Expressing a fractional increase as a fraction of the original
About this video
Dara practiced piano 3/8 more hours this week than last week. Calling last week's hours H, this week is H + 3/8 H = (1 + 3/8)H = 11/8 H. So this week's hours are 11/8 of last week's.
You'll be able to
- write an amount that is a fraction more than an original as an expression like H + 3/8 H.
- combine 1H + 3/8 H into a single fraction of the original, such as 11/8 H.
- explain why an increase gives a fraction greater than 1.
Key words
- variable
- A letter, like H, that stands for an unknown number.
- coefficient
- The number multiplied by a variable, like 3/8 in 3/8 H.
- improper fraction
- A fraction whose top number is bigger than its bottom number, like 11/8.
- mixed number
- A whole number and a fraction together, like 1 3/8.
Transcript
- [Instructor] This week, Dara practiced piano 3/8 more hours than last week. Write the number of hours Dara practiced this week as a fraction of last week's number. So we really just need to fill in this blank. This week's number of hours is blank of last week's number of hours.
Pause the video, have a go at that. Okay, so let's just make a variable here. Let's just say, let's say H is the hours last week. That's last week. So this week, Dara practiced H, but practiced more than H. This is what Dara did last week. That is last week. I just defined it that way.
She practiced 3/8 more hours than last week. So it's gonna be H plus 3/8 of H. This is how much more she practiced. How much more? So the total number of, the total amount of practice this week is H plus 3/8 H. Another way to think about it is this is the same thing as one H plus 3/8 H, or another way to think about it, and this, you could view this as factoring out the H or adding coefficients, either way, this would be one plus 3/8 times H, one H plus 3/8 H is gonna be one plus 3/8 H.
And so this is going to be the same thing as actually we could say this is one and 3/8 H, or we could write it, or we could write it instead of writing it as a mixed number. One is 8/8 plus 3/8 is 11/8 H. So this week Dara practiced 11/8 of last week. So this week's number of hours is 11/8 of last week's number of hours.
And notice it is last week, 8/8 or one plus another 3/8, so it all works out.
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