Free Math Worksheets

- Count all equal parts or objects to find the denominator. - Count the shaded parts or objects to find the numerator. - Read the numerator as a counting number and use the fraction name for the denominator.

1. In a), \(3\) of \(8\) equal sectors are shaded, so the fraction is \(\frac{3}{8}\), or three eighths. 2. In b), \(2\) of \(5\) equal parts are shaded, so the fraction is \(\frac{2}{5}\), or two fifths. 3. In c), \(7\) of \(12\) objects are shaded, so the fraction is \(\frac{7}{12}\), or seven twelfths.

a) \(\frac{3}{8}\); three eighths b) \(\frac{2}{5}\); two fifths c) \(\frac{7}{12}\); seven twelfths

- How many equal sections make the whole bed? That number is the denominator. - Count how many sections each flower type covers. - After accounting for the red and blue flowers, how many sections remain for the yellow flowers? - Compare the fractions for the red and yellow flowers.

1. The whole bed has \(4\) equal sections. 2. The blue flowers cover \(2\) of the \(4\) sections, so they cover \(\frac{2}{4} = \frac{1}{2}\). 3. The yellow flowers cover \(4 - 1 - 2 = 1\) section, so they cover \(\frac{1}{4}\). 4. The red roses and yellow sunflowers each cover \(1\) of the \(4\) equal sections, so their fractions are equal.

a) \(\frac{2}{4}\), or \(\frac{1}{2}\) b) \(\frac{1}{4}\) c) The fractions are equal because each flower type covers \(\frac{1}{4}\) of the bed.

- Count the total number of equal parts in the whole cake. - How many parts are shaded yellow? - Use the number of selected parts as the numerator and the total number of parts as the denominator. - How many unshaded slices are needed to complete the whole cake?

1. Count the yellow slices: \(5\) slices remain. 2. The cake has \(8\) equal slices, so the fraction remaining is \(\frac{5}{8}\). 3. The number eaten is \(8 - 5 = 3\), so the fraction eaten is \(\frac{3}{8}\).

a) \(5\) slices b) \(\frac{5}{8}\) c) \(\frac{3}{8}\)

- Count the total number of equal boards. - Count the blue-shaded boards, then find how many are unshaded. - Write the number of unshaded boards over the total number of boards.

1. The fence has \(8\) equal boards in all. 2. The diagram shows \(3\) painted boards, so \(8-3=5\) boards remain unpainted. 3. Therefore, the fraction that still needs to be painted is \(\frac{5}{8}\).

\(\frac{5}{8}\) of the fence still needs to be painted.

- Identify the labeled sector that covers half of the circle. - Find the labeled sector that is half as large as the one-half sector. - Compare the two smallest labeled sectors with the one-fourth sector.

1. Sector A covers one half of the circle, so it represents the peanuts. 2. Sector B covers one fourth of the circle, so it represents the cashews. 3. Sectors C and D each cover one eighth of the circle. They represent the almonds and raisins in either order.

Peanuts: A, \(\frac{1}{2}\) Cashews: B, \(\frac{1}{4}\) Almonds and raisins: C and D in either order, \(\frac{1}{8}\) each

- Count the total number of equal pizza slices. - Count the shaded and unshaded slices. - The numerator tells how many slices are selected, and the denominator tells how many equal slices make the whole. - All the slices together make one whole pizza.

1. Four of the \(10\) slices have pepperoni, so \(10 - 4 = 6\) slices have only cheese. 2. The pepperoni fraction is \(\frac{4}{10}\). 3. The cheese-only fraction is \(\frac{6}{10}\). 4. The two fractions combine to make the whole: \(\frac{4}{10} + \frac{6}{10} = \frac{10}{10} = 1\).

a) \(6\) slices b) \(\frac{4}{10}\) c) \(\frac{6}{10}\) d) \(\frac{4}{10}\) and \(\frac{6}{10}\)

- First count how many equal parts make the whole. - Then count how many of those parts are shaded. - Does the total number of parts go in the numerator or denominator? - The numerator tells how many parts are selected or shaded.

1. For each part, count the total number of equal parts. This number is the denominator. 2. Count the shaded parts. This number is the numerator. 3. Write the fraction as \(\frac{\text{shaded parts}}{\text{total parts}}\). 4. Results: - a) The circle has \(5\) parts, and \(2\) are shaded: \(\frac{2}{5}\). - b) The grid has \(2 \times 4 = 8\) squares, and \(3\) are shaded: \(\frac{3}{8}\). - c) The bar has \(6\) sections, and \(5\) are shaded: \(\frac{5}{6}\). - d) The group has \(12\) circles, and \(7\) are shaded: \(\frac{7}{12}\).

a) \(\frac{2}{5}\) b) \(\frac{3}{8}\) c) \(\frac{5}{6}\) d) \(\frac{7}{12}\)

- The numerator is the top number, and the denominator is the bottom number. - The denominator describes how many equal parts make the whole. - Subtract the shaded squares from the total to find the unshaded squares.

1. Since \(5\) of \(12\) squares are shaded, the shaded fraction is \(\frac{5}{12}\). 2. The numerator is \(5\), and the denominator is \(12\). 3. The denominator tells the number of equal parts in the whole rectangle. 4. The number of unshaded squares is \(12-5=7\), so the unshaded fraction is \(\frac{7}{12}\).

a) Numerator: \(5\); denominator: \(12\) b) The denominator represents the \(12\) equal parts in the whole rectangle. c) \(\frac{7}{12}\)

- One-fourth means that four equal parts make one whole. - Use the number in one part to find the number in all four parts.

One-fourth is one of four equal parts. If one part has \(18\) dots, the whole set has four groups of \(18\) dots: \(4 \times 18 = 72\).

There are \(72\) dots. One-fourth is one of four equal parts, so \(4 \times 18 = 72\).

- Add the slice values to find the whole. - Find one-half of the whole. - Match that value to a slice.

1. The total is \(12 + 6 + 6 = 24\). 2. One-half of \(24\) is \(24 \div 2 = 12\). 3. Reading has a value of \(12\), so it takes up one-half of the chart.

Reading takes up exactly one-half of the pie chart.

- Add all four values to find the whole. - Find one-half of the whole. - Look for two equal slice values.

1. The total is \(4 + 8 + 4 + 16 = 32\). 2. One-half of \(32\) is \(16\), so walking takes up one-half of the chart. 3. Train and bike each have a value of \(4\), so their slices are equal.

1) Walking takes up one-half of the chart. 2) Train and bike have equal-sized slices.

- Compare the slice sizes. - Look for two equal smaller slices. - Use the whole circle to identify halves and fourths.

1. The water slice is as large as the other two slices combined, so it takes up one-half of the circle. 2. The juice and milk slices are equal and split the other half into two equal parts. 3. Therefore, juice and milk each take up one-fourth of the circle.

1) Water takes up one-half. 2) Juice and milk each take up one-fourth.

- Think of the whole pizza as \(8\) equal parts. - Write one half as an equivalent fraction with denominator \(8\). - Subtract the number eaten from \(8\) to find the number remaining.

1. Three of the \(8\) slices have been eaten, so the eaten fraction is \(\frac{3}{8}\). 2. Half of \(8\) slices is \(4\) slices. Since \(3\) have already been eaten, \(4-3=1\) more slice must be eaten. 3. If \(5\) slices have been eaten, \(8-5=3\) slices remain. The remaining fraction is \(\frac{3}{8}\).

a) \(\frac{3}{8}\) b) \(1\) more slice c) \(\frac{3}{8}\)