Testinar Grade 5 math

Multiplication as Scaling

Students will interpret multiplication as scaling and compare the size of products.

CH05-05 Fraction Multiplication

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

Which is larger: \(8\) or \(8 \times \frac{2}{3}\)?
1. They are equal
2. \(8\)
3. \(8 \times \frac{2}{3}\)
4. Cannot be determined
A recipe calls for \(6\) cups of flour. If you double the recipe, how much flour do you need?
1. \(3\) cups
2. \(6\) cups
3. \(9\) cups
4. \(12\) cups
What is the value at the endpoint (product)?
1. \(5\frac{1}{3}\)
2. \(3\)
3. \(8\)
4. \(10\)
A piece of fabric is \(12\) feet long. If you cut it to \(\frac{1}{4}\) of its original length, how long is the piece?
1. \(6\) feet
2. \(9\) feet
3. \(12\) feet
4. \(3\) feet
If the large bar represents \(12\) inches, what length does the colored part represent?
1. \(3\) inches
2. \(2\) inches
3. \(4\) inches
4. \(6\) inches
Which statement is true?
1. \(6 \times 1 = 6\) and \(6 \times \frac{3}{4} < 6\)
2. \(6 \times 1 = 6\) and \(6 \times \frac{3}{4} > 6\)
3. \(6 \times 1 = 6\) and \(6 \times \frac{3}{4} = 6\)
4. \(6 \times \frac{3}{4} > 6 \times 1\)
A cookie recipe makes \(20\) cookies. If you make \(\frac{1}{2}\) of the recipe, how many cookies will you make?
1. \(10\) cookies
2. \(20\) cookies
3. \(30\) cookies
4. \(40\) cookies
A ribbon is \(15\) inches long. You need to cut it to \(\frac{2}{5}\) of its length. How long will the cut piece be?
1. \(3\) inches
2. \(9\) inches
3. \(12\) inches
4. \(6\) inches

Teacher and parent reference

Answer key and explanations

B. \(8\)
When you multiply by a fraction less than 1, the result is smaller. Since \(\frac{2}{3} < 1\), we have \(8 \times \frac{2}{3} < 8\). Therefore, \(8\) is larger.
D. \(12\) cups
Doubling means multiplying by \(2\). \(6 \times 2 = 12\) cups. Scaling by a factor greater than \(1\) increases the amount.
A. \(5\frac{1}{3}\)
\(8 \times \frac{2}{3} = \frac{16}{3} = 5\frac{1}{3}\). The product is less than 8 because the scaling factor is less than 1.
D. \(3\) feet
\(12 \times \frac{1}{4} = 3\) feet. Multiplying by a fraction less than \(1\) shrinks the quantity.
A. \(3\) inches
The colored part is \(\frac{1}{4}\) of the whole bar. \(12 \times \frac{1}{4} = 3\) inches.
A. \(6 \times 1 = 6\) and \(6 \times \frac{3}{4} < 6\)
Multiplying by \(1\) keeps the value the same. Multiplying by \(\frac{3}{4}\) (less than \(1\)) makes it smaller: \(6 \times \frac{3}{4} = 4\frac{1}{2} < 6\).
A. \(10\) cookies
Half of \(20\) is \(20 \times \frac{1}{2} = 10\) cookies. Scaling by \(\frac{1}{2}\) halves the amount.
D. \(6\) inches
\(15 \times \frac{2}{5} = \frac{30}{5} = 6\) inches. The product is smaller because the scaling factor is less than \(1\).