Adding and Subtracting Fractions with Unlike Denominators (Word ... - Free Printable

Let's solve each problem step by step.

---

Problem 1:

Jane and Ann like pizza. Jane ate \( \frac{1}{3} \) and Ann ate \( \frac{2}{5} \) of that pizza. How much did they eat in total?

#### Solution:
To find the total amount of pizza they ate, we need to add the fractions \( \frac{1}{3} \) and \( \frac{2}{5} \).

1. Find a common denominator for \( \frac{1}{3} \) and \( \frac{2}{5} \). The least common denominator (LCD) of 3 and 5 is 15.
2. Convert each fraction to have the denominator of 15:
\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]
\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]
3. Add the fractions:
\[
\frac{5}{15} + \frac{6}{15} = \frac{5 + 6}{15} = \frac{11}{15}
\]

So, the total amount of pizza they ate is \( \frac{11}{15} \).

Answer:
\[
\boxed{\frac{11}{15}}
\]

---

Problem 2:

Jane and Ann went for a run. Ann ran \( \frac{1}{3} \) of a mile and Jane ran \( \frac{1}{2} \) of a mile. How far did they run in total?

#### Solution:
To find the total distance they ran, we need to add the fractions \( \frac{1}{3} \) and \( \frac{1}{2} \).

1. Find a common denominator for \( \frac{1}{3} \) and \( \frac{1}{2} \). The least common denominator (LCD) of 3 and 2 is 6.
2. Convert each fraction to have the denominator of 6:
\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\]
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
3. Add the fractions:
\[
\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}
\]

So, the total distance they ran is \( \frac{5}{6} \) of a mile.

Answer:
\[
\boxed{\frac{5}{6}}
\]

---

Problem 3:

Jane and Ann had lasagna for dinner. Jane ate \( \frac{1}{6} \) of the lasagna and Ann ate \( \frac{1}{8} \) of the lasagna. Who ate more? How much more?

#### Solution:
To determine who ate more, we need to compare the fractions \( \frac{1}{6} \) and \( \frac{1}{8} \).

1. Find a common denominator for \( \frac{1}{6} \) and \( \frac{1}{8} \). The least common denominator (LCD) of 6 and 8 is 24.
2. Convert each fraction to have the denominator of 24:
\[
\frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}
\]
\[
\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}
\]
3. Compare the fractions:
\[
\frac{4}{24} > \frac{3}{24}
\]
So, Jane ate more.

4. To find how much more Jane ate than Ann, subtract the fractions:
\[
\frac{4}{24} - \frac{3}{24} = \frac{4 - 3}{24} = \frac{1}{24}
\]

So, Jane ate \( \frac{1}{24} \) more of the lasagna than Ann.

Answer:
\[
\boxed{\text{Jane, } \frac{1}{24}}
\]

---

Problem 4:

Jane and Ann own a car. The gas tank was half full. They added enough gas to add \( \frac{2}{5} \) more gas to the tank. How FULL is the tank now?

#### Solution:
The gas tank was initially half full, which means it was \( \frac{1}{2} \) full. They added \( \frac{2}{5} \) more gas to the tank. To find the new level of the tank, we add \( \frac{1}{2} \) and \( \frac{2}{5} \).

1. Find a common denominator for \( \frac{1}{2} \) and \( \frac{2}{5} \). The least common denominator (LCD) of 2 and 5 is 10.
2. Convert each fraction to have the denominator of 10:
\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\]
\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
\]
3. Add the fractions:
\[
\frac{5}{10} + \frac{4}{10} = \frac{5 + 4}{10} = \frac{9}{10}
\]

So, the tank is now \( \frac{9}{10} \) full.

Answer:
\[
\boxed{\frac{9}{10}}
\]

---

Problem 5:

Jane spent \( \frac{8}{9} \) of her savings on a gift for Ann. Ann spent \( \frac{7}{8} \) of her savings on a gift for Jane. Who spent less? How much LESS?

#### Solution:
To determine who spent less, we need to compare the fractions \( \frac{8}{9} \) and \( \frac{7}{8} \).

1. Find a common denominator for \( \frac{8}{9} \) and \( \frac{7}{8} \). The least common denominator (LCD) of 9 and 8 is 72.
2. Convert each fraction to have the denominator of 72:
\[
\frac{8}{9} = \frac{8 \times 8}{9 \times 8} = \frac{64}{72}
\]
\[
\frac{7}{8} = \frac{7 \times 9}{8 \times 9} = \frac{63}{72}
\]
3. Compare the fractions:
\[
\frac{64}{72} > \frac{63}{72}
\]
So, Ann spent less.

4. To find how much less Ann spent than Jane, subtract the fractions:
\[
\frac{64}{72} - \frac{63}{72} = \frac{64 - 63}{72} = \frac{1}{72}
\]

So, Ann spent \( \frac{1}{72} \) less of her savings than Jane.

Answer:
\[
\boxed{\text{Ann, } \frac{1}{72}}
\]

---

Final Answers:

1. \(\boxed{\frac{11}{15}}\)
2. \(\boxed{\frac{5}{6}}\)
3. \(\boxed{\text{Jane, } \frac{1}{24}}\)
4. \(\boxed{\frac{9}{10}}\)
5. \(\boxed{\text{Ann, } \frac{1}{72}}\)