Middle School

Xavier bought [tex]\frac{2}{3}[/tex] pound of bananas and [tex]\frac{3}{4}[/tex] pound of apples. How many pounds of fruit did he buy?

Answer :

Xavier bought a total of 1 5/12 pounds (approximately 1.42 pounds) of fruit.

To find the total weight of fruit, we need to add 2/3 and 3/4. Since the denominators are different, we first determine the least common denominator (LCD). The LCD of 3 and 4 is 12.

Now, we convert both fractions to have a denominator of 12:

  • Convert 2/3 by multiplying both numerator and denominator by 4:

(2 × 4) / (3 × 4) = 8/12

  • Convert 3/4 by multiplying both numerator and denominator by 3:

(3 × 3) / (4 × 3) = 9/12

Adding these fractions:

8/12 + 9/12 = (8 + 9)/12 = 17/12

Since 17/12 is an improper fraction, we convert it into a mixed number:

17 ÷ 12 gives a quotient of 1 and a remainder of 5, so:

17/12 = 1 5/12

To express this in decimal form, we divide 5 by 12:

5 ÷ 12 = 0.4167, so 1 5/12 ≈ 1.42 pounds.

Thus, Xavier bought a total of 1 5/12 pounds or approximately 1.42 pounds of fruit. The calculation follows the correct procedure of finding the LCD, converting fractions, adding them, and simplifying to a mixed number or decimal form.

Here is a bar graph representing the total weight of fruit Xavier bought. The graph shows:

  • Bananas: 2/3 (≈ 0.67) pounds
  • Apples: 3/4 (≈ 0.75) pounds
  • Total Fruit: 1 5/12 (≈ 1.42) pounds

Answer:

[tex]1 \dfrac{5}{12}[/tex]

Step-by-step explanation:

Find a common denominator (LCM of 3 and 4 is 12).

Convert the fractions:

[tex]\dfrac{2}{3} = \dfrac{8}{12}\\\\\dfrac{3}{4} = \dfrac{9}{12}[/tex]

Add the fractions:

[tex]\dfrac{8}{12} + \dfrac{9}{12} = \dfrac{17}{12}[/tex]

Convert [tex]\dfrac{17}{12}[/tex] into a mixed number:

[tex]\dfrac{17}{12} = 1 \dfrac{5}{12}[/tex]