Welcome! Today we're going to learn how to subtract fractions. Just like adding fractions, the method we use depends on whether the fractions have the same bottom number (denominator) or different ones. Don't worry - we'll take it step by step and make it easy to understand!
When fractions have the same denominator (same bottom number), subtracting them is super easy! You only subtract the top numbers and keep the bottom number the same.
You have \(\frac{5}{8}\) of a pizza and you eat \(\frac{2}{8}\). How much is left?
Solution:
\[\frac{5}{8} - \frac{2}{8} = \frac{5-2}{8} = \frac{3}{8}\]
Answer: You have \(\frac{3}{8}\) of the pizza left.
Calculate: \(\frac{7}{10} - \frac{3}{10}\)
Solution:
\[\frac{7}{10} - \frac{3}{10} = \frac{7-3}{10} = \frac{4}{10}\]
We can simplify: \(\frac{4}{10} = \frac{2}{5}\)
Answer: \(\frac{2}{5}\)
When fractions have different denominators, we need to make them the same first. This is like making sure we're talking about the same-sized pieces before we subtract!
Calculate: \(\frac{3}{4} - \frac{1}{2}\)
Step 1: Find LCD of 4 and 2 → LCD = 4
Step 2: Convert fractions:
\(\frac{3}{4}\) stays as \(\frac{3}{4}\)
\(\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}\)
Step 3: Subtract:
\[\frac{3}{4} - \frac{2}{4} = \frac{1}{4}\]
Answer: \(\frac{1}{4}\)
Calculate: \(\frac{2}{3} - \frac{1}{6}\)
Step 1: Find LCD of 3 and 6 → LCD = 6
Step 2: Convert fractions:
\(\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}\)
\(\frac{1}{6}\) stays as \(\frac{1}{6}\)
Step 3: Subtract:
\[\frac{4}{6} - \frac{1}{6} = \frac{3}{6} = \frac{1}{2}\]
Answer: \(\frac{1}{2}\)
Now let's apply what we've learned to real-world situations! The key to solving word problems is to identify what fractions we're working with and what operation we need to perform.
Maria planted flowers in \(\frac{3}{4}\) of her garden. If \(\frac{1}{8}\) of the garden has roses, what fraction of the garden has other types of flowers?
Understanding: Total flowers = \(\frac{3}{4}\), Roses = \(\frac{1}{8}\)
Solution: Other flowers = Total flowers - Roses
LCD of 4 and 8 is 8
\(\frac{3}{4} = \frac{6}{8}\)
\[\frac{6}{8} - \frac{1}{8} = \frac{5}{8}\]
Answer: \(\frac{5}{8}\) of the garden has other types of flowers.
A recipe calls for \(\frac{2}{3}\) cup of sugar. You've already added \(\frac{1}{4}\) cup. How much more sugar do you need?
Understanding: Total needed = \(\frac{2}{3}\), Already added = \(\frac{1}{4}\)
Solution: Still needed = Total - Already added
LCD of 3 and 4 is 12
\(\frac{2}{3} = \frac{8}{12}\) and \(\frac{1}{4} = \frac{3}{12}\)
\[\frac{8}{12} - \frac{3}{12} = \frac{5}{12}\]
Answer: You need \(\frac{5}{12}\) cup more sugar.
Tom walked \(\frac{7}{10}\) of a mile to school. On his way, he stopped at a store after walking \(\frac{2}{5}\) of a mile. How much farther did he walk after the store?
Understanding: Total distance = \(\frac{7}{10}\), Distance to store = \(\frac{2}{5}\)
Solution: Distance after store = Total - Distance to store
LCD of 10 and 5 is 10
\(\frac{2}{5} = \frac{4}{10}\)
\[\frac{7}{10} - \frac{4}{10} = \frac{3}{10}\]
Answer: Tom walked \(\frac{3}{10}\) of a mile after the store.
Great job! You've learned how to subtract fractions. Here's what we covered:
Keep practicing! The more problems you solve, the easier fraction subtraction becomes. You're doing great! 🌟