1 batch of muffins included 2/3 cups of raisins. We can use this to set a proportion: 1 : 2/3. That means for every 1 batch, she uses 2/3 cups of raisins.
Now, Ina made 2 1/2 batches. To find out how, we need to look at our proportion again: 1 : 2/3. Whatever operation you do to one side, you must do to the other. So, to get 2 1/2 batches, we need to multiply the left side of the proportion, which is 1 batch, by 2 1/2 to get 2 1/2 batches.
BUT, we also need to multiply the other side, 2/3 cups, by 2 1/2. We can start by converting this into an improper fraction, 5/2. (Because 1=2/2, so 2=4/2, and 4/2+1/2=5/2.) When multiplying fractions, you multiply the numerators together to get the new numerator, and the denominators to get the new denominator. 2*5=10, and 3*2=6. Our new fraction is 10/6. Since these are both divisible by 2, we simplify by dividing each side by 2 to get 5/3. Finally, we can convert this into a mixed number: 1 2/3. (Because 1=3/3 and 5/3 - 3/3 = 2/3, and 1 + 2/3 = 1 2/3.) This is the cups of raisins she used.
Answer: She used 1 2/3 cups of raisins.
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Midpoint Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
Endpoint A (-2, 1)
Endpoint B (-1, 1)
<u>Step 2: Find Midpoint</u>
Simply plug in your coordinates into the midpoint formula to find midpoint
- Substitute [MF]:
- Subtract/Add:
- Divide:
Answer: To clear an equation of decimals, multiply each term on both sides by the power of ten that will make all the decimals whole numbers. In our example above, if we multiply .25 by 100, we will get 25, a whole number. Since each decimal only goes to the hundredths place, 100 will work for all three terms.
So let's multiply each term by 100 to clear the decimals:
(100)0.25x + (100)0.35 = (100)(-0.29)
25x + 35 = -29
Now we can solve the equation as normal:
25x + 35 - 35 = -29 - 35
25x = -64
x = -2.56 Since the original was in decimal form, the answer should most likely also be in decimal form.
Let's look at one more:
1.75x + 4 = 6.2
We have to think a little more carefully about what multiple of ten to use here. 6.2 only needs to be multiplied by 10, but 1.25 needs 100, so we will multiply every term by 100. Don't forget to multiply the 4 by 100 as well.
(100)(1.75x) + (100)(4) = (100)(6.2)
175x + 400 = 620
We had to be extra careful as we multiplied by 100. Now we can solve the equation as normal:
175x + 400 - 400 = 620 - 400
175x = 220
x = 1.26
Step-by-step explanation:
Answer:x=-2
Step-by-step explanation:
3 x -2^2
3 x -4 = -12
