Answer :
To find out the total weight of the fruit you bought, you need to add the weight of the apples and the bananas together. Here's a step-by-step explanation:
1. Convert the fractions to decimals (optional for understanding):
- [tex]$\frac{2}{3}$[/tex] of a pound of apples is approximately [tex]\(0.67\)[/tex] pounds.
- [tex]$\frac{1}{2}$[/tex] of a pound of bananas is [tex]\(0.5\)[/tex] pounds.
2. Add the decimals to find the total:
- Adding [tex]\(0.67\)[/tex] pounds of apples and [tex]\(0.5\)[/tex] pounds of bananas equals approximately [tex]\(1.17\)[/tex] pounds.
3. Fraction addition (for precision):
- First, find a common denominator for the fractions. The common denominator for 3 and 2 is 6.
- Convert [tex]$\frac{2}{3}$[/tex] to a fraction with a denominator of 6: [tex]\(\frac{2}{3} = \frac{4}{6}\)[/tex].
- Convert [tex]$\frac{1}{2}$[/tex] to a fraction with a denominator of 6: [tex]\(\frac{1}{2} = \frac{3}{6}\)[/tex].
- Now add the fractions: [tex]\(\frac{4}{6} + \frac{3}{6} = \frac{7}{6}\)[/tex].
4. Convert the improper fraction to a mixed number:
- [tex]\(\frac{7}{6}\)[/tex] is equal to 1 whole number and [tex]\(\frac{1}{6}\)[/tex].
- Therefore, the total weight is [tex]\(1\frac{1}{6}\)[/tex] pounds.
So, in total, you bought [tex]\(1.17\)[/tex] pounds of fruit, which is equivalent to [tex]\(1\frac{1}{6}\)[/tex] pounds when expressed as a fraction.
1. Convert the fractions to decimals (optional for understanding):
- [tex]$\frac{2}{3}$[/tex] of a pound of apples is approximately [tex]\(0.67\)[/tex] pounds.
- [tex]$\frac{1}{2}$[/tex] of a pound of bananas is [tex]\(0.5\)[/tex] pounds.
2. Add the decimals to find the total:
- Adding [tex]\(0.67\)[/tex] pounds of apples and [tex]\(0.5\)[/tex] pounds of bananas equals approximately [tex]\(1.17\)[/tex] pounds.
3. Fraction addition (for precision):
- First, find a common denominator for the fractions. The common denominator for 3 and 2 is 6.
- Convert [tex]$\frac{2}{3}$[/tex] to a fraction with a denominator of 6: [tex]\(\frac{2}{3} = \frac{4}{6}\)[/tex].
- Convert [tex]$\frac{1}{2}$[/tex] to a fraction with a denominator of 6: [tex]\(\frac{1}{2} = \frac{3}{6}\)[/tex].
- Now add the fractions: [tex]\(\frac{4}{6} + \frac{3}{6} = \frac{7}{6}\)[/tex].
4. Convert the improper fraction to a mixed number:
- [tex]\(\frac{7}{6}\)[/tex] is equal to 1 whole number and [tex]\(\frac{1}{6}\)[/tex].
- Therefore, the total weight is [tex]\(1\frac{1}{6}\)[/tex] pounds.
So, in total, you bought [tex]\(1.17\)[/tex] pounds of fruit, which is equivalent to [tex]\(1\frac{1}{6}\)[/tex] pounds when expressed as a fraction.
