Question

int math 2a pringle operations on rational and irrational numbers multiply rational numbers choose the correct option from the drop-down for each equation. ( 5\frac{1}{6} cdot left(-\frac{2}{5}
ight) = -\frac{31}{15} ), ( 1.9 cdot left(\frac{1}{4}
ight) = \frac{19}{40} ), and ( 2.5 cdot 0.overline{3} = 0.8333 ) all of the numbers in these multiplication problems are rational, which means that each of these numbers can be written as a drop-down. since the answers to these problems can be written as fractions, the answers are drop-down. this shows that the product of two rational numbers will always be drop-down.

Explanation:

To solve this, we recall the definition of rational numbers: a rational number is a number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. Decimals (terminating or repeating) and mixed numbers can also be written as fractions.

First Drop - Down:

Rational numbers can be written as a fraction (or ratio) of two integers (where the denominator is non - zero). For example, $5\frac{1}{6}=\frac{31}{6}$, $- \frac{2}{5}$ is already a fraction, $1.9=\frac{19}{10}$, $\frac{1}{4}$ is a fraction, $2.5=\frac{5}{2}$, and $0.\overline{3}=\frac{1}{3}$. So the first blank should be filled with "fraction (or ratio) of two integers".

Second Drop - Down:

Since the answers $-\frac{31}{15}$, $\frac{19}{40}$, and $0.8333\cdots=\frac{5}{6}$ (because $2.5\times0.\overline{3}=\frac{5}{2}\times\frac{1}{3}=\frac{5}{6}$) can be written as fractions, and by the definition of rational numbers, numbers that can be written as fractions are rational. So the second blank should be filled with "rational".

Third Drop - Down:

From the examples, when we multiply two rational numbers ($5\frac{1}{6}$ and $-\frac{2}{5}$; $1.9$ and $\frac{1}{4}$; $2.5$ and $0.\overline{3}$), the product is also a rational number. This is a property of rational numbers: the product of two rational numbers is always rational. So the third blank should be filled with "rational".

Final Answers:

1. fraction (or ratio) of two integers
2. rational
3. rational

Answer:

To solve this, we recall the definition of rational numbers: a rational number is a number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. Decimals (terminating or repeating) and mixed numbers can also be written as fractions.

First Drop - Down:

Rational numbers can be written as a fraction (or ratio) of two integers (where the denominator is non - zero). For example, $5\frac{1}{6}=\frac{31}{6}$, $- \frac{2}{5}$ is already a fraction, $1.9=\frac{19}{10}$, $\frac{1}{4}$ is a fraction, $2.5=\frac{5}{2}$, and $0.\overline{3}=\frac{1}{3}$. So the first blank should be filled with "fraction (or ratio) of two integers".

Second Drop - Down:

Since the answers $-\frac{31}{15}$, $\frac{19}{40}$, and $0.8333\cdots=\frac{5}{6}$ (because $2.5\times0.\overline{3}=\frac{5}{2}\times\frac{1}{3}=\frac{5}{6}$) can be written as fractions, and by the definition of rational numbers, numbers that can be written as fractions are rational. So the second blank should be filled with "rational".

Third Drop - Down:

From the examples, when we multiply two rational numbers ($5\frac{1}{6}$ and $-\frac{2}{5}$; $1.9$ and $\frac{1}{4}$; $2.5$ and $0.\overline{3}$), the product is also a rational number. This is a property of rational numbers: the product of two rational numbers is always rational. So the third blank should be filled with "rational".

Final Answers:

1. fraction (or ratio) of two integers
2. rational
3. rational