A certain recipe requires #5/6# cup of flour and #5/9# cup of sugar. If only #7/10# of the recipe is to be made, how much sugar is needed?

Question

Julia Adams · Accepted Answer

#7/18" cup"# Initial condition is #5/9# cup of sugar. Need #7/10# of the recipe so we have to use #7/10# of the sugar. #ubrace(color(red)(7/10)xxcolor(green)(5/9)" cup: this is the same as " color(green)(cancel(5)^1)/color(red)(cancel(10)^2) xxcolor(red)(7)/color(green)(9))=7/18" cup"# #color(white)("ddddddddddd")7/cancel(10)^2xxcancel(5)^1/9=7/18 #

Nathan Axel · Answer

undefined To find out how much sugar is needed for 7/10 of the recipe, you need to multiply the amount of sugar required for the whole recipe by 7/10.

Given that the recipe requires 5/9 cup of sugar, to find out how much sugar is needed for 7/10 of the recipe, you would multiply:

$$ \frac{5}{9} \text{ cup} \times \frac{7}{10} = \frac{5}{9} \times \frac{7}{10} \text{ cup} $$

To simplify the calculation, you can multiply the numerators and the denominators separately:

$$ \frac{5}{9} \times \frac{7}{10} = \frac{5 \times 7}{9 \times 10} $$

$$ = \frac{35}{90} $$

Now, you can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5:

$$ \frac{35}{90} = \frac{7}{18} $$

So, 7/10 of the recipe requires $ \frac{7}{18} $ cup of sugar.