Grade 7 Rational Numbers Practice Test

Correct answer: A

The correct answer is $\frac{2}{3}$.

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: Use a common denominator: $\frac{2}{3}=\frac{10}{15}$ and $\frac{3}{5}=\frac{9}{15}$, so $\frac{2}{3}$ is greater.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.

Correct answer: B

The correct answer is $-\frac{3}{4}$.

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: On a number line, $-0.75$ is to the left of $-0.666\ldots$, so $-\frac{3}{4}$ is smaller.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.

Correct answer: C

The correct answer is $-0.5, -\frac{1}{4}, \frac{1}{3}, \frac{3}{4}$.

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: Convert to decimals or use a common denominator: $-0.5<-0.25<0.333\ldots<0.75$.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.

Correct answer: D

The correct answer is $\frac{7}{8}$.

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: Absolute value is distance from zero, so $\left|-\frac{7}{8}\right|=\frac{7}{8}$.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.

Correct answer: A

The correct answer is $\frac{2}{5}$.

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: The opposite has the same distance from zero and the opposite sign: $-(-\frac{2}{5})=\frac{2}{5}$.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.

Correct answer: B

The correct answer is $\frac{5}{4}$.

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: Subtract the lower value from the higher value: $\frac{3}{4}-(-\frac{1}{2})=\frac{3}{4}+\frac{2}{4}=\frac{5}{4}$.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.

Correct answer: C

The correct answer is $-\frac{1}{3}$.

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: Compare absolute values: $\left|-\frac{1}{3}\right|=\frac{1}{3}<\frac{1}{2}$, so $-\frac{1}{3}$ is closer.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.

Correct answer: D

The correct answer is $-\frac{4}{5}< -\frac{3}{5}$.

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: Among negative numbers, the number with the greater absolute value is farther left, so $-\frac{4}{5}< -\frac{3}{5}$.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.

Correct answer: A

The correct answer is Every integer is a rational number..

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: An integer $n$ can be written as $\frac{n}{1}$, so it is rational.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.

Correct answer: B

The correct answer is $2.4$.

1. Identify the rational number operation: Determine whether the question asks about a representation, comparison, absolute value, addition, subtraction, multiplication, division, or an equation.
2. Use equivalent representations: Absolute value gives the nonnegative distance from zero, so $\left|-2.4\right|=2.4$.
3. Check the sign and value: Confirm the denominator is nonzero, apply the operation in the correct order, and check whether the result is reasonable.