can you please check my answers?
12, 20, and 35 LCM =420
1/3+5/12+4+5=60 LCD
13/15-11/20=19/60
What is the combined price for a 1/2-in. sheet and a 5/8-in. sheet? 1/2PRICE $17.88 5/8 PRICE$19.13 =37.01
1 1/15+3 3/10-2 4/5=1 17/30
5 1/3+2 1/4+3 1/2=11 1/12
The interest rate on an auto loan in May was 12 3/8%. By
September the rate was up to14 1/4 %. How many percentage points did the interest
rate increase over the period?=1 7/8%
12, 20, and 35 LCM =420
1/3+5/12+4+5=60 LCD
13/15-11/20=19/60
What is the combined price for a 1/2-in. sheet and a 5/8-in. sheet? 1/2PRICE $17.88 5/8 PRICE$19.13 =37.01
1/15+3 3/10-2 4/5=1 17/30
5 1/3+2 1/4+3 1/2=11 1/12
The interest rate on an auto loan in May was 12 3/8%. By
September the rate was up to14 1/4 %. How many percentage points did the interest
rate increase over the period?=1 7/8%
Yes, those are all correct. Yay!!
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O Thank you so much!!!!!
You're very welcome. :-)
Let's go through each question and I'll explain how to check your answers:
1. LCM (Least Common Multiple)
To find the Least Common Multiple (LCM) of a set of numbers, you need to find the smallest multiple that is divisible by all of those numbers. In this case, the numbers are 12, 20, and 35.
To find the LCM:
- List the prime factors of each number.
12 = 2^2 * 3
20 = 2^2 * 5
35 = 5 * 7
- Take the highest power of each prime factor found in the numbers, and multiply them together.
2^2 * 3 * 5 * 7 = 420
So, the LCM of 12, 20, and 35 is indeed 420. Your answer is correct.
2. LCD (Least Common Denominator)
To find the Least Common Denominator (LCD) when adding or subtracting fractions, you need to find the smallest multiple that the denominators can both divide into evenly. In this case, the fractions are 1/3, 5/12, and 4/5.
To find the LCD:
- List the prime factors of each denominator.
3 = 3
12 = 2^2 * 3
5 = 5
- Take the highest power of each prime factor found in any denominator, and multiply them together.
2^2 * 3 * 5 = 60
So, the LCD of 1/3, 5/12, and 4/5 is indeed 60. Your answer is correct.
3. Subtracting Fractions
To subtract fractions, you need to have a common denominator. In this case, you have 13/15 and 11/20.
To subtract fractions with the same denominator:
- Subtract the numerators and keep the common denominator.
(13 - 11) / 15 = 2 / 15
So, the result of 13/15 minus 11/20 is indeed 2/15. Your answer is correct.
4. Combining Prices
To find the combined price, you need to add the prices of a 1/2-in. sheet and a 5/8-in. sheet. The prices are given as $17.88 for 1/2-in. and $19.13 for 5/8-in.
To combine the prices:
- Add the prices together.
$17.88 + $19.13 = $37.01
So, the combined price for a 1/2-in. sheet and a 5/8-in. sheet is indeed $37.01. Your answer is correct.
5. Adding and Subtracting Mixed Numbers
To add or subtract mixed numbers, you need to convert them into improper fractions if necessary. In this case, you have 1 1/15, 3 3/10, and 2 4/5.
To add or subtract mixed numbers:
- Convert each mixed number into an improper fraction.
1 1/15 = (15 * 1 + 1) / 15 = 16/15
3 3/10 = (10 * 3 + 3) / 10 = 33/10
2 4/5 = (5 * 2 + 4) / 5 = 14/5
- Perform the addition or subtraction with the improper fractions.
(16/15) + (33/10) - (14/5) = 1 17/30
So, the result of 1 1/15 plus 3 3/10 minus 2 4/5 is indeed 1 17/30. Your answer is correct.
6. Adding Mixed Numbers
To add mixed numbers, you use the same process as adding and subtracting mixed numbers. In this case, you have 5 1/3, 2 1/4, and 3 1/2.
To add mixed numbers:
- Convert each mixed number into an improper fraction.
5 1/3 = (3 * 5 + 1) / 3 = 16/3
2 1/4 = (4 * 2 + 1) / 4 = 9/4
3 1/2 = (2 * 3 + 1) / 2 = 7/2
- Perform the addition with the improper fractions.
(16/3) + (9/4) + (7/2) = 11 + 1/12
So, the result of 5 1/3 plus 2 1/4 plus 3 1/2 is indeed 11 1/12. Your answer is correct.
7. Percentage Increase
To find the percentage increase between two numbers, you subtract the initial value from the final value, and then divide that difference by the initial value. In this case, the initial interest rate is 12 3/8% and the final interest rate is 14 1/4%.
To find the percentage increase:
- Convert the mixed numbers into improper fractions.
12 3/8 = (8 * 12 + 3) / 8 = 99/8
14 1/4 = (4 * 14 + 1) / 4 = 57/4
- Calculate the difference between the final and initial values.
(57/4) - (99/8) = -1/8
- Convert the difference to a percentage.
-1/8 * 100 = -12.5%
So, the interest rate increased by -12.5% over the period. The answer should be -12 1/2%. It seems there was an error in your calculation.