Question

example 3 compare rational numbers
compare -0.51 and $-\frac{12}{25}$
step 1 write the fraction as a decimal.
$-\frac{12}{25}=\square$
rewrite the fraction as a decimal so that the values are in the same form.
step 2 graph the values on the number line
the number -0.51 is farther to the left on the number line.
so, $-0.51<-\frac{12}{25}$
check
compare $-\frac{3}{8}$ and -0.413.
pause and reflect
describe some examples of where you might have to compare rational numbers in your everyday life.
think about it
how can you compare rational numbers when they are written in different forms?
talk about it
how can you compare the numbers without graphing them on a number line?

Explanation:

Step1: Convert fraction to decimal

To compare \(-\frac{12}{25}\) and \(-0.51\), first convert \(-\frac{12}{25}\) to a decimal. Divide 12 by 25: \(12\div25 = 0.48\), so \(-\frac{12}{25}=- 0.48\).

Step2: Compare the two decimals

Now we have \(-0.51\) and \(-0.48\). On the number line, the more negative a number is, the farther to the left it is. Since \(-0.51\) is more negative than \(-0.48\) (because \(0.51>0.48\), so \(- 0.51<-0.48\)).

For the check part (comparing \(-\frac{3}{8}\) and \(-0.413\)):

Step1: Convert fraction to decimal

Convert \(-\frac{3}{8}\) to a decimal. \(3\div8 = 0.375\), so \(-\frac{3}{8}=-0.375\).

Step2: Compare the two decimals

Now we have \(-0.375\) and \(-0.413\). Since \(0.375 < 0.413\), then \(-0.375>-0.413\) (because the larger the positive value of the decimal part, the more negative the number is, so the smaller number is more negative). So \(-\frac{3}{8}>-0.413\).

For the "Pause and Reflect" part, examples of comparing rational numbers in everyday life:

• Shopping: Comparing prices of items. For example, a shirt costs \(\$19.99\) and another costs \(\frac{80}{4}=20\) dollars. We compare \(19.99\) and \(20\) to see which is cheaper.
• Cooking: Measuring ingredients. If a recipe calls for \(\frac{1}{2}\) cup of flour and you have a measuring cup that shows \(0.4\) cups left, you compare \(\frac{1}{2}=0.5\) and \(0.4\) to see if you have enough.
• Sports: Comparing statistics. For example, a basketball player has a free - throw percentage of \(\frac{12}{15} = 0.8\) and another has a percentage of \(0.75\). We compare \(0.8\) and \(0.75\) to see who is a better free - throw shooter.

Answer:

For comparing \(-0.51\) and \(-\frac{12}{25}\): \(-0.51<-\frac{12}{25}\) (since \(-\frac{12}{25}=-0.48\) and \(-0.51 < - 0.48\)).

For comparing \(-\frac{3}{8}\) and \(-0.413\): \(-\frac{3}{8}>-0.413\) (since \(-\frac{3}{8}=-0.375\) and \(-0.375>-0.413\)).

Examples of comparing rational numbers in everyday life include shopping (comparing prices), cooking (measuring ingredients), and sports (comparing statistics).