Fractions A

Answer explanation

To simplify \(\frac{9}{12}\), divide both the numerator and denominator by 3, resulting in \(\frac{3}{4}\). For \(\frac{3}{6}\), divide by 3 to get \(\frac{1}{2}\). The correct simplifications are \(\frac{9}{12} = \frac{3}{4}\) and \(\frac{3}{6} = \frac{1}{2}\).

Answer explanation

Max is incorrect. The fraction \( \frac{6}{8} \) can be simplified further by dividing both the numerator and denominator by 2, resulting in \( \frac{3}{4} \), which is the simplest form.

• 6 1/6

• 5 1/2

• 7 1/3

• 6 2/3

Answer explanation

The arrow points to the number 6 1/6, which is the correct choice. The other options, 5 1/2, 7 1/3, and 6 2/3, do not match the indicated value on the number line.

Answer explanation

To order the fractions, convert them to decimals: \(\frac{2}{9} \approx 0.22\), \(\frac{4}{9} \approx 0.44\), \(\frac{4}{7} \approx 0.57\), \(\frac{6}{7} \approx 0.86\). Thus, the order is \(\frac{2}{9}, \frac{4}{9}, \frac{4}{7}, \frac{6}{7}\).

• The question involves calculating the results of three different mathematical expressions involving fractions.

• The question involves solving algebraic equations.

• The question involves finding the derivative of a function.

• The question involves calculating the area of a circle.

Answer explanation

The question involves calculating the results of three different mathematical expressions involving fractions, as indicated by the operations performed on the fractions.

Answer explanation

The fraction \( \frac{17}{17} \) equals 1 because the numerator and denominator are the same. The other fractions, \( \frac{42}{48} \) and \( \frac{15}{60} \), do not equal 1.

Answer explanation

Kim reads \(\frac{2}{5} + \frac{2}{4} = \frac{8}{20} + \frac{10}{20} = \frac{18}{20}\) of the book by Tuesday. The remaining fraction is \(1 - \frac{18}{20} = \frac{2}{20} = \frac{1}{10}\). Thus, she reads \(\frac{7}{20}\) on Wednesday.

Did Eva, Jack, and Dora each get an equal slice of cake?

• Yes, because all fractions are equivalent.

Answer explanation

No, because \(\frac{4}{16}\) and \(\frac{2}{8}\) are both equivalent to one quarter, while \(\frac{6}{20}\) is greater than one quarter, indicating they did not receive equal slices.

A paper rectangle has an area of 12 2/3 cm². Max cuts a circle from the rectangle. The circle has an area of 4 5/6 cm². What is the area of the paper that is left?

• 7 5/6 cm²

• 8 cm²

• 6 1/2 cm²

• 7 cm²

Answer explanation

To find the area left after cutting the circle from the rectangle, subtract the area of the circle (4 5/6 cm²) from the area of the rectangle (12 2/3 cm²). This results in 7 5/6 cm², which is the correct answer.