On Monday Sarah had homework in [tex]$7 / 10$[/tex] of her classes, Tuesday [tex]$3 / 5$[/tex], Wednesday [tex]$9 / 11$[/tex], and Thursday [tex]$1 / 2$[/tex]. Which day did she have the most homework?
A) Thursday
B) Tuesday
C) Monday
Answer (2)
Sarah had the most homework on Wednesday, with a decimal equivalent of approximately 0.82 when compared to the other days. The values for the other days were 0.7 for Monday, 0.6 for Tuesday, and 0.5 for Thursday. Therefore, the correct answer is Wednesday.
;
Convert each fraction to a decimal: Monday 7/10 = 0.7 , Tuesday 3/5 = 0.6 , Wednesday $9/11
= 0.82$, Thursday 1/2 = 0.5 .
Compare the decimal values: 0.7 , 0.6 , 0.82 , 0.5 .
Identify the largest value: 0.82 .
Conclude that Sarah had the most homework on W e d n es d a y .
Explanation
Problem Analysis We are given the fraction of classes Sarah had homework in for four days: Monday ( 7/10 ), Tuesday ( 3/5 ), Wednesday ( 9/11 ), and Thursday ( 1/2 ). We need to determine on which day she had the most homework. To do this, we will convert each fraction to a decimal and compare the values.
Monday's Homework First, let's convert the fraction for Monday to a decimal: 7/10 = 0.7 .
Tuesday's Homework Next, convert the fraction for Tuesday to a decimal: 3/5 = 0.6 .
Wednesday's Homework Now, convert the fraction for Wednesday to a decimal: 9/11 = 0.818181... which is approximately 0.82 .
Thursday's Homework Finally, convert the fraction for Thursday to a decimal: 1/2 = 0.5 .
Comparing Homework Loads Comparing the decimal values, we have: Monday ( 0.7 ), Tuesday ( 0.6 ), Wednesday ( 0.82 ), and Thursday ( 0.5 ). The largest value is 0.82 , which corresponds to Wednesday.
Conclusion Therefore, Sarah had the most homework on Wednesday.
Examples
Understanding fractions and comparing them is useful in many real-life situations. For example, if you are baking and a recipe calls for 3/4 cup of flour and another recipe calls for 2/3 cup of flour, you need to be able to compare these fractions to know which recipe requires more flour. Similarly, when comparing discounts at different stores, such as 1/3 off at one store and 2/5 off at another, you need to compare the fractions to determine which discount is better. These skills are also essential in understanding financial concepts, such as interest rates and investment returns, which are often expressed as fractions or percentages.
