1.)Which of the following statements is true?
Positive numbers are always rational numbers.
Negative numbers are always irrational numbers.
Negative numbers are sometimes rational numbers.*********
Negative numbers are always integers.
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2.)Are ratios 80/96 and 77/84 proportional?
Yes, because they both reduce to the equivalent fraction 5/6.
Yes, because the cross products 80x84 and 96x77 are equal.
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No, Because one has a quotient of 0.83 and the other has a quotient of 0.916
No, because one ratio reduce to5/6 and the other reduces to 3/4.
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3.)Ben's cookie recipe calls for 3 1/4 cups of flour. if the recipe was increase by a factr of 1 1/2, how much flour would ben need?
4 1/3
4 1/2
4 3/4
4 7/8
Please explain how to do the problems 2 and 3 :(.
#1 ok
#2 If they are proportional, then you need
80/96 = 77/84
Thus, you need 80*84 = 77*96, clearly false
or,
since 80/96 = 5/6 = 0.833 and 77/84 = 11/12 = 0.916
they are not equal
#3 increased by a factor of 1 1/2 means you multiply by 1 1/2
3 1/4 * 1 1/2 = 13/4 * 3/2 = 39/8 = 4 7/8
Ok thank you for explaining it to me it. :)!
2.) To determine if ratios are proportional, we can check if their cross products are equal. The cross products of 80/96 and 77/84 are calculated by multiplying the numerator of one ratio with the denominator of the other.
For 80/96 and 77/84:
Cross product 1: 80 × 84 = 6,720
Cross product 2: 96 × 77 = 7,392
Since the cross products are not equal (6,720 ≠ 7,392), the ratios 80/96 and 77/84 are not proportional.
Therefore, the correct answer is:
No, because the cross products 80x84 and 96x77 are not equal.
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3.) Ben's original cookie recipe calls for 3 1/4 cups of flour. To increase the recipe by a factor of 1 1/2, we need to multiply the original amount of flour by 1 1/2.
To find the new amount of flour, we multiply 3 1/4 by 1 1/2:
3 1/4 × 1 1/2
First, convert the mixed numbers to improper fractions:
3 1/4 = (3 × 4 + 1) / 4 = 13/4
Multiply the fractions:
(13/4) × (1 1/2) = (13/4) × (3/2) = (13 × 3) / (4 × 2) = 39/8
The result is the new amount of flour needed, which is 39/8 cups.
To simplify the fraction, we can write it as a mixed number:
39/8 = 4 7/8
Therefore, Ben would need 4 7/8 cups of flour after increasing the recipe by a factor of 1 1/2.
The correct answer is:
4 7/8.
2.) To determine if the ratios 80/96 and 77/84 are proportional, we can use the concept of cross products. Cross products involve multiplying the numerator of one fraction with the denominator of the other fraction. If the cross products are equal, then the ratios are proportional.
For the given ratios:
Cross product of the first ratio: 80 x 84 = 6,720
Cross product of the second ratio: 96 x 77 = 7,392
Since the cross products are not equal (6,720 ≠ 7,392), the answer is "No, the ratios are not proportional."
3.) To calculate how much flour Ben would need if the recipe was increased by a factor of 1 1/2, we can multiply the original amount of flour by the factor.
Given:
Original amount of flour = 3 1/4 cups
Increase factor = 1 1/2
To multiply a whole number by a fraction, we first convert the whole number to an equivalent fraction. Thus, we can rewrite the increase factor as a fraction: 1 1/2 = 3/2.
To find the increased amount of flour, we multiply the original amount by the factor:
3 1/4 x 3/2
To multiply fractions, we multiply the numerators together and the denominators together:
(3 x 13) / (4 x 2) = 39/8
The resulting fraction, 39/8, can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator, which is 1. So, the answer is "4 7/8".