Jane has 5 1/4 yards of lace. If a handkerchief requires 3/4 yards of lace and Jane will make 3 handkerchiefs, how many yards of lace will be left?
Understand the Problem
The question is asking how much lace will be left after Jane uses some to make three handkerchiefs. To solve this, we will first calculate the total amount of lace she uses for the handkerchiefs and then subtract that from the initial amount she has.
Answer
$3$
Answer for screen readers
Jane will have $3$ yards of lace left.
Steps to Solve
- Convert Mixed Number to Improper Fraction
First, convert ( 5 \frac{1}{4} ) into an improper fraction.
To do this: [ 5 \frac{1}{4} = \frac{(5 \times 4) + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} ]
- Calculate Total Lace Used for Handkerchiefs
Next, calculate the total amount of lace needed for 3 handkerchiefs. Each handkerchief requires ( \frac{3}{4} ) yards of lace, so for 3 handkerchiefs, we need: [ 3 \times \frac{3}{4} = \frac{9}{4} ]
- Subtract the Used Lace from the Initial Amount
Now, subtract the total lace used from the initial amount of lace: [ \frac{21}{4} - \frac{9}{4} = \frac{21 - 9}{4} = \frac{12}{4} = 3 ]
Jane will have $3$ yards of lace left.
More Information
This problem involves basic arithmetic operations with fractions, specifically addition, multiplication, and subtraction. Understanding how to convert mixed numbers and calculate with fractions are key skills in this type of problem.
Tips
- Not converting mixed numbers: Forgetting to convert (5 \frac{1}{4}) into an improper fraction can lead to confusion.
- Incorrect multiplication of fractions: Make sure to multiply correctly when calculating the total lace needed.
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