I have a question and I have read and read and cant comprend how to figure the problem.
a girl has 1/5 of her portfolio in us stocks and 1/8 in euro stocks and 1/10 in japanese stocks the rest is in municipal bonds.
what percent is in muncipal bonds and what fraction is in mucipal bonds. I know I need to start with making the fractions the same but I am so confused
Let's first find the common denominators of the fractions.
1/5 = 8/40
1/8 = 5/40
1/10 = 4/40
The total for stocks is 17/40 of her portfolio.
40/40 - 17/40 = 23/40
To find the percentage, divide:
23/40 = ??
Then change that decimal to a percent.
first find the common denominator. which is 40 so the fractions become 8/40 5/40 4/40. add them up and u get 17/40. then subtract 17/40 from 40/40 and you get 23/40 and that's your fraction. then divide 23 by 40 and you get 57.5% and that's your percent.
Thanks i was getting confused but you explained it well.
To determine the percentage and fraction of the girl's portfolio that is invested in municipal bonds, we first need to make the fractions for each type of stock and the bonds the same denominator.
Let's find the common denominator for 1/5, 1/8, and 1/10. The lowest common multiple (LCM) of 5, 8, and 10 is 40.
To convert 1/5 to a fraction with a denominator of 40, we multiply both the numerator and denominator by 8:
1/5 = (1 × 8) / (5 × 8) = 8/40.
To convert 1/8 to a fraction with a denominator of 40, we multiply both the numerator and denominator by 5:
1/8 = (1 × 5) / (8 × 5) = 5/40.
To convert 1/10 to a fraction with a denominator of 40, we multiply both the numerator and denominator by 4:
1/10 = (1 × 4) / (10 × 4) = 4/40.
Now, we can calculate the fraction and percentage of the girl's portfolio in municipal bonds.
Since we have accounted for 8/40 (or 1/5), 5/40 (or 1/8), and 4/40 (or 1/10) of the portfolio, the remaining fraction in municipal bonds can be found by subtracting the sum of those fractions from 1 (the total):
1 - (8/40 + 5/40 + 4/40) = 1 - 17/40 = 23/40.
Therefore, the fraction of the girl's portfolio in municipal bonds is 23/40.
To determine the percentage, we can multiply the fractional value by 100:
(23/40) × 100 = 0.575 × 100 = 57.5%.
Hence, 57.5% of the girl's portfolio is invested in municipal bonds, and the fraction is 23/40.