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1.
When is the product of two fractions less than the value of either factor?
when both fractions are improper
when one fraction is improper and the other is a proper fraction
when both numbers are proper fractions
when one factor is a mixed number and the other is a proper fraction
The product of two improper fractions is larger than either factor.
This product will be smaller than the improper fraction but larger than the proper fraction.
The product of two proper fractions is smaller than either factor.
This product will be smaller than the mixed number but larger than the proper fraction.
2.
Which represents the final grid model of \( \frac{2}{3} \times \frac{4}{5} \)
A rectangle that is vertically divided into 3 equal columns and horizontally divided into 4 equal rows. There are 12 total sections. Of the 12 total sections, 8 are shaded green and 4 are shaded blue. The green shading represents the overlap.
A rectangle that is vertically divided into 3 equal columns and horizontally divided into 5 equal rows. There are 15 total sections. Of the 15 total sections, 8 are shaded green, 4 are shaded blue, and 2 are shaded light green. The green shading represents the overlap.
A rectangle that is vertically divided into 3 equal columns. One column is divided into 5 equal rows. The two columns are shaded green, and one column has 4 blue shaded boxes. The green shading represents the overlap.
A rectangle that is vertically divided into 8 equal columns. Two columns are shaded green. Then there is an unshaded column. The next four columns are shaded blue. The final column is unshaded. The green shading represents the overlap.
To represent the fraction \( \frac{4}{5} \), this model should have 5 rows.
In this model, the fraction \( \frac{2}{3} \) is represented by the green columns. The fraction \( \frac{4}{5} \) is represented by the blue rows. The overlap is represented by the dark green squares.
This grid model has 3 columns, but not 5 rows. There are no overlapping sections.
This grid model has no rows. There are no overlapping sections.
3.
What multiplication problem is represented by this grid model?
A rectangle that is vertically divided into 4 equal columns and horizontally divided into 3 equal rows. There are 12 total sections. Of the 12 total sections, 3 are shaded green, 1 is shaded blue, and 6 are shaded yellow. The green shading represents the overlap.
Count the total number of columns and then the total number of shaded columns. This represents one factor. Count the total number of rows and then the total number of shaded rows. This is the other factor. Determine where the overlap occurs. This represents the numerator of the product, while the product’s denominator is the total number of boxes in the grid.
Count the total number of columns and then the total number of shaded columns. This represents one factor. Count the total number of rows and then the total number of shaded rows. This is the other factor. Determine where the overlap occurs. This represents the numerator of the product, while the product’s denominator is the total number of boxes in the grid.
Count the total number of columns and then the total number of shaded columns. This represents one factor. Count the total number of rows and then the total number of shaded rows. This is the other factor. Determine where the overlap occurs. This represents the numerator of the product, while the product’s denominator is the total number of boxes in the grid.
There are 4 columns, and 3 are shaded. One factor is \( \frac{3}{4} \). There are 3 rows, and 1 of them is shaded. The other factor is \( \frac{1}{3} \). To calculate the product, count the overlapping shading, 3, and place that number over the total number of boxes, 12. The product is \( \frac{3}{12} \).
4.
What is \( \frac{5}{6} \) of \( \frac{3}{2} \)?
\( \frac{5}{4} \)
\( \frac{17}{12} \)
\( \frac{2}{3} \)
\( \frac{7}{3} \)
Multiply \( \frac{5}{6} \times \frac{2}{3} \). You can use the standard algorithm or a grid model. Reduce the product if needed. Using the standard algorithm:
\( \frac{5}{6} \times \frac{2}{3} = \frac{5 \times 3}{6 \times 2} = \frac{15}{12}\)
Both 15 and 12 share a GCF of 3. Then:
\( \frac{15 \div 3}{12 \div 3} = \frac{5}{4}\)
Multiply \( \frac{5}{6} \times \frac{2}{3} \). You can use the standard algorithm or a grid model. Reduce the product if needed.
Multiply \( \frac{5}{6} \times \frac{2}{3} \). You can use the standard algorithm or a grid model. Reduce the product if needed.
Multiply \( \frac{5}{6} \times \frac{2}{3} \). You can use the standard algorithm or a grid model. Reduce the product if needed.
5.
What is the first step to best predict the product of \( \frac{9}{4} \times \frac{4}{15} \)?
Simplify the product.
Carry out the multiplication.
Determine what kinds of fractions are being multiplied.
Calculate the sum of 2 and 4, then multiply it by 1.
Start by determining if the factors are proper fractions, improper fractions, or mixed numbers.
Start by determining if the factors are proper fractions, improper fractions, or mixed numbers.
You can predict the product by classifying the factors.
Start by determining if the factors are proper fractions, improper fractions, or mixed numbers.
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Multiply fractions using grid models and the standard algorithm.
Predict if the product of two fractions is greater or less than the value of its factors.
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