Solving Mixed-Number Subtraction for Dragonfly and Mayfly Wingspans
To solve this problem, we will subtract the wingspan of the mayfly from the wingspan of the dragonfly. The dragonfly's wingspan is given as 6 2/7 centimeters, and it is said to be 1 3/10 centimeters wider than the wingspan of the mayfly. Let's perform the subtraction:
Dragonfly's wingspan: 6 2/7 cm
Wingspan wider than mayfly's wingspan: 1 3/10 cm
To subtract these mixed numbers, first convert them to improper fractions.
For 6 2/7:
6 * 7 = 42
42 + 2 = 44
So, 6 2/7 = 44/7
For 1 3/10:
1 * 10 = 10
10 + 3 = 13
So, 1 3/10 = 13/10
Now we need to have a common denominator to subtract the fractions. The lowest common denominator for 7 and 10 is 70. Convert the fractions to equivalent fractions with a denominator of 70:
44/7 becomes (44 * 10)/(7 * 10) = 440/70
13/10 becomes (13 * 7)/(10 * 7) = 91/70
Now, subtract the wingspan difference from the dragonfly's wingspan:
440/70 (dragonfly's wingspan in cm) - 91/70 (difference in cm) = 349/70
Now we convert this improper fraction back to a mixed number:
349 divided by 70 equals 4 with a remainder of 69. Convert the remainder to a fraction by placing it over the original denominator:
The mayfly's wingspan = 4 69/70 centimeters
a. The whole box would show the number 4 because that's the whole number part of the wingspan for the mayfly.
b. Number model with unknown:
Let the wingspan of the mayfly be W.
W + 1 3/10 = 6 2/7
Convert fractions to equivalent fractions with a common denominator and solve for W. Using the working above, we get the wingspan of the mayfly, W = 4 69/70 cm.
c. A different way to solve a mixed-number subtraction problem could involve a visual fraction model or using a calculator that can handle mixed numbers. Additionally, it's sometimes easier to convert mixed numbers to improper fractions, perform the subtraction, and then convert the result back to a mixed number, as done above.
