Mathematics, 22.02.2020 05:08 Ramel360

Olivia is doing her math homework. For each problem she uses 3/4 sheet of paper. How many sheets of paper will Olivia need to complete 20 math problems?

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Answer from: wittlemarie

Step-by-step explanation:

problem = $\frac{3}{4}$ a page

problems = __ pages

- First, we need to figure out what this problem is asking us. This problem is asking for how many pieces of paper we need to do math questions. Well, the first step is knowing how many pieces of paper are needed for a single question. Luckily the question tells us that we need $\frac{3}{4}$ a paper for problem. So I have shown above what we know, and what we need to know. How do we figure out how many pages are needed for math problems?

There are a couple ways to solve this problem:Add $\frac{3}{4}$ to itself

times to get our resultant.Multiply $\frac{3}{4}$ by

(I listed them in order of time it takes to solve; #1 will take the longest, and #2 the shortest)

I'll do both methods and you can decide which you are most comfortable with.

Addition Method:

If we need to do

problems, and

problem is $\frac{3}{4}$ a page, doing

problems is the same as doing $\frac{3}{4}$ a page

times, so let's do just that by adding $\frac{3}{4}$ to itself

times.

Yep, that's going to be a lot of work, but I'll show that you can add $\frac{3}{4}$ to itself this many times and get the same answer as the

step solution seen with multiplication. Here's my work.

Note: (in case you struggle with fractions) Fractions when added together do NOT have a change in denominator (bottom number), only the numerator (top number) is added. Treat this as the same thing as addition, but you've got a number on the bottom that we'll deal with later.

In this step, I'm taking every pair of $\frac{3}{4}$ s and adding them together.

$\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}\\\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}$

Now, I'm again going to add my pairs together. Using this method saves time adding long chains of numbers and keeps your work minimized.

$\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}+\frac{6}{4}\\\frac{12}{4}+\frac{12}{4}+\frac{12}{4}+\frac{12}{4}+\frac{12}{4}$

Note: at this point you can actually convert your fractions to the whole number . Four goes into twelve times, so you'll end up with a clean number as your answer without any difficult conversions. Not converting now won't change your end result if you chose not to, but it will make things easier.

$\frac{12}{4}+\frac{12}{4}+\frac{12}{4}+\frac{12}{4}+\frac{12}{4}\\\frac{24}{4}+\frac{24}{4}+\frac{12}{4}\\\frac{48}{4}+\frac{12}{4}\\\frac{60}{4}\\ 15$

$\frac{12}{4}+\frac{12}{4}+\frac{12}{4}+\frac{12}{4}+\frac{12}{4}\\3+3+3+3+3\\15$

Multiplication Method:

This method is much, much less time consuming compared to doing the addition, so I recommend using this method in most word problems like this one.

Note: (read if you're having trouble with multiplication.) We have problem, $\frac{3}{4}$ a paper, being done times, so we are taking the value $\frac{3}{4}$ and adding it to itself times; we are multiplying $\frac{3}{4}$ by . Adding a number to itself times and multiplying a certain number by the value holds no difference except in how it's written and how many steps we have to use to solve it.

$\frac{3}{4}$ ×

If you're used to seeing only whole numbers being multiplied, this may help you grasp it:

$\frac{3}{4}$ × ⇒ $\frac{3}{4}$ × $\frac{20}{1}$

Remember that not only are both the numerators and denominators being multiplied, but separately. Here's the multiplications I did for both top and bottom.

numorater: × 20=60 (look up "long-multiplication if you are confused by this answer.)

denominator: × 4=1+1+1+1=4

Once we have multiplied the numerators and denominators together, this is your

$\frac{3}{4}$ × $\frac{20}{1}$

$\frac{3(20)}{4(1)}$

$\frac{60}{4}$

Look familiar? This is exactly what our unsimplified answer when adding our fractions together was.

$\frac{60}{4}=15$

Answer from: Quest

4.5%

step-by-step explanation:

Answer from: Quest

the answer is 150.6

step-by-step explanation:

you multiply .02 by 30 and get .6.

and then you multiply 5.00 by 30 and get 150.

hope this !

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