Susie spent 4 1/4 hours on Monday and 3 5/8 hours on Tuesday working on a history project. About how long did she spend working on the project?
4 1/4 + 3 5/8
= 17/4 + 29/8
= 34/8 + 29/8
= ...
= ...
To find out how long Susie spent working on the history project, you need to add the number of hours she spent on Monday and Tuesday.
On Monday, she spent 4 1/4 hours, which can also be written as 4 + 1/4 hours.
To add this, you need to convert the mixed number 4 1/4 into an improper fraction. To do this, multiply the whole number (4) by the denominator (4) and add the numerator (1), then write the sum over the denominator: (4 * 4 + 1) / 4 = 17/4.
So, on Monday, Susie spent a total of 17/4 hours working on the project.
On Tuesday, she spent 3 5/8 hours, which can be written as 3 + 5/8 hours.
Similarly, you need to convert the mixed number 3 5/8 into an improper fraction. Multiply the whole number (3) by the denominator (8) and add the numerator (5), then write the sum over the denominator: (3 * 8 + 5) / 8 = 29/8.
So, on Tuesday, Susie spent a total of 29/8 hours working on the project.
To find the total time, you need to add the fractions together.
17/4 + 29/8.
To add fractions with different denominators, you need to find a common denominator. The least common multiple (LCM) of 4 and 8 is 8.
To convert 17/4 to have a denominator of 8, multiply both the numerator and denominator by 2: (17 * 2) / (4 * 2) = 34/8.
Now you can add the fractions: 34/8 + 29/8 = 63/8.
The result is a fraction, 63/8 hours.
To express this as a mixed number, divide the numerator (63) by the denominator (8). The quotient (whole number) becomes the whole part of the mixed number, and the remainder becomes the numerator of the fraction:
63 ÷ 8 = 7 remainder 7.
So, the total amount of time that Susie spent working on the project is 7 7/8 hours.