12 and 26
A larger rectangle whose width is twice as long as one of the smaller rectangles and whose length is three times that of one of the smaller rectangles.
No. Consider 0 and 1. Or negative numbers, whose sum produces a smaller number.
As long as the whole number is not zero, it becomes a unit fraction with a larger denominator, ie one with a smaller value.
3 and 84.
Call the numbers s for the smaller number and l for the larger. From the problem statement, s + l = 35 and l = 2s + 7. From the first of these equations, s = 35 - l. Substituting this expression into the second equation yields: l = 2(35 - l) + 7. Multiplying out yields: l = 70 - 2l + 7. Adding like terms after collecting the terms with "l" on the left yields: 3l = 77 or l = 77/3. Then from the first equation s = 35 - 77/3 = 28/3
In that case, the smaller number is a factor of the larger one. The larger one is a multiple of the smaller one.
12 and 12, whose squares will be 144 each. If either of the numbers is smaller than 12, then the other will be larger than 12 and its square will be larger than 144.
Since one number is twice the other, the smaller number must be the greatest common factor. Since the greatest common factor is 7, that would make the other number 14. But, 7 is a prime number and has only one prime factor. However, the larger number, 14, has two prime factors. Also, the sum of the two numbers is 21, not 105. So, the information in the problem does not have a solution. Let us ignore the greatest common factor information. Let the smaller number be x. That means the larger number is 2x. x + 2x = 105 => 3x = 105 => x = 35. The two numbers are 35 and 70. The greatest common factor is 35. The smaller number, 35, has only two prime factors.
Edge of the larger cube = 32 cm Volume of the larger cube = (32 cm)3 = 32768 cm3 Edge of the smaller cube = 4 cm Volume of the smaller cube = (4 cm)3 = 64 cm3 Since the smaller cubes are cut from the larger cube, volume of all of them will be equal to that of the larger cube. ∴ Total number of smaller cubes × Volume of the smaller cube = Volume of the larger cube ⇒ Total number of smaller cubes = Volume of the larger cube ÷ Volume of the smaller cube ⇒ Total number of smaller cubes = 32768 ÷ 64 = 512 Thus, 512 smaller cubes can be cut from the larger one.
Designate the smaller number by s and the larger by l. Then l = s + 8; s + l = 2s + 8 = 20; 2s = 20 - 8 = 12; s = 6 and l = 14.
Subtract the difference and half your answer, giving 9 which is the smaller number, add the difference to this and you get 38 which is the larger number.
If the fractions have the same numerator (top number), then the fraction with the larger denominator (bottom number) is the smaller fraction, which implies that the fraction with the smaller denominator is the larger fraction. For example with 1/2 and 1/4, it can be easily seen that 1/2 is the larger of the two.
A larger rectangle whose width is twice as long as one of the smaller rectangles and whose length is three times that of one of the smaller rectangles.
the answer is of course 12
44 & 45
No. Consider 0 and 1. Or negative numbers, whose sum produces a smaller number.
As long as the whole number is not zero, it becomes a unit fraction with a larger denominator, ie one with a smaller value.