1.) Which of the following numbers could be added to 3/16 to make a sum greater than 1/2?
5/16
10/32
2/6
1/4
Which of the following pairs of numbers provides the best estimate of (square root of 45)?
(square root of 25) and (square root of 36
(square root of 36 and (square root of 49
(square root of 49 and (square root of 64
(square root of 25 and (square root of 49
I am very confused about these questions please explain how I can do this. :(
Thanks so much this helped a lot :) !
Oh, dear user, don't worry! I'll gladly explain these questions to you, and hopefully bring a smile to your face along the way!
For the first question, we need to find a number that, when added to 3/16, will make the sum greater than 1/2. Let's go through the options one by one:
- Adding 5/16 to 3/16 will give you 8/16, which simplifies to 1/2. So this option won't work because it would equal but not exceed 1/2.
- Adding 10/32 to 3/16 is the same as adding 5/16 to 3/16, which we already saw won't work.
- Adding 2/6 to 3/16 will give you 13/16, which is definitely greater than 1/2.
- Adding 1/4 to 3/16 will give you 7/16, still less than 1/2.
So, the only option that works is 2/6. Hooray!
Now for the second question, we need to find the best estimate for the square root of 45. Let's match up the pairs:
- The square root of 25 is 5, and the square root of 36 is 6. Both are close to the square root of 45, but 6 is closer. So this pair is a decent estimate.
- The square root of 36 is 6, and the square root of 49 is 7. Again, both are close, but 7 is even closer to the square root of 45. So this is a better pair.
- The square root of 49 is 7, and the square root of 64 is 8. Here, 7 is farther away from the square root of 45 compared to our previous option. So this pair isn't as good.
- The square root of 25 is 5, and the square root of 49 is 7. Both numbers are a bit off from the square root of 45, but 7 is closer. This pair is also a decent estimate.
Therefore, the second option of pairing the square root of 36 with the square root of 49 provides the best estimate for the square root of 45.
I hope this clears things up for you, and remember, a little laughter always helps with confusion!
To determine which of the following numbers could be added to 3/16 to make a sum greater than 1/2, we need to find their respective sums.
Let's calculate the sums:
1) 3/16 + 5/16 = 8/16 = 1/2
2) 3/16 + 10/32 = 3/16 + 5/16 = 8/16 = 1/2
3) 3/16 + 2/6 = 9/48 + 16/48 = 25/48
4) 3/16 + 1/4 = 6/48 + 12/48 = 18/48
Based on these calculations, the only sum greater than 1/2 is 18/48. Therefore, the number we can add to 3/16 to make a sum greater than 1/2 is 1/4.
Moving on to the next question:
To find the best estimate for the square root of 45, we need to find the closest square numbers.
Let's calculate the square roots:
1) The square root of 25 = 5, and the square root of 36 = 6
2) The square root of 36 = 6, and the square root of 49 = 7
3) The square root of 49 = 7, and the square root of 64 = 8
4) The square root of 25 = 5, and the square root of 49 = 7
Based on these calculations, the best estimate for the square root of 45 would be between the square roots of 36 and 49, which gives us 6 and 7, respectively. Therefore, the pair (square root of 36) and (square root of 49) provides the best estimate for the square root of 45.
Sure! Let's tackle each question step-by-step:
1.) To answer the first question, we need to find a number that, when added to 3/16, will result in a sum greater than 1/2.
To do this, we can follow these steps:
- Convert 3/16 and 1/2 to a common denominator. The common denominator of 16 and 2 is 32.
- Rewrite 3/16 and 1/2 with the common denominator of 32:
- 3/16 = 6/32
- 1/2 = 16/32
- We need to find a number that, when added to 6/32, will result in a larger numerator than 16/32.
Now we can examine the answer choices:
- 5/16: If we add 5/16 to 6/32, the numerator becomes 11/32, which is still less than 16/32. So this number will not make the sum greater than 1/2.
- 10/32: Adding 10/32 to 6/32 gives us a numerator of 16/32, which is equal to 1/2. So this number will not make the sum greater than 1/2.
- 2/6: We can simplify 2/6 to 1/3. Adding 1/3 to 6/32 gives us a numerator of 17/32, which is greater than 16/32. Therefore, this number will make the sum greater than 1/2.
- 1/4: Adding 1/4 to 6/32 gives us a numerator of 13/32, which is less than 16/32. So this number will not make the sum greater than 1/2.
Therefore, the number that could be added to 3/16 to make a sum greater than 1/2 is 2/6 (or 1/3).
2.) For the second question, we are asked to estimate the square root of 45 using the answer choices provided.
To find the estimate, we need to determine which pair of numbers surrounds the square root of 45.
Let's consider the answer choices:
- Square root of 25 and square root of 36: The square root of 25 is 5, and the square root of 36 is 6. 45 falls between 25 and 36, so this pair of numbers provides a good estimate for the square root of 45.
- Square root of 36 and square root of 49: The square root of 36 is 6, and the square root of 49 is 7. 45 falls between 36 and 49, so this pair of numbers also provides a good estimate for the square root of 45.
- Square root of 49 and square root of 64: The square root of 49 is 7, and the square root of 64 is 8. 45 falls between 49 and 64, so this pair of numbers is also a good estimate for the square root of 45.
- Square root of 25 and square root of 49: The square root of 25 is 5, and the square root of 49 is 7. Although 45 falls between 25 and 49, this pair of numbers does not provide the best estimate for the square root of 45, as it is further from 45 compared to the other answer choices.
Based on the analysis, the pair of numbers that provides the best estimate for the square root of 45 is the square root of 25 and the square root of 36.
I hope this helps! Let me know if you have any further questions.
If you add x, then you need
3/16 + x > 1/2
3/16 + x > 8/16
x > 5/16
Note that the question should have specified "at least" 1/2, rather than "greater than"
45 is between 36 and 49, so √45 is between √36 and √49