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Chapter 7: Problem 365

In the following exercises, simplify. $$ \frac{1}{6} \cdot 17 \cdot 12 $$

Short Answer

Expert verified
34

Step by step solution

01

Understand the operation

The given expression is \(\frac{1}{6} \times 17 \times 12\). The task is to simplify this expression by performing the multiplication.
02

First Multiplication

Start by multiplying \(\frac{1}{6}\) by 12. This can be written as \(\frac{1}{6} \times 12 = \frac{12}{6}\). Simplify \(\frac{12}{6} = 2\).
03

Second Multiplication

Now, multiply the result from Step 2, which is 2, by 17. This can be written as \(2 \times 17 = 34\).
04

Write the final answer

The simplified form of the expression \(\frac{1}{6} \times 17 \times 12\) is \(34\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fraction Multiplication
Multiplying fractions may seem tricky at first, but it gets easier with practice. The key is to remember that you multiply the numerators together and the denominators together. For instance, when you multiply \(\frac{a}{b} \times \frac{c}{d}\), you get \(\frac{a \times c}{b \times d}\). In our specific problem, we need to multiply a fraction by an integer, and that's done by multiplying the integer with the numerator of the fraction. So, multiply the fraction \(\frac{1}{6}\) by 12.\br)The expression is \(\frac{1}{6} \times 17 \times 12\). First, multiply \(\frac{1}{6}\) by 12 to get \(\frac{12}{6}\). This immediately simplifies to 2.
Simplification Steps
The simplification steps make complex operations easy to handle. The process involves breaking down the multiplication into more manageable steps. Here are the steps:
  • Step 1: Write down the expression clearly: \(\frac{1}{6} \times 17 \times 12\).
  • Step 2: Start with the first multiplication. Multiply the numerator of the fraction with the integer: \(\frac{1 \times 12}{6} = \frac{12}{6}\).
  • Step 3: Simplify \(\frac{12}{6} = 2\).
  • Step 4: Take the result from Step 3 and multiply it with the next number in the sequence: 2 \(\times 17 = 34\).
  • Step 5: Write the final simplified answer: 34.
It鈥檚 important to simplify fractions wherever possible, as it makes the calculation much easier to manage.
Multiplying Fractions With Whole Numbers
Multiplying fractions with whole numbers is straightforward. The key point is multiplying the whole number by the numerator of the fraction. This is followed by simplifying the resulting fraction if possible.
Here鈥檚 how it鈥檚 done step-by-step:
  • Step 1: Multiply the numerator of the fraction by the whole number. For \(\frac{1}{6} \times 12\), multiply 1 by 12, which gives 12.
  • Step 2: The resulting fraction is \(\frac{12}{6}\). Simplify it by dividing the numerator by the denominator. In this case, \(\frac{12}{6} = 2\).
  • Step 3: Continue multiplying the result with the next whole number in the sequence, here it鈥檚 17. So, multiply 2 by 17, which equals 34.
By understanding these steps and practicing, you can easily handle any problem that involves multiplying fractions with whole numbers.

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