Which sign makes the statement true? 5/10 ? 1/2 − 1/10 Choices: (A)> (B)< (C)=

Simplify Fractions: Simplify the fractions to make comparison easier. 5/10 simplifies to 1/2. So, the comparison is now between 1/2 ? 1/2 - 1/10. Subtract to Compare: Subtract 1/10 from 1/2 to find the value to compare with 1/2. Convert 1/2 to 5/10 to have a common denominator with 1/10. Now, 5/10 - 1/10 = 4/10, which simplifies to 2/5. Compare Fractions: Compare 1/2 with 2/5. Convert both fractions to have a common denominator, which is 10. 1/2 becomes 5/10 and 2/5 becomes 4/10. Since 5/10 is greater than 4/10, the correct sign is '>'.

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Math Problems

Grade 7

Inequalities with addition and subtraction of fractions and mixed numbers

Full solution

Q. Which sign makes the statement true?

\newline

\frac{5}{10}

\text{?}

\frac{1}{2} - \frac{1}{10}

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Simplify Fractions: Simplify the fractions to make comparison easier. $\frac{5}{10}$ simplifies to $\frac{1}{2}$ . So, the comparison is now between $\frac{1}{2} \,?\, \frac{1}{2} - \frac{1}{10}$ .
Subtract to Compare: Subtract $\frac{1}{10}$ from $\frac{1}{2}$ to find the value to compare with $\frac{1}{2}$ . Convert $\frac{1}{2}$ to $\frac{5}{10}$ to have a common denominator with $\frac{1}{10}$ . Now, $\frac{5}{10} - \frac{1}{10} = \frac{4}{10}$ , which simplifies to $\frac{2}{5}$ .
Compare Fractions: Compare $\frac{1}{2}$ with $\frac{2}{5}$ . Convert both fractions to have a common denominator, which is $10$ . $\frac{1}{2}$ becomes $\frac{5}{10}$ and $\frac{2}{5}$ becomes $\frac{4}{10}$ . Since $\frac{5}{10}$ is greater than $\frac{4}{10}$ , the correct sign is '>'.