Question - Solving Mixed-Number Subtraction for Dragonfly and Mayfly Wingspans
Solution:
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 cmWingspan wider than mayfly's wingspan: 1 3/10 cmTo subtract these mixed numbers, first convert them to improper fractions. For 6 2/7:6 * 7 = 4242 + 2 = 44So, 6 2/7 = 44/7For 1 3/10:1 * 10 = 1010 + 3 = 13So, 1 3/10 = 13/10Now 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) = 440/7013/10 becomes (13 * 7)/(10 * 7) = 91/70Now, subtract the wingspan difference from the dragonfly's wingspan:440/70 (dragonfly's wingspan in cm) - 91/70 (difference in cm) = 349/70Now 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 centimetersa. 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 2/7Convert 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.
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