Problem 95 - Algebra 1

Question

Evaluate the expression. $$8+(91 \div 13) \cdot \frac{4}{7}$$

Step-by-Step Solution

Answer

The value of the expression is 12.

Step 1: Evaluate Division

Start with the operation inside the parentheses first, which is division. Calculate 91 \div 13 to get 7.

Step 2: Multiply

Multiply the obtained result 7 with the fraction \(\frac{4}{7}\). This equals 4.

Step 3: Perform Addition

Finally, perform the addition. Calculate 8 + 4 to get 12.

Key Concepts

Division

When solving mathematical expressions, division is a fundamental operation. In the expression

• \(8 + (91 \div 13) \cdot \frac{4}{7}\),
we start by focusing on the division inside the parentheses.

This helps simplify breaking down numbers into smaller, manageable parts. In this exercise, we need to

• divide 91 by 13.

Performing this calculation results in 7. Division helps to simplify the values we will later use in other operations. It's crucial to perform division accurately to ensure all other calculations are correct.
By understanding the division step, you'll be able to clearly see how the expression is simplified. Let's move on to the next steps now!

Multiplication

After completing division, the next operation in this problem is multiplication.

• We need to multiply the result from the division, which is 7, by the fraction \(\frac{4}{7}\).

It's helpful to remember that multiplying by a fraction is like dividing by its denominator and multiplying by its numerator. This makes maths simpler and easier to visualize in real-world contexts. In equation terms,

• \(7 \cdot \frac{4}{7} = 4\).

Here, you notice the 7s cancel, resulting in just 4, thanks to the properties of fractions in multiplication. It is crucial to follow the order of operations (PEMDAS/BODMAS) which prioritizes multiplication after division when both are in the same expression. Carrying out operations in proper order helps prevent errors in longer and more complex calculations.

Addition

Once we have done the multiplication, we move to addition, which is often seen as simpler but is just as important in expressions.

• In the original expression \(8 + (91 \div 13) \cdot \frac{4}{7}\),
we now add 8 to the result from the multiplication step.

This is the final step in the original expression.

• The goal is to calculate \(8 + 4\), which results in 12.

Addition usually serves to combine values into a total sum. Even though it comes last in this case, always remember that addition rounds off the entire operation. An accurate addition step is integral in providing the final answer.

Fractions

Fractions are fundamental in mathematics and are vital for representing parts of a whole. In this expression, the fraction

• \(\frac{4}{7}\)
participates in the multiplication step.

A fraction consists of a numerator and a denominator, with the numerator representing the parts of the whole and the denominator showing how many parts make up the whole. Simplifying fractions before multiplying or dividing can ease computations.
Proper understanding of fractions will greatly enhance your efficiency when dealing with numbers not in their full form. Learning how fractions interact with other mathematical operations, helps strengthen core arithmetic skills and builds foundations for more advanced topics.