Introduction to Fractions: practice solutions, Grade 3 – download the PDF

1 Name the shaded fraction ★★★

The bar has 6 equal parts, so the denominator is 6. Five parts are colored, so the numerator is 5.

The colored part is \(\dfrac{5}{6}\) of the bar.

2 Unit fractions in words ★★★

1. The sandwich has 2 equal pieces, so one piece is \(\dfrac{1}{2}\).
2. One of 6 equal parts is \(\dfrac{1}{6}\).
3. Three copies of \(\dfrac{1}{4}\) make \(\dfrac{3}{4}\).

3 Shade the fractions ★★★

1. The numerator is 3, so you color 3 parts.
2. \(8 - 3 = 5\) parts stay white. The white part is \(\dfrac{5}{8}\) of the strip.

4 Read a number line ★★★

Each length is \(\dfrac{1}{4}\). Point A is 3 jumps from 0, so A is at \(\dfrac{3}{4}\). Point B is 1 jump from 0, so B is at \(\dfrac{1}{4}\).

5 Which piece is bigger? ★★★

1. Ines has \(\dfrac{1}{3}\) and Theo has \(\dfrac{1}{6}\). Fewer parts means bigger parts, so Ines has the bigger piece.
2. The whole cut in 2 gives bigger parts than the whole cut in 8, so \(\dfrac{1}{2} > \dfrac{1}{8}\).

6 Whole numbers as fractions ★★★

A whole is \(\dfrac{n}{n}\), so \(1 = \dfrac{4}{4}\), \(1 = \dfrac{8}{8}\) and \(1 = \dfrac{6}{6}\).

\(\dfrac{n}{1} = n\), so \(\dfrac{5}{1} = 5\).

7 True or false? ★★★

1. True. All 3 of the 3 equal parts make the whole.
2. False. Fourths need 4 equal parts. These pieces are not the same size.
3. False. Cutting into 5 parts gives smaller parts than cutting into 4, so \(\dfrac{1}{5} < \dfrac{1}{4}\).

8 Same denominator ★★★

1. The denominators are the same, and 4 > 2, so \(\dfrac{4}{6} > \dfrac{2}{6}\).
2. 7 > 5, so \(\dfrac{5}{8} < \dfrac{7}{8}\).

With sixths, the order of the numerators 1, 3, 4, 5 gives \(\dfrac{1}{6} < \dfrac{3}{6} < \dfrac{4}{6} < \dfrac{5}{6}\).

9 Same numerator ★★★

The numerators are the same, so the smaller denominator gives the greater fraction.

1. 4 < 8, so \(\dfrac{3}{4} > \dfrac{3}{8}\).
2. 6 < 8, so \(\dfrac{5}{6} > \dfrac{5}{8}\).

The denominators from greatest to least are 6, 4, 3, so the order is \(\dfrac{2}{6} < \dfrac{2}{4} < \dfrac{2}{3}\).

10 Equal or not? ★★★

1. Yes. The colored parts cover the same length of the bar, so \(\dfrac{2}{3} = \dfrac{4}{6}\).
2. Cut each half into 3 equal pieces: 1 half becomes 3 sixths, so \(\dfrac{1}{2} = \dfrac{3}{6}\). Cut each fourth into 2 pieces: 3 fourths become 6 eighths, so \(\dfrac{3}{4} = \dfrac{6}{8}\).

11 Fractions beyond 1 ★★★

1. Each jump is \(\dfrac{1}{3}\). P is 5 jumps from 0, so P is at \(\dfrac{5}{3}\). Q is 2 jumps from 0, so Q is at \(\dfrac{2}{3}\).
2. Point P is closer to 2, since \(2 = \dfrac{6}{3}\) and P is only one jump away from it.

12 Crayons in a box ★★★

1. \(12 \div 4 = 3\), so \(\dfrac{1}{4}\) of 12 is 3. There are 3 red crayons.
2. 3 of the 4 groups are not red, so \(\dfrac{3}{4}\) of the crayons are not red. That is \(3 \times 3 = 9\) crayons.

13 Slices of banana bread ★★★

1. Nora ate \(\dfrac{3}{8}\) and her brother ate \(\dfrac{2}{8}\).
2. \(3 + 2 = 5\) slices, so together they ate \(\dfrac{5}{8}\) of the loaf.
3. \(8 - 5 = 3\) slices are left, which is \(\dfrac{3}{8}\) of the loaf.

14 Wholes written as fractions ★★★

1. Each whole has 6 sixths, and 2 wholes have \(2 \times 6 = 12\) sixths, so \(2 = \dfrac{12}{6}\).
2. \(3 \times 4 = 12\) fourths, so \(3 = \dfrac{12}{4}\).
3. Each whole has 2 halves, so 4 wholes have \(4 \times 2 = 8\) halves. Then \(4 = \dfrac{8}{2}\).

15 Compare to one whole ★★★

1. \(\dfrac{4}{4} = 1\). The fraction \(\dfrac{5}{6}\) is only 5 of 6 parts, so it is less than 1. Therefore \(\dfrac{4}{4} > \dfrac{5}{6}\).
2. \(\dfrac{6}{3} = 2\) and \(2 = \dfrac{8}{4}\). Since \(8 > 7\) with the same denominator 4, \(\dfrac{7}{4} < \dfrac{8}{4}\). So \(\dfrac{6}{3} > \dfrac{7}{4}\).

16 Find the mistake ★★★

1. Leo compares the denominators as if they were the sizes of the pieces. But a greater denominator means the whole is cut into more parts, so each part is smaller.
2. Take two paper strips of the same length. Fold one into 3 equal parts and the other into 8 equal parts. A third is a long piece and an eighth is a short piece. So \(\dfrac{1}{8} < \dfrac{1}{3}\).

17 Marbles in a bag ★★★

1. \(24 \div 8 = 3\), so one eighth is 3 marbles. Then \(\dfrac{3}{8}\) of 24 is \(3 \times 3 = 9\) blue marbles.
2. \(24 \div 6 = 4\), so there are 4 green marbles. The others are \(\dfrac{5}{6}\) of the bag: \(5 \times 4 = 20\) marbles are not green.
3. \(24 \div 3 = 8\), so \(\dfrac{2}{3}\) of 24 is \(2 \times 8 = 16\) glass marbles.

18 Trail race ★★★

The denominators are different, so we write \(\dfrac{3}{4}\) with eighths: cutting each fourth into 2 equal parts gives \(\dfrac{3}{4} = \dfrac{6}{8}\).

Now we compare \(\dfrac{6}{8}\) and \(\dfrac{5}{8}\). Since \(6 > 5\), \(\dfrac{6}{8} > \dfrac{5}{8}\). Sam ran farther.

19 Find the equal fractions ★★★

1. The colored parts of the first and third bars match, so \(\dfrac{1}{2} = \dfrac{3}{6}\).
2. The second and fourth bars match, so \(\dfrac{2}{3} = \dfrac{4}{6}\).
3. Same denominator and \(3 < 4\), so \(\dfrac{3}{6} < \dfrac{4}{6}\). Because \(\dfrac{1}{2} = \dfrac{3}{6}\) and \(\dfrac{2}{3} = \dfrac{4}{6}\), we get \(\dfrac{1}{2} < \dfrac{2}{3}\).

20 Ribbon in inches ★★★

1. One piece is \(\dfrac{1}{4}\) of the ribbon. \(12 \div 4 = 3\), so it is 3 inches long.
2. Three pieces are \(\dfrac{3}{4}\) of the ribbon, and \(3 \times 3 = 9\), so she uses 9 inches.

21 Paper strip in centimeters ★★★

1. \(24 \div 8 = 3\), so one piece is 3 centimeters long.
2. The blue part is \(\dfrac{5}{8}\) of the strip, and \(5 \times 3 = 15\), so it is 15 centimeters.
3. \(8 - 5 = 3\) pieces are red, so \(\dfrac{3}{8}\) of the strip is red.