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Chapter 7: Problem 34

Divide. Write your answers as decimals. $$7 \div 35$$

Short Answer

Expert verified
The decimal representation of \(7 \div 35\) is 0.2.

Step by step solution

01

Understanding the Division

The problem asks us to divide 7 by 35 and express the result as a decimal. This means we want to find the number of times 35 fits into 7.
02

Perform the Division

To convert the division into a fraction, write it as \( \frac{7}{35} \). Now, perform the division using long division or by simplifying the fraction. Since 7 is smaller than 35, this is a division that will result in a number less than 1.
03

Simplifying the Fraction

First, check if \( \frac{7}{35} \) can be simplified. Both 7 and 35 are divisible by 7, so divide the numerator and the denominator by 7: \( \frac{7}{35} = \frac{7 \div 7}{35 \div 7} = \frac{1}{5} \).
04

Converting to Decimal

To convert \( \frac{1}{5} \) into a decimal, perform the division 1 divided by 5. This results in 0.2.

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Key Concepts

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

Fraction to Decimal Conversion
Converting a fraction to a decimal is a skill that helps in many math problems, including dividing fractions. When you have a fraction, such as \( \frac{1}{5} \), turning it into a decimal involves division. The numerator (the top number) is divided by the denominator (the bottom number). In this case, you divide 1 by 5.
Here's a simple way to think about it:
  • The numerator (1) goes inside the division bar.
  • The denominator (5) goes outside the division bar, acting as the divisor.
Performing the division \(1 \div 5 \), you'll find that
  • 1 goes into 5 a total of 0 times, so you have your 0 before the decimal point.
  • Add a decimal point after this zero, and annex a zero to the right of the dividend to continue the division.
  • Now, divide 10 by 5, which goes 2 times exactly, leaving no remainder.
Thus, \( \frac{1}{5} = 0.2 \) in decimal form. Remember, knowing how to convert fractions to decimals can help you easily transition between different types of numerical representations.
Simplifying Fractions
Simplifying fractions makes numbers easier to work with by reducing them to their smallest equivalent form. Consider the fraction \( \frac{7}{35} \) from our example. Here鈥檚 a step-by-step guide to simplifying it:
  • First, find a common factor that divides both the numerator and the denominator without leaving a remainder. In this case, both numbers are divisible by 7.
  • Divide both parts of the fraction by this common factor, which simplifies the fraction. So, divide 7 by 7 and 35 by 7.
  • This gives you \( \frac{1}{5} \), which is the simplest form of the fraction \( \frac{7}{35} \).
Simplifying fractions is valuable because it maintains the original value of the fraction while making calculations, like fraction addition and subtraction, more straightforward.
Long Division
Long division is a methodical process used for dividing large numbers, but it's also helpful with fractions when converting them to decimals or when performing larger division operations. Here's a simple guide:
  • Set up your division by placing the numerator as the dividend (inside the division bar) and the denominator as the divisor (outside the division bar).
  • Step through the division, determining how many times the divisor fits into pieces of the dividend in descending order from the left; this number will help form your answer.
  • With each step, multiply, subtract, bring down the next number, and repeat until you reach the end of your dividend or until the remainder is zero.
Let's say you start with \(7 \div 35 \), switch to \(\frac{1}{5}\) after simplifying. To convert to a decimal, when dividing 1 by 5 using long division, it gives a careful, structured way of understanding \(0.2\), confirming your calculations. Mastering long division offers a foundational skill to tackle not only whole numbers but fractional computations as well.

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Most popular questions from this chapter

Write as a decimal. $$\frac{3}{16}$$

Write as a percent. Write the remainder in fractional form. $$2 \frac{5}{8}$$

Write as a percent. Write the remainder in fractional form. $$\frac{3}{8}$$

Write as a percent. $$0.125$$

The problems below will allow you to review subtraction of fractions and mixed numbers. $$\frac{5}{8}-\frac{1}{4}$$
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