Testinar Grade 4 math

Multiples of a Fraction

Students will generate multiples of a fraction and represent them with equations, number lines, and models.

CH05-03 Fraction Multiplication

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Which shows a multiple of \(\frac{2}{3}\)?
1. \(\frac{2}{6}\)
2. \(\frac{4}{9}\)
3. \(\frac{4}{3}\)
4. \(\frac{5}{6}\)
Sam has a number line with hops of \(\frac{1}{4}\). Which point represents \(3\times\frac{1}{4}\)?
1. Point A
2. Point B
3. Point C
4. Point D
Which fraction is a multiple of \(\frac{1}{5}\)?
1. \(\frac{2}{5}\)
2. \(\frac{1}{10}\)
3. \(\frac{3}{4}\)
4. \(\frac{2}{7}\)
Maya lined up 4 unit-fraction tiles. If each tile is \(\frac{1}{6}\), what is the total?
1. \(\frac{1}{6}\)
2. \(\frac{2}{6}\)
3. \(\frac{4}{6}\)
4. \(\frac{6}{6}\)
Which shows the first four consecutive multiples of \(\frac{1}{3}\) in order?
1. \(\frac{1}{3}, \frac{2}{3}, \frac{4}{3}, \frac{5}{3}\)
2. \(\frac{1}{3}, \frac{2}{3}, \frac{3}{3}, \frac{4}{3}\)
3. \(\frac{1}{3}, \frac{1}{6}, \frac{1}{9}, \frac{1}{12}\)
4. \(\frac{1}{3}, \frac{2}{3}, \frac{3}{9}, \frac{4}{9}\)
What is \(5 \times \frac{1}{4}\)?
1. \(\frac{1}{20}\)
2. \(\frac{4}{5}\)
3. \(\frac{5}{4}\)
4. \(\frac{5}{8}\)
A number line shows hops of \(\frac{2}{5}\). How many hops to reach \(\frac{10}{5}\)?
1. 2 hops
2. 3 hops
3. 4 hops
4. 5 hops
Noah skipped by \(\frac{1}{8}\) along a number line. He stopped at \(\frac{3}{8}\). How many skips did he make?
1. 1 skip
2. 2 skips
3. 3 skips
4. 4 skips

Teacher and parent reference

Answer key and explanations

C. \(\frac{4}{3}\)
The multiples of \(\frac{2}{3}\) are: \(\frac{2}{3}, \frac{4}{3}, \frac{6}{3}, \ldots\) Each one is obtained by multiplying \(\frac{2}{3}\) by whole numbers. Since \(\frac{4}{3} = 2 \times \frac{2}{3}\), the answer is \(\mathbf{\frac{4}{3}}\).
C. Point C
Starting at 0, each hop moves us forward by \(\frac{1}{4}\). After three hops, we land at \(3 \times \frac{1}{4} = \frac{3}{4}\), which is Point C.
A. \(\frac{2}{5}\)
A multiple of \(\frac{1}{5}\) means we count by fifths. We can write \(\frac{2}{5} = 2 \times \frac{1}{5}\), so it"s a multiple. The others don"t fit that pattern.
C. \(\frac{4}{6}\)
Four tiles, each \(\frac{1}{6}\), combine to make \(4 \times \frac{1}{6} = \frac{4}{6}\).
B. \(\frac{1}{3}, \frac{2}{3}, \frac{3}{3}, \frac{4}{3}\)
Multiples of \(\frac{1}{3}\) count by thirds: first \(\frac{1}{3}\), then \(\frac{2}{3}\), then \(\frac{3}{3}\), then \(\frac{4}{3}\). The fraction \(\frac{3}{3}\) equals \(1\), but it is written in thirds here to show the counting pattern. That"s exactly what choice B shows!
C. \(\frac{5}{4}\)
When we multiply by the numerator, we keep the denominator the same. So \(5 \times \frac{1}{4} = \frac{5}{4}\).
D. 5 hops
Each hop is \(\frac{2}{5}\). To reach \(\frac{10}{5}\), we need \(5 \times \frac{2}{5} = \frac{10}{5}\), so it takes 5 hops.
C. 3 skips
Noah skips in eighths: \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}\). After 3 skips, he"s at \(\frac{3}{8}\).