8}\).
3. Solve this equation to find the value of \(W\), the total weight of the brick.
4. Once we have \(W\), calculate \(\frac{5}{7}\) of \(W\) by multiplying \(\frac{5}{7}\) by the value of \(W\).

Detailed Calculation for Brick Weight

Let \(W\) be the weight of the brick in kilograms.

From the problem statement, we have:

\(\frac{3}{4} \times W = \frac{7}{8}\)

To find \(W\), we need to isolate it. We can do this by multiplying both sides of the equation by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\).

\(W = \frac{7}{8} \div \frac{3}{4}\)

\(W = \frac{7}{8} \times \frac{4}{3}\)

Now, multiply the numerators and the denominators:

\(W = \frac{7 \times 4}{8 \times 3}\)

\(W = \frac{28}{24}\)

We can simplify the fraction \(\frac{28}{24}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

\(W = \frac{28 \div 4}{24 \div 4} = \frac{7}{6}\) kg

So, the total weight of the brick is \(\frac{7}{6}\) kg.

Now, we need to find \(\frac{5}{7}\) of the weight of the brick:

\(\frac{5}{7} \times W = \frac{5}{7} \times \frac{7}{6}\)

Multiply the fractions:

\(\frac{5 \times 7}{7 \times 6}\)

We can cancel out the common factor of 7 in the numerator and the denominator:

\(\frac{5 \times \cancel{7}}{\cancel{7} \times 6} = \frac{5}{6}\)

So, \(\frac{5}{7}\) of the weight of the brick is \(\frac{5}{6}\) kg.

Final Answer Calculation

The calculation shows that if \(\frac{3}{4}\) of the brick's weight is \(\frac{7}{8}\) kg, then \(\frac{5}{7}\) of the brick's weight is \(\frac{5}{6}\) kg.

Revision Table: Key Concepts

Additional Information: Working with Fractions

Working with fractions is a fundamental skill in mathematics. When solving word problems involving fractions of quantities, it's often helpful to represent the unknown total quantity with a variable. Then, set up an equation based on the given information. Solving for the variable will give you the total quantity, allowing you to find any other fraction of that quantity.

Remember that 'of' in mathematical phrases usually means multiplication. So, "\(\frac{3}{4}\) of the weight" translates to \(\frac{3}{4} \times \text{Weight}\).

Simplifying fractions at each step or at the end can make calculations easier and help in reaching the final answer in its simplest form.