Determine the difference. [tex]$\frac{3}{4}-\frac{5}{16}= ?$[/tex]
Answer (2)
Find a common denominator for the two fractions, which is 16.
Convert 4 3 to an equivalent fraction with a denominator of 16: 4 3 = 16 12 .
Subtract the two fractions: 16 12 − 16 5 = 16 7 .
The difference is 16 7 .
Explanation
Understanding the Problem We are asked to find the difference between two fractions: 4 3 and 16 5 . To subtract these fractions, we need to find a common denominator.
Finding a Common Denominator The least common denominator (LCD) of 4 and 16 is 16. We need to convert 4 3 to an equivalent fraction with a denominator of 16.
Converting Fractions To convert 4 3 to a fraction with a denominator of 16, we multiply both the numerator and the denominator by 4: 4 3 = 4 × 4 3 × 4 = 16 12
Subtracting Fractions Now we can subtract the two fractions: 16 12 − 16 5 = 16 12 − 5 = 16 7
Final Answer The difference between 4 3 and 16 5 is 16 7 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have a pizza that is cut into 4 slices and you eat 3 of those slices, you have eaten 4 3 of the pizza. If your friend eats 16 5 of the same pizza, you can use subtraction of fractions to determine how much more pizza you ate than your friend.
The difference between 4 3 and 16 5 is 16 7 after finding a common denominator and converting the fractions appropriately. We first converted 4 3 to 16 12 , then performed the subtraction. The final result is 16 7 .
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