Free Math Worksheets

- How many equal slices make the whole pizza? - A fraction tells how many equal parts of a whole are being described. - How many slices remain after Lucas and Sarah eat theirs? - Can any fraction be written in an equivalent simpler form?

1. The whole pizza has \(8\) equal slices. 2. Lucas eats \(2\) of the \(8\) slices, so his fraction is \(\frac{2}{8} = \frac{1}{4}\). 3. Sarah eats \(1\) of the \(8\) slices, so her fraction is \(\frac{1}{8}\). 4. The parents receive \(8 - 2 - 1 = 5\) slices, so their fraction is \(\frac{5}{8}\).

Lucas: \(\frac{1}{4}\) (or \(\frac{2}{8}\)) Sarah: \(\frac{1}{8}\) Parents: \(\frac{5}{8}\)

- Count all the sections to find the denominator. - The number of shaded sections gives the numerator for the shaded fraction. - For the unshaded fraction, determine how many sections remain.

1. Count all the sections: the strip has \(6\) equal sections. 2. Count the shaded sections: \(2\) sections are shaded. 3. The shaded fraction is \(\frac{2}{6} = \frac{1}{3}\). 4. The number of unshaded sections is \(6 - 2 = 4\). 5. The unshaded fraction is \(\frac{4}{6} = \frac{2}{3}\).

a) \(6\) b) \(2\) c) \(\frac{2}{6}\), or \(\frac{1}{3}\) d) \(\frac{4}{6}\), or \(\frac{2}{3}\)

- Count the equal parts in each figure. That number is the denominator. - Count the shaded parts for the numerator of the first fraction. - The remaining parts form the numerator of the unshaded fraction.

1. Figure a) has \(5\) equal parts, with \(2\) shaded. The shaded fraction is \(\frac{2}{5}\), and the unshaded fraction is \(\frac{3}{5}\). 2. Figure b) has \(4\) equal parts, with \(1\) shaded. The shaded fraction is \(\frac{1}{4}\), and the unshaded fraction is \(\frac{3}{4}\). 3. Figure c) has \(6\) equal parts, with \(4\) shaded. The shaded fraction is \(\frac{4}{6} = \frac{2}{3}\), and the unshaded fraction is \(\frac{2}{6} = \frac{1}{3}\). 4. Figure d) has \(6\) equal parts, with \(5\) shaded. The shaded fraction is \(\frac{5}{6}\), and the unshaded fraction is \(\frac{1}{6}\).

a) shaded: \(\frac{2}{5}\); unshaded: \(\frac{3}{5}\) b) shaded: \(\frac{1}{4}\); unshaded: \(\frac{3}{4}\) c) shaded: \(\frac{4}{6}\), or \(\frac{2}{3}\); unshaded: \(\frac{2}{6}\), or \(\frac{1}{3}\) d) shaded: \(\frac{5}{6}\); unshaded: \(\frac{1}{6}\)

- Write the shaded fraction for each figure. - Look for fractions that name the same amount even though the numerators and denominators differ. - Use the models to compare the shaded portions.

1. Figure a) shows \(\frac{1}{4}\). 2. Figure b) shows \(\frac{2}{8}\), which is equivalent to \(\frac{1}{4}\). 3. Figure c) shows \(\frac{2}{6}\), which is equivalent to \(\frac{1}{3}\). 4. Figures a) and b) show the same fraction, while figure c) shows a different fraction.

Figure c). Figures a) and b) both show \(\frac{1}{4}\), while figure c) shows \(\frac{1}{3}\).

- Find the total in each chart. - Compare each color as a fraction of its chart total. - Equal fractions make equal proportional slices.

1. Red is the largest slice in both charts. 2. In a), the total is \(12 + 8 + 4 = 24\). The slices are \(\frac{12}{24} = \frac{1}{2}\), \(\frac{8}{24} = \frac{1}{3}\), and \(\frac{4}{24} = \frac{1}{6}\). 3. In b), the total is \(9 + 6 + 3 = 18\). The slices are \(\frac{9}{18} = \frac{1}{2}\), \(\frac{6}{18} = \frac{1}{3}\), and \(\frac{3}{18} = \frac{1}{6}\). 4. The corresponding fractions are equal, so the charts have the same proportions.

1) Red is largest in both charts. 2) Yes, the charts are divided in the same proportions.

- Find the total in each chart. - Write A as a fraction of each total. - Compare the two fractions.

1. The total in a) is \(10 + 10 + 10 = 30\). 2. The total in b) is \(10 + 15 + 5 = 30\). 3. In both charts, Section A is \(\frac{10}{30} = \frac{1}{3}\) of the whole. 4. Therefore, its slices are equal in size.

Yes. Section A is one-third of each chart, so its slices are equal in size.