Lesson 53: Decimals Chart

New Concept

We simplify fractions in two ways. We reduce fractions to lowest terms, and we convert improper fractions to mixed numbers. A fraction is in lowest terms if the only common factor of the numerator and denominator is 1.

What’s next

This is a foundational skill. Next, you’ll work through examples where you add fractions first and then simplify the answer, a process you will use often.

Property

Memory cues help you place the decimal point correctly for each operation. Addition/Subtraction (+, -): line up. Multiplication (×): multiply, then count decimal places. Division by whole (W): up. Division by decimal (D): over, over, up. You may need to add a decimal point to whole numbers or fill empty places with zeros.

Examples

• $5 - 4.2 \implies 5.0 - 4.2 = 0.8$
• $0.4 \times 0.2 \implies 0.08 \text{ (Multiply } 4 \times 2=8, \text{ then count 2 decimal places)}$
• $5 \div 0.4 \implies 50 \div 4 = 12.5 \text{ (Over, over, up)}$

Explanation

This chart is your secret weapon for decimal operations! For adding or subtracting, you line up the decimal points like soldiers in a parade. When multiplying, you ignore the points, multiply, then count the places to put it back. For division, you just shift the points around. It keeps your math neat and accurate!

Property

We simplify fractions in two ways. We reduce fractions to lowest terms, and we convert improper fractions to mixed numbers. Sometimes a fraction can be reduced and converted to a mixed number.

Examples

• Reduce first: $\frac{10}{6} \rightarrow \text{Reduce to } \frac{5}{3} \rightarrow \text{Convert to } 1\frac{2}{3}$
• Convert first: $\frac{10}{6} \rightarrow \text{Convert to } 1\frac{4}{6} \rightarrow \text{Reduce to } 1\frac{2}{3}$
• Just reduce: $\frac{9}{12} \rightarrow \text{Reduce to } \frac{3}{4}$

Explanation

Think of simplifying fractions as giving them a makeover! We either shrink them down by reducing or change their outfit from an improper fraction to a stylish mixed number. Sometimes, you do both to get the final, polished look. This process makes unwieldy fractions much easier to understand and compare with others.