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Chapter 1: Problem 692

Locate the numbers on a number line. $$ \frac{1}{4}, \frac{9}{5}, \frac{11}{3} $$

Short Answer

Expert verified
Points should be at roughly 0.25, 1.8, and 3.67 on the number line.

Step by step solution

01

- Convert fractions to decimals

To easily place the numbers on a number line, it's helpful to first convert the fractions to decimals. \(\frac{1}{4} = 0.25\), \(\frac{9}{5} = 1.8\), and \(\frac{11}{3} \approx 3.67\).
02

- Identify the positions on the number line

Next, identify where these decimals are located on a number line. \(0.25\) is slightly to the right of 0, \(1.8\) is between 1 and 2, and \(3.67\) is between 3 and 4.
03

- Plot the numbers

Now plot the numbers on the number line. Place a point at each of the calculated decimal values: - Point at \(0.25\)- Point at \(1.8\)- Point at \(3.67\)

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Key Concepts

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

fractions to decimals conversion
To accurately place fractions on a number line, the first step is to convert them into decimals. This is because decimals are generally easier to locate and understand on a number line.

Converting a fraction to a decimal involves dividing the numerator (top number) by the denominator (bottom number). For example, in the fraction \( \frac{1}{4} \), you divide 1 by 4, which gives 0.25. Similarly, \( \frac{9}{5} \) converts to 1.8, and \( \frac{11}{3} \) converts to approximately 3.67.

These conversions help simplify the task of plotting the points, as it is easier to understand the placement of 0.25, 1.8, and 3.67 on a number line than their fractional counterparts.
decimal placement
Once the fractions are converted to decimals, the next step is to decide where these decimals appear on the number line.

Let's break down each:
  • 0.25: This value is greater than 0 but less than 1, so it sits between these two whole numbers. More precisely, it's situated one-quarter of the way between 0 and 1.
  • 1.8: This decimal is more than 1 but less than 2. It's closer to 2, at slightly less than halfway between 1 and 2.
  • 3.67: This value is more than 3 but less than 4. It's located slightly more than halfway between 3 and 4.
Understanding where each decimal fits provides a clear mental image of their positions on the number line.
number line representation
Finally, we need to plot these decimals on the number line.

When placing a point on a number line, visualize the whole numbers first. For example, if you need to place 0.25, look between 0 and 1. Locate the quarter mark for precise placement. For 1.8, identify its location between 1 and 2, leaning towards 2. Similarly, for 3.67, find the spot between 3 and 4, slightly beyond the midpoint towards 4.

To summarize the process:
  • Mark a point at 0.25 between 0 and 1.
  • Mark a point at 1.8 between 1 and 2.
  • Mark a point at 3.67 between 3 and 4.
Following these steps ensures that the numbers are correctly represented on the number line, making your mathematical understanding clearer and more precise.

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Most popular questions from this chapter

Trader Joe's grocery stores sold a bottle of wine they called "Two Buck Chuck" for $$\$ 1.99 .\( They sold a case of 12 bottles for \)\$ 23.88\(. To find the cost of 12 bottles at \)\$ 1.99,\( notice that 1.99 is \)2-0.01\( (a) Multiply 12(1.99) by using the distributive property to multiply \)12(2-0.01)$$. (b) Was it a bargain to buy "Two Buck Chuck" by the case?

Insurance copayment Carrie had to have 5 fillings done. Each filling cost $$\$ 80\(. Her dental insurance required her to pay \)20 \%\( of the cost as a copay. Calculate Carrie's copay: (a) First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings. (b) Next, by multiplying \)[5(0.20)](80)\( (c) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \)5[(0.20)(80)]\( and \)(b),\( where you multiplied \)[5(0.20)](80),$$ should be equal?

Simplify using the distributive property. $$ (5 m-3)-(m+7) $$

Simplify using the distributive property. $$ -4(q-7) $$

Simplify using the distributive property. $$ -(5 p-4) $$
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