Fractions and Decimals - Adding and Subtracting Fractions with Like Denominators

Understanding Like Denominators: The denominator (the bottom number) tells us how many equal parts make up one whole. 'Like' denominators mean the parts are exactly the same size. Visually, if you have two circles both divided into 8 equal slices, they have a like denominator of 8.

Adding Numerators: When adding fractions with like denominators, you only add the numerators (the top numbers). For example, if you shade 2 parts of a 6-part rectangle and then shade 1 more part, you have shaded $2 + 1 = 3$ parts. The fraction is $\\frac{3}{6}$.

Keeping the Denominator Constant: In addition and subtraction, the denominator does not change. This is because the total number of parts that make a whole remains the same. If you add pieces of a pizza cut into 8 slices, the result will still be expressed in slices of 8 (eighths).

Subtracting Numerators: To subtract fractions, take the numerator of the second fraction away from the first. Imagine a bar with 10 equal segments where 7 are colored. If you erase 3 of those colored segments, you are left with $7 - 3 = 4$ segments, written as $\\frac{4}{10}$.

Number Line Movement: Fractions can be visualized on a number line marked from 0 to 1. To add $\\frac{2}{5}$, you move two marks to the right. To subtract $\\frac{2}{5}$, you move two marks to the left. The distance between each mark represents the unit fraction $\\frac{1}{5}$.

The Whole Number Rule: When the numerator becomes equal to the denominator, it represents 1 whole. Visually, if a shape has 4 parts and all 4 are shaded ($\\frac{4}{4}$), the entire shape is filled. This is important when sums like $\\frac{2}{4} + \\frac{2}{4}$ result in $\\frac{4}{4}$ or $1$.

Comparing Parts: Adding and subtracting is only simple when denominators are the same because we are comparing 'like' items. Think of it like adding 3 apples and 2 apples; the 'denominator' is the type of fruit (apples), which stays the same in the total.