- Calculate the total fabric needed: \(4 \times 1 \frac{7}{8} = 7.5\) yards.
- Convert fabric amounts to decimals: Moons and Stars (\(7.5\)), Softballs (\(7.4\)), Stripes (\(7.6\)), Tie-Dye (\(7.9\)).
- Compare each amount with 7.5 to find sufficient fabrics: Moons and Stars, Stripes, and Tie-Dye are all \(\geq 7.5\).
- Final Answer: \(\boxed{\text{Moons and Stars, Stripes, and Tie-Dye}}\)
Explanation
- Calculate the Total Required Fabric
To determine which fabrics are sufficient, we must first calculate the total amount of fabric Jessica needs for 4 book bags. Each bag requires \(1 \frac{7}{8}\) yards. We convert the mixed number to an improper fraction:
\(1 \frac{7}{8} = 1 + \frac{7}{8} = \frac{8}{8} + \frac{7}{8} = \frac{15}{8}\) yards per bag.
For 4 bags, the total amount of fabric required is:
\(4 \times \frac{15}{8} = \frac{60}{8} = 7.5\) yards.
- Convert Available Fabric to Decimals
Next, we convert each available fabric amount into decimal form to make it easy to compare with our required amount of 7.5 yards.
- Moons and Stars: \(7 \frac{1}{2} = 7.5\) yards.
- Softballs: \(7.4\) yards.
- Stripes: \(7 \frac{3}{5} = 7 + 0.6 = 7.6\) yards.
- Tie-Dye: \(7.9\) yards.
- Evaluate and Conclude
Now, we compare each available fabric amount to the required 7.5 yards. A fabric can be used if the amount available is greater than or equal to 7.5 yards.
- Moons and Stars: \(7.5 \geq 7.5\) (Sufficient)
- Softballs: \(7.4 < 7.5\) (Insufficient)
- Stripes: \(7.6 \geq 7.5\) (Sufficient)
- Tie-Dye: \(7.9 \geq 7.5\) (Sufficient)
Jessica can use the Moons and Stars, Stripes, and Tie-Dye fabrics.
Examples
Knowing how to compare quantities, such as fabric requirements for multiple projects, is a fundamental skill in everyday life. Whether you are buying groceries for a recipe, calculating materials for a DIY home project, or budgeting your time and money, converting units and performing comparisons helps ensure you have enough resources. For instance, if you are planning a road trip and need to know if your gas tank will cover the distance, you calculate your total consumption and compare it against your fuel capacity, just like Jessica did with her fabric.