Iris is cutting fleece to make scarves for her friends. She has ten and one-half feet of fleece to make 3 scarves. How long can she make each scarf? Show your work, and include cancellation in your steps
10 1/2 = 21/2
(21/2) / 3
(21/2) * (1/3) = 21/6 = 3 3/6 = 3 1/2 feet
To find out how long Iris can make each scarf, we need to divide the total length of the fleece by the number of scarves she wants to make.
Step 1: Convert the mixed number "ten and one-half" into an improper fraction.
- Multiply the whole number (10) by the denominator (2) and add the numerator (1), which gives us 10 x 2 + 1 = 20 + 1 = 21.
- The denominator remains the same, so the improper fraction is 21/2.
Step 2: Divide the improper fraction by the number of scarves.
- Divide 21/2 by 3.
To simplify the division, we can cancel out common factors in the numerator and denominator. The largest factor that 21 and 2 have in common is 1, so we can simplify further.
21 ÷ 3 = 7
2 ÷ 1 = 2
So, 21/2 ÷ 3 can be simplified to 7/2.
Step 3: Divide the numerator by the denominator.
- Divide 7 by 2.
When dividing fractions, we actually multiply by the reciprocal of the second fraction. So, dividing 7 by 2 is equivalent to multiplying 7 by 1/2.
7 × 1/2 = (7 × 1) ÷ 2 = 7/2
Therefore, Iris can make each scarf 7/2 feet long.
To further simplify the answer, you could convert the mixed number back to a mixed number or decimal if desired.